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Any replacements are listed farther down

[2878] **viXra:1809.0298 [pdf]**
*submitted on 2018-09-14 14:24:04*

**Authors:** Toshiro Takami

**Comments:** 4 Pages.

Simulation of the nontrivial zero of Riemann's prediction succeeded in mimicking with rotational force alone. Although it is a simulation with only the rotational force, it is a very approximate value because the initial value was set as the first nonzero point of the Riemann zeta function. We adopted a method of placing a rotating force on the previous value and stacking it.
I could reproduce how the dragon climbs up the x = 0.5 axis.
In 1.0 of the interval of the nuclear energy, simulation did not hold and it was forced to take the value of 1.1.
At first, although it is out of the nonobvious point of Riemann's prediction, it gradually becomes an approximate value.
However, this may also be lower than the previous value, and it should be improved in the future.

**Category:** General Mathematics

[2877] **viXra:1809.0230 [pdf]**
*submitted on 2018-09-12 02:51:37*

**Authors:** Chaitali Kar, Bappa Mondal, Tapan Kumar Roy

**Comments:** 17 Pages.

In this paper, an inventory model is developed without shortages where the production cost is inversely related to the set up cost and production quantity. In addition, the holding cost is considered time dependent. Here impreciseness is introduced in the storage area. The objective and constraint functions are defined by the truth (membership) degree, indeterminacy (hesitation) degree and falsity (non-membership) degree. Likewise, a non-linear programming problem with a constraint is also considered.

**Category:** General Mathematics

[2876] **viXra:1809.0229 [pdf]**
*submitted on 2018-09-12 02:53:15*

**Authors:** Shyamal Dalapati, Surapati Pramanik

**Comments:** 11 Pages.

Multi attribute group decision making with VIKOR (VlseKriterijuska Optimizacija I Komoromisno Resenje) strategy has been widely applied to solving real-world problems. Recently, Pramianik et al. [S. Pramanik, S. Dalapati, S. Alam, and T. K. Roy. NCVIKOR based MAGDM strategy under neutrosophic cubic set environment, Neutrosophic Sets and Systems, 20 (2018), 95-108]proposed VIKOR strategy for solving MAGDM, where compromise solutions are not identified in neutrosophic cubic environment. To overcome the shortcomings of the paper, we further modify the VIKOR strategy by incorporating compromise solution in neutrosophic cubic set environment. Finally, we solve an MAGDM problem using the modified NC-VIKOR strategy to show the feasibility,
applicability and effectiveness of the proposed strategy. Further, we present sensitivity analysis to show the impact of different values
of the decision making mechanism coefficient on ranking order of the alternatives.

**Category:** General Mathematics

[2875] **viXra:1809.0228 [pdf]**
*submitted on 2018-09-12 03:02:12*

**Authors:** Surapati Pramanik, Partha Pratim Dey

**Comments:** 12 Pages.

The paper presents a novel strategy for solving bi-level linear programming problem based on goal programming in neutrosophic numbers environment. Bi-level linear programming problem comprises of two levels namely upper or first level and lower or second level with one objective at each level. The objective function of each level decision maker and the system
constraints are considered as linear functions with neutrosophic numbers of the form [p + q I], where p, q are real numbers and I represents indeterminacy.

**Category:** General Mathematics

[2874] **viXra:1809.0227 [pdf]**
*submitted on 2018-09-12 03:03:19*

**Authors:** Nguyen Xuan Thao, Florentin Smarandache

**Comments:** 11 Pages.

In this paper, we first propose the concept of divergence measure on neutrosophic sets. We also provide some formulas for the divergence measure for neutrosophic sets. After that, we investigate the properties of proposed neutrosophic divergence measure. Finally, we also apply these formulas in medical problem and the classification problem.

**Category:** General Mathematics

[2873] **viXra:1809.0226 [pdf]**
*submitted on 2018-09-12 03:04:38*

**Authors:** Fatimah M. Mohammed, Shaymaa F. Matar

**Comments:** 10 Pages.

In this paper, we state a new class of sets and called them fuzzy neutrosophic Alpham-closed sets, and we prove some theorem related to this definition. Then, we investigate the relation between fuzzy neutrosophic Alpham-closed sets, fuzzy neutrosophic α closed sets, fuzzy neutrosophic closed sets, fuzzy neutrosophic semi closed sets and fuzzy neutrosophic pre closed sets. On the other hand, some properties of the fuzzy neutrosophic Alpham-closed set are given.

**Category:** General Mathematics

[2872] **viXra:1809.0225 [pdf]**
*submitted on 2018-09-12 03:05:42*

**Authors:** Sahidul Islam, Partha Ray

**Comments:** 10 Pages.

In this paper, we first consider a multi-objective Portfolio Selection model and then we add another entropy objective function and next we generalized the model. We solve the problems using Neutrosophic optimization technique. The models are illustrated with numerical examples.

**Category:** General Mathematics

[2871] **viXra:1809.0224 [pdf]**
*submitted on 2018-09-12 03:06:52*

**Authors:** A. A. Salama, Florentin Smarandache, Hewayda ElGhawalby

**Comments:** 7 Pages.

In this paper, we propose a new technique for the enhancing images. It will work on removing the noise contained in the image as well as improving its contrast based on three different enhancing transforms, we commence by embedding the image into a neutrosophic domain; where the image will be mapped in three different levels, a level of trueness, a level of falseness
and a level of indeterminacy. Hence, we act separately on each level using the enhancement transforms. Finally, we introduce a new analysis in the field of analysis and processing of images using the neutrosophic crisp set theory via Mat lab program where has been obtained three images, which helps in a new analysis to improve and retrieve images.

**Category:** General Mathematics

[2870] **viXra:1809.0223 [pdf]**
*submitted on 2018-09-12 03:07:51*

**Authors:** Riad Khidr Al-Hamido

**Comments:** 8 Pages.

In this paper, neutrosophic crisp bi-topological spaces, new types of open and closed sets in neutrosophic crisp bitopological spaces, the closure and interior neutrosophic crisp set and a new concept of open and closed sets are introduced. The basic properties of these types of open and closed sets and their properties are studied.

**Category:** General Mathematics

[2869] **viXra:1809.0222 [pdf]**
*submitted on 2018-09-12 03:08:53*

**Authors:** Mehmet Şahin, Abdullah Kargın

**Comments:** 8 Pages.

In this article, a notion of neutrosophic triplet (NT) normed ring space is given and properties of NT normed ring spaces are studied. We demonstrate that NT normed ring is different from the classical one. Also, we show that a neutrosophic
triplet normed ring can be a neutrosophic triplet norm when certain conditions are met.

**Category:** General Mathematics

[2868] **viXra:1809.0221 [pdf]**
*submitted on 2018-09-12 03:10:00*

**Authors:** T. Chalapathi, R. V. M. S. S. Kiran Kumar

**Comments:** 8 Pages.

In recent years, the inter connection between classical structures and Neutrosophic structures is studied by few researchers. For such kind of study, researchers defined new algebraic structures whose elements aregenerated by elements in classical algebraic set and indeterminate of the real world problem with respect to algebraic operations on the well defined Neutrosophic elements.

**Category:** General Mathematics

[2867] **viXra:1809.0220 [pdf]**
*submitted on 2018-09-12 03:12:48*

**Authors:** Riad K. Al-Hamido, Qays Hatem Imran, Karem A. Alghurabi, Taleb Gharibah

**Comments:** 8 Pages.

In this paper, we presented another concept of neutrosophic crisp generalized closed sets called neutrosophic crisp semi-alpha-closed sets and studied their fundamental properties in neutrosophic crisp topological spaces.

**Category:** General Mathematics

[2866] **viXra:1809.0219 [pdf]**
*submitted on 2018-09-12 03:17:21*

**Authors:** Ramona Parraga Alava, José Muñoz Murillo, Roy Barre Zambrano, María Isabel Zambrano Vélez, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic cognitive maps and its application in decision making have become a topic of great importance for researchers and practitioners alike.PEST (Political, Economic, Social and Technological), analysis is a precondition analysis with the main functions of the identification of the environment within which and organization or project the operates and pr
viding data and information for enabling the organization to make predictions about new situations and circumstances.

**Category:** General Mathematics

[2865] **viXra:1809.0218 [pdf]**
*submitted on 2018-09-12 03:18:18*

**Authors:** Florentin Smarandache

**Comments:** 14 Pages.

In this paper, we introduce the plithogenic set (as generalization of crisp, fuzzy, intuitionistic fuzzy, and neutrosophic sets), which is a set whose elements are characterized by many attributes’ values. An attribute value v has a corresponding (fuzzy, intuitionistic fuzzy, or neutrosophic) degree of appurtenance d(x,v) of the element x, to the set P, with respect to some
given criteria.

**Category:** General Mathematics

[2864] **viXra:1809.0217 [pdf]**
*submitted on 2018-09-12 03:19:20*

**Authors:** Suriana Alias, Daud Mohamad, Adibah Shuib

**Comments:** 20 Pages.

The concepts of rough neutrosophic multisets can be easily extended to a relation, mainly since a relation is also a set, i.e. a subset of a Cartesian product. Therefore, the objective of this paper is to define the definition of rough
neutrosophic multisets relation of Cartesian product over a universal set.

**Category:** General Mathematics

[2863] **viXra:1809.0216 [pdf]**
*submitted on 2018-09-12 03:20:37*

**Authors:** Milton Villegas Alava, Stella Paola Delgado Figueroa, Hilda Mercedes Blum Alcivar, Maikel Leyva Vázquez

**Comments:** 9 Pages.

Neutrosophic sets and its application to decision support have become a topic of great importance. In this paper, a new model for decision making in the selection of projects is presented based on single valued neutrosophic number (SVNnumbers) and the analytic hierarchy process (AHP). The proposed framework is composed of five activities, framework, criteria weighting, gathering information, rating alternatives and project selection. Project alternatives are rated based on aggregation operator and the ranking of alternatives is based on scoring and accuracy functions.

**Category:** General Mathematics

[2862] **viXra:1809.0146 [pdf]**
*submitted on 2018-09-08 02:45:06*

**Authors:** Toshiro Takami

**Comments:** 11 Pages.

We found that prime numbers repeat every 30, and all prime numbers are represented by 30 m + n (positive integer including m is 0, n is a prime number smaller than 30 excluding 2 and 5).
If the end of the multiplication of the giant prime and the giant prime here is 5, it can be seen that any of the ends of each gigantic prime is 5.
In other words, the one multiplied by a huge prime number and a huge prime number,
(30 m + n) * (30 s + t) = 900 ms + 30 (mt + ns) + nt
(positive integer including s is 0, t is a prime number smaller than 30 excluding 2 and 5)
.
nt includes something that is not a prime number. 33, 63, 93 and so on.
For example
1976869607 = 27109 * 72923 (both primes 27109 and 72923)
, But this factorization is unknown to third parties.
1976869607 is a 10 digit integer and has 1 first. ms is counted as a positive integer of 6 digits (although there is a possibility of 7 digits).
Register with the last number of nt (the last digit) and prime factorize.
In the upper number, the last digit of nt is 7.
The last digit of nt is 7
(3, 19) (7, 11) (13, 19) (13, 29) (19, 23) (23, 29)
.
A program that prime factorization can be solved quickly when paying attention to the last 7.
First, divide by 3, 7, 11, 13, 17, 19, 23, 29 to see if it is an integer. If it is an integer it has that number as a prime factor.
The last 607 of 1976869607 is a prime number.
A huge odd number (one multiplied by a huge prime number and a huge prime number) can be factorized using this factor.
By using this, it seems that the rupture of the RSA encryption becomes faster.

**Category:** General Mathematics

[2861] **viXra:1809.0009 [pdf]**
*submitted on 2018-09-01 03:51:18*

**Authors:** Han Geurdes

**Comments:** 4 Pages.

With the use of the even/odd number analysis it was found that there is no non-Goldbach even integer >4 number possible.

**Category:** General Mathematics

[2860] **viXra:1808.0684 [pdf]**
*submitted on 2018-08-31 10:12:33*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 4 Pages.

The Riemann zeta-function is one of the most studied complex function in mathematics. Riemann in his 1859 paper On the Number of Prime Numbers less than a Given Quantity [1] claimed that the analytic continuation of the zeta-function extends its domain over the entire complex plane except at s = 1. But, as I’ve shown in my two papers: A Short Disproof of the Riemann Hypothesis [2] and Riemann’s Functional Equation is Not a Valid Function and Its Implication on the Riemann Hypothesis [3], the zeta-function is only defined on the right half-plane. It is the purpose of this present work to precisely locate the domain of this function on the right half-plane.

**Category:** General Mathematics

[2859] **viXra:1808.0627 [pdf]**
*submitted on 2018-08-28 07:39:51*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents a definite integral.

**Category:** General Mathematics

[2858] **viXra:1808.0624 [pdf]**
*submitted on 2018-08-28 11:37:38*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 10 Pages.

Riemann’s functional equation was formulated by Riemann himself in order to extend the domain of the zeta function from the right half-plane into the entire complex plane except at s = 1. It also lead him to find a real function, so that, at s = ½ + ωi, the real function has zeros for some values of ω. Now, the real function was also related to the zeta function, which in turn has something to do with the distribution of prime numbers. This drove him to developed a formula of relating the zeros of the zeta function to the number of primes given a certain number. Riemann then conjectured that all the zeros of the zeta function are at s = ½ + ωi, which is now known as the Riemann Hypothesis. Hence, Riemann’s functional equation is the foundation upon which the Riemann Hypothesis is based. But, there is one problem, the function as shall be shown here, suffers from not being able to yield meaningful or valid values, as it should. Also, if one carefully examine on how Riemann arrived at his formula, I for one, found it to be unsatisfactory or unconvincing. It is, therefore, the aim of this present work to show, that, if carefully examined, Riemann’s functional equation could not be a valid function, and consequently, the Riemann Hypothesis crumbles on its claim.

**Category:** General Mathematics

[2857] **viXra:1808.0599 [pdf]**
*submitted on 2018-08-28 00:09:35*

**Authors:** Armando M. Evangelista Jr.

**Comments:** 3 Pages.

The Riemann Hypothesis is one of the most important unsolved problem in Mathematics: its validity will have have a great consequence on the precise calculation of the number of primes. Riemann developed an explicit formula relating the number of primes with the hypothesized non-trivial zeros of the Riemann zeta function. Riemann hypothesis states that all the non-trivial zeros of the zeta function have real part equal to one-half on the critical strip.
Despite many attempts to solve it for about 150 years, no one have, so far succeeded. Riemann hypothesis is based on the existence of the zeros of the zeta function. If it can be shown, that, such zeros do not exist, then, the Riemann Hypothesis is false.

**Category:** General Mathematics

[2856] **viXra:1808.0578 [pdf]**
*submitted on 2018-08-26 10:01:32*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

I found a prime number equation.
(a = positive integer, t = prime number etc.)
For other positive integers(a), t is an irrational number.
This generates prime numbers, but also generates a composite number of prime numbers and irrational numbers.
However, at this time
Nevertheless, it never happens to generate all the prime numbers. About half of the prime numbers are generated.
This generates prime numbers, but also generates a composite number of prime numbers and irrational numbers.
It has regularity of prime number prime number.
However, at this time
Nevertheless, it never happens to generate all the prime numbers. About half of the prime numbers are generated.
(p) is prime-number
2, 19, 33, 134, 168, 253…….are (a).
Display only those whose t is an integer
49, 151, 199, 401, 449……are (t).

**Category:** General Mathematics

[2855] **viXra:1808.0552 [pdf]**
*submitted on 2018-08-24 21:33:42*

**Authors:** Toshiro Takami

**Comments:** 8 Pages.

I found a prime number equation.
(a = positive integer, t = prime number etc.)
For other positive integers(a), t is an irrational number.
This generates prime numbers, but also generates a composite number of prime numbers and irrational numbers.
However, at this time
Nevertheless, it never happens to generate all the prime numbers. About half of the prime numbers are generated.

**Category:** General Mathematics

[2854] **viXra:1808.0540 [pdf]**
*submitted on 2018-08-23 10:25:55*

**Authors:** Toshiro Takami

**Comments:** 20 Pages.

We investigated prime numbers corresponding to nontrivial zeros.
We used walframalpha which exists on the net for all calculation and drawing.
In the complex plane, the non-trivial zeros of the zeta function were thought that there were non-trivial zeros besides x = 0.5, and I examined them variously, but they did not show the tendency to converge at all and were inferred to be absent.
The zeros of the zeta function probably existed indefinitely at x = 0.5, but they were inferred to be absent elsewhere. In the walframalpha 's Parametric plot, I understood the convergence well.
The first zero point at x = 0.5 was set as T1 = 14.1347, and the corresponding prime number was obtained.
In the following, prime numbers corresponding to nontrivial zero points T2 = 21.022, T3 = 25.0108, etc. were obtained.

**Category:** General Mathematics

[2853] **viXra:1808.0539 [pdf]**
*submitted on 2018-08-23 10:36:47*

**Authors:** Alexander Nieguth, Sebastian Scholz

**Comments:** 8 Pages.

Let $\varepsilon'$ be a Riemannian category. Recently, there has been much interest in the characterization of groups. We show that $\frac{1}{{O_{G}}} \ge {\pi_{t}} \left(-1, \dots, \frac{1}{\aleph_0} \right)$. Hence this could shed important light on a conjecture of Pascal. So a central problem in non-standard number theory is the derivation of manifolds. Furthermore the awesomeness-intelligence paradoxon is solved introducing units of Scholz

**Category:** General Mathematics

[2852] **viXra:1808.0537 [pdf]**
*submitted on 2018-08-23 11:47:32*

**Authors:** Abdalla M. Aboarab

**Comments:** 12 Pages.

In this paper, the power series is looked at from a different perspective.
The Summation of $n^{m}a^{-bn}$ is evaluated using a new method. An assumption
is made that the power $-bn$ is multiplied by $x$ where $ x=1$; then the series
is integrated m times in order to cancel the term $n^{m} $ out leaving the term
$a^{-bn}$. By simply taking the derivative of the result m-times, an expression
to evaluate the series arises, which include only a constant term and the
m$^{th}$ order derivative of the summation of a simple geometric series.
Further applications of the method are used to evaluate the series with the
cosine, sine, hyperbolic sine, and hyperbolic cosine. Finally, the method is
used to further simplify some of the hardest forms of series to deal with: the
series $n^{m}$sinh$^{v}(ny)$, and $n^{m}$cosh$^{v}(ny)$ and
$n^{m}$sin$^{v}(ny)$.

**Category:** General Mathematics

[2851] **viXra:1808.0531 [pdf]**
*submitted on 2018-08-23 20:46:02*

**Authors:** Toshiro Takami

**Comments:** 11 Pages.

I did proof of Goldbach expectation.
Even numbers are supplemented with prime numbers and prime numbers, but that proof has not been done yet.
We found that even numbers and prime numbers have regularity.
I found that the prime number is (6n-1) or (6n-1) except 2 and 3 (n is a positive integer).
No exception was found.

**Category:** General Mathematics

[2850] **viXra:1808.0519 [pdf]**
*submitted on 2018-08-22 12:10:45*

**Authors:** Colin James III

**Comments:** 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com. (We instruct troll Mikko L at Disqus to read this entire article twice before typing.)

Neutrosophy combines A and nonA, getting a degree of A, a degree of neutA, and a degree of antiA, where A actually gives birth to antiA and neutA.
The logic of neutrosophy is not tautologous, and hence not a theory of everything in logics.

**Category:** General Mathematics

[2849] **viXra:1808.0508 [pdf]**
*submitted on 2018-08-21 08:04:27*

**Authors:** En Fan, Weixin Xie, Jihong Pei, Keli Hu, Xiaobin Li

**Comments:** 13 Pages.

A neutrosophic Hough transform-based track initiation method (NHT-TI) is proposed to solve the uncertain track initiation problem in a complex surveillance environment. In the proposed method, a neutrosophic set is employed to describe the uncertain association of a measurement with different targets, which is divided into three categories including the association with real targets, uncertain targets and false targets, respectively.

**Category:** General Mathematics

[2848] **viXra:1808.0507 [pdf]**
*submitted on 2018-08-21 08:05:31*

**Authors:** Mehmet Ali Ozturk, Young Bae Jun

**Comments:** 17 Pages.

The concept of neutrosophic set (NS) developed by Smarandache is a more general platform which extends the concepts of the classic set and fuzzy set, intuitionistic fuzzy set and interval valued intuitionistic fuzzy set.

**Category:** General Mathematics

[2847] **viXra:1808.0505 [pdf]**
*submitted on 2018-08-21 08:08:02*

**Authors:** Abbas Y. Al-Bayati

**Comments:** 1 Page.

It is our pleasure and honor to invite all interested academic in both Telafer and Mosul universities , for hope to get benefit from those important knowledge aspects which represent the basic that all modern science will emanate from it, because of the Neutrosophic logic is more general and more comprehensive from fuzzy logic and intuitionistic fuzzy logic.

**Category:** General Mathematics

[2846] **viXra:1808.0504 [pdf]**
*submitted on 2018-08-21 08:09:06*

**Authors:** A. Solairaju, M. Shajahan

**Comments:** 6 Pages.

Yager [1988] developed the ordered weighted averaging (OWA) operator and applied in decision making problems. Xu & Yager [2006] developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple
attribute group decision making with intuitionistic fuzzy information. Xu [2007e] and Xu & Chen [2007a, 2007b] also developed
some arithmetic aggregation operators for decision making problems.

**Category:** General Mathematics

[2845] **viXra:1808.0503 [pdf]**
*submitted on 2018-08-21 08:10:10*

**Authors:** Surapati Pramanik, Durga Banerjee

**Comments:** 8 Pages.

The purpose of the paper is to propose goal programming strategy to multi-objective linear programming problem with neutrosophic numbers which we call NN-GP. The coefficients of objective functions and the constraints are considered as neutrosophic numbers of the form (m+nI), where m, n are real numbers and I denotes indeterminacy.

**Category:** General Mathematics

[2844] **viXra:1808.0502 [pdf]**
*submitted on 2018-08-21 08:11:19*

**Authors:** Jun Ye, Wenhua Cui, Zhikang Lu

**Comments:** 9 Pages.

In practical situations, we often have to handle programming problems involving indeterminate information.

**Category:** General Mathematics

[2843] **viXra:1808.0501 [pdf]**
*submitted on 2018-08-21 08:12:30*

**Authors:** S. Thiruveni, A. Solairaju

**Comments:** 8 Pages.

In this paper, the notation of concept of neutrosopy in Q-fuzzy set is introduced. Further some properties and results on neutrosophic Q-fuzzy subgroups are discussed.

**Category:** General Mathematics

[2842] **viXra:1808.0500 [pdf]**
*submitted on 2018-08-21 08:13:11*

**Authors:** Kemale Veliyeva, Sadi Bayramov

**Comments:** 12 Pages.

Molodtsov initiated the concept of soft sets in [17]. Maji et al. defined some operations on soft sets in [13]. Aktaş et al. generalized soft sets by defining the concept of soft groups in [2]. After then, Qiu-Mei Sun et al. gave soft modules in [20]. In this paper, the concept of neutrosophic soft module is introduced and some of its basic properties are studied.

**Category:** General Mathematics

[2841] **viXra:1808.0499 [pdf]**
*submitted on 2018-08-21 08:14:16*

**Authors:** Cemil KURU

**Comments:** 42 Pages.

Ordu Oniversitesi Fen Bilimleri Enstitlisti ogrencisi Cemil KURU tarafmdan haz1rlanan ve Yrd. Do9. Dr. Mehmet KORKMAZ dam~manhgmda yilrilttilen
"Neutrosophic Topolojik Uzaylar "adh bu tez, jurimiz tarafmdan 18 I 12 I 2017 tarihinde oy birligi I ov coklueu ile Matematik Anabilim Dalmda Yuksek Lisans tezi olarak kabul edilmistir.

**Category:** General Mathematics

[2840] **viXra:1808.0496 [pdf]**
*submitted on 2018-08-21 16:02:10*

**Authors:** Toshiro Takami

**Comments:** 11 Pages.

【Abstract】
I found a prime number equation. All prime numbers except 2 and 3 are expressed by the following formula.
(a = positive integer, t = prime number etc.)
For other positive integers(a), t is an irrational number.
As an exception, This generates all prime numbers except 2 and 3, but also generates a composite number of prime numbers and irrational number.
The composite number of the prime has regularity.

**Category:** General Mathematics

[2839] **viXra:1808.0494 [pdf]**
*submitted on 2018-08-22 01:53:10*

**Authors:** Burak KILIC

**Comments:** 35 Pages.

Ordu Oniversitesi Fen Bilimleri Enstitilsti ogrencisi Burak KILIC; tarafmdan haz1rlanan ve Yrd.Doc. Dr. Yild1ray CELiK damsmanhgmda ytirtiti.ilen "Neutrosophic Topolojik Uzaylarda Kompakthk" adh bu tez, jtirimiz tarafmdan 18/12/2017 tarihinde oy birligi I ov coklugu ile Matematik Anabilim Dalmda YtiksekLisans tezi olarak kabul edilmistir.

**Category:** General Mathematics

[2838] **viXra:1808.0493 [pdf]**
*submitted on 2018-08-22 01:54:22*

**Authors:** Mikail Bal, Moges Mekonnen Shalla, Necati Olgun

**Comments:** 13 Pages.

In this paper, by utilizing the concept of a neutrosophic extended triplet (NET), we define
the neutrosophic image, neutrosophic inverse-image, neutrosophic kernel, and the NET subgroup. The notion of the neutrosophic triplet coset and its relation with the classical coset are defined and the
properties of the neutrosophic triplet cosets are given. Furthermore, the neutrosophic triplet normal subgroups, and neutrosophic triplet quotient groups are studied.

**Category:** General Mathematics

[2837] **viXra:1808.0491 [pdf]**
*submitted on 2018-08-22 02:30:14*

**Authors:** Ashraf Al-Quran, Nasruddin Hassan

**Comments:** 16 Pages.

The notion of classical soft multisets is extended to neutrosophic vague soft multisets by applying the theory of soft multisets to neutrosophic vague sets to be more effective and useful. We also define its basic operations, namely complement,subset, union, intersection along with illustrative examples, and study some related properties with supporting proofs. Lastly, this notion is applied to a decision making problem and its effectiveness is demonstrated using an illustrative example.

**Category:** General Mathematics

[2836] **viXra:1808.0490 [pdf]**
*submitted on 2018-08-22 02:31:45*

**Authors:** Luu Huu Van, Vincent F. Yu, Luu Quoc Dat, Canh Chi Dung, Shuo-Yan Chou, Nguyen Viet Loc

**Comments:** 13 Pages.

Green supplier evaluation and selection plays a crucial role in the green supply chain management of any organization to reduce the purchasing cost of materials and increase the flexibility and quality of products.

**Category:** General Mathematics

[2835] **viXra:1808.0489 [pdf]**
*submitted on 2018-08-22 02:34:03*

**Authors:** Wei Yang, Yongfeng Pang

**Comments:** 16 Pages.

Interval neutrosophic fuzzy decision making is an important part of decision making under uncertainty, which is based on preference order. In this study, a new multi-valued interval neutrosophic fuzzy multiple attribute decision making method has been developed by integrating the DEMATEL (decision making trial and evaluation laboratory) method and the TOPSIS (the technique for order preference by similarity to an ideal solution) method. Evaluation values are given in the form of multi-valued interval neutrosophic fuzzy values. By using DEMATEL, dependencies among
attributes can be modeled, and attribute weights are determined.

**Category:** General Mathematics

[2834] **viXra:1808.0488 [pdf]**
*submitted on 2018-08-22 02:35:12*

**Authors:** Chunfang Liu

**Comments:** 11 Pages.

The simplified neutrosophic set (SNS) is a generalization of fuzzy set that is designed for some practical situations in which each element has truth membership function, indeterminacy membership function and falsity membership function. In this paper, we propose a new method to construct similarity measures of single valued neutrosophic sets (SVNSs) and interval valued neutrosophic sets (IVNSs), respectively. Then we prove that the proposed formulas satisfy the axiomatic definition of the similarity measure. At last, we apply
them to pattern recognition under the single valued neutrosophic environment and multi-criteria decision making problems under the interval valued neutrosophic environment. The results show that our methods are effective and reasonable.

**Category:** General Mathematics

[2833] **viXra:1808.0485 [pdf]**
*submitted on 2018-08-22 02:38:51*

**Authors:** Francisco Gallego Lupiáñez

**Comments:** 6 Pages.

Recently, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy sets and other
kinds of sets to neutrosophic sets (NSs). Also, this author introduced a general definition of
neutrosophic topology. On the other hand, there exist various kinds of paraconsistent logics, where some contradiction is admissible. The purpose of this paper is to show that a Smarandache’s definition of neutrosophic paraconsistent topology is not a generalization of C¸ oker’s intuitionistic fuzzy topology
(IFT) or Smarandache’s general neutrosophic topology.

**Category:** General Mathematics

[2832] **viXra:1808.0484 [pdf]**
*submitted on 2018-08-22 02:40:01*

**Authors:** Francisco Gallego Lupianez

**Comments:** 6 Pages.

Recently, Smarandache generalized the Atanassov’s intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs). Also, this author defined the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy
topology (IFT) on an IFS and the neutrosophic topology. This paper aims to show that this is false.

**Category:** General Mathematics

[2831] **viXra:1808.0483 [pdf]**
*submitted on 2018-08-22 02:41:26*

**Authors:** Esra Betul Koc Ozturk, Ufuk Ozturk, Kazim Elarslan, Emilija Nešovic

**Comments:** 8 Pages.

We define pseudohyperbolical Smarandache curves according to the Sabban frame in Minkowski 3-space.We obtain the geodesic curvatures and the expression for the Sabban frame vectors of special pseudohyperbolic Smarandache curves. Finally, we give some examples of such curves.

**Category:** General Mathematics

[2830] **viXra:1808.0482 [pdf]**
*submitted on 2018-08-22 02:42:18*

**Authors:** H. S. Abdel-Aziz, M. Khalifa Saad

**Comments:** 21 Pages.

In the light of great importance of curves and their frames in many different branches of science, especially differential geometry as well as geometric properties and the uses in various fields, we are interested here to study a special kind of curves called Smarandache curves in Lorentz 3-space.

**Category:** General Mathematics

[2829] **viXra:1808.0481 [pdf]**
*submitted on 2018-08-22 02:43:19*

**Authors:** Francisco Gallego Lupiáñez

**Comments:** 6 Pages.

Recently, F. Smarandache generalized the Atanassov’s intuitionistic fuzzy sets (IFSs) and other kinds of sets to neutrosophic sets (NSs) and also defined various notions of neutrosophic topologies on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology (IFT) on an IFS and neutrosophic topologies on the non-standard interval. The purpose of this paper is to show that this is false.

**Category:** General Mathematics

[2828] **viXra:1808.0480 [pdf]**
*submitted on 2018-08-22 02:44:28*

**Authors:** Y Rameswara Reddy, B Chandra Mohan Reddy

**Comments:** 7 Pages.

The work presents optimization of process parameters in wire electrical discharge machining process. This paper presents the results of experimental work carried out in Wire Electrical Discharge Machining of Super Ni 718 super alloy. Experiments have been conducted using 8 process parameters such as Pulse on time, Spark gap, Wire feed, Wire tension, flushing pressure, servo speed and peak current at 3 levels for obtaining responses like surface finish, material removal rate and dimensional deviation. The optimal setting of parameters is determined through experiments planned, conducted and analyzed using Neutrosophic sets and TOPSIS method.

**Category:** General Mathematics

[2827] **viXra:1808.0479 [pdf]**
*submitted on 2018-08-22 02:45:26*

**Authors:** Y.Rameswara Reddy, B.Chandra Mohana Reddy

**Comments:** 7 Pages.

This paper presents a study that investigates the effect of the WEDM process parameters on the surface roughness, MRR and DD of the Super Ni 718 supper alloy. Twenty seven experimental runs based on an orthogonal array of Taguchi method are performed and grey relational analysis with SVNS for weightages is applied to determine an optimal WEDM parameter setting. Surface roughness, MRR and DD are selected as the quality targets. An optimal parameter combination of the WEDM process is obtained using Grey relational analysis with SVNS. By analyzing the Grey relational grade matrix, the degree of influence for each controllable process factor onto individual quality targets can be found and the ranks are obtained.

**Category:** General Mathematics

[2826] **viXra:1808.0478 [pdf]**
*submitted on 2018-08-22 02:47:00*

**Authors:** 张扬， 杨建华, 侯宏

**Comments:** 7 Pages.

摘 要：针对水声目标信号复杂、样本获取难度大且富含不确定信息的问题，研究了一种证据聚类识 别算法。首先在水声目标的各类训练样本中，根据特征距离大小选取待识别目标的Ｋ 近邻，并采用证 据近邻分类优化算法为各目标数据构造一组合理的初始基本置信指派。然后对算法的目标函数进行 循环迭代优化，计算出目标数据最终的全局基本置信指派。最后根据融合结果和所设立的分类规则 即可判断目标的类别属性。通过水声目标实测数据的实验，将新算法与其他几种常用的水声目标识 别算法进行了对比分析，结果表明其能有效提高识别准确率。

**Category:** General Mathematics

[2825] **viXra:1808.0476 [pdf]**
*submitted on 2018-08-22 02:50:15*

**Authors:** Maheswara Rao Valluri

**Comments:** 3 Pages.

A natural number is a prime if it has only factors of 1 and itself. There are, by Euclidean theorem (about 350BC) infinitely many primes.

**Category:** General Mathematics

[2824] **viXra:1808.0475 [pdf]**
*submitted on 2018-08-22 02:51:28*

**Authors:** Majdoleen Abu Qamar, Nasruddin Hassan

**Comments:** 14 Pages.

Q-neutrosophic soft sets are essentially neutrosophic soft sets characterized by three
independent two-dimensional membership functions which stand for uncertainty, indeterminacy and falsity. Thus, it can be applied to two-dimensional imprecise, indeterminate and inconsistent data which appear in most real life problems.

**Category:** General Mathematics

[2823] **viXra:1808.0474 [pdf]**
*submitted on 2018-08-22 02:52:44*

**Authors:** Nivetha Martin, P.Pandiammal

**Comments:** 5 Pages.

In this present scenario the job market is getting detained due to growing competitions in almost all fields. The stratification of gender plays a significant role in getting employed. To overcome the condition of unemployment the state of entrepreneurship came into existence which paved way for the development of new paradigm of self employment. In the earlier days male entrepreneurs were predominant, but now the women folk have also stepped into it.

**Category:** General Mathematics

[2822] **viXra:1808.0473 [pdf]**
*submitted on 2018-08-22 02:53:31*

**Authors:** Ali Amer Mohammed Saeed

**Comments:** 6 Pages.

Knowledge Representation and Processing (KRP)
plays an important role in the development of expert systems as engines for accelerating the processes of economic and social life development.

**Category:** General Mathematics

[2821] **viXra:1808.0472 [pdf]**
*submitted on 2018-08-22 02:54:30*

**Authors:** U. Solang, J. Ye

**Comments:** 12 Pages.

Refined simplified neutrosophic sets (RSNSs) are appropriately used in decision-making problems with sub-attributes considering their truth components, indeterminacy components and falsity components independently.

**Category:** General Mathematics

[2820] **viXra:1808.0471 [pdf]**
*submitted on 2018-08-22 02:55:55*

**Authors:** Shengjun Wu, Jie Wang, Guiwu Wei, Yu Wei

**Comments:** 26 Pages.

In this paper, we expand the Hamy mean (HM) operator, weighted Hamy mean (WHM),
dual Hamy mean (DHM) operator, and weighted dual Hamy mean (WDHM) operator with 2-tuple
linguistic neutrosophic numbers (2TLNNs) to propose a 2-tuple linguistic neutrosophic Hamy
mean (2TLNHM) operator, 2-tuple linguistic neutrosophic weighted Hamy mean (2TLNWHM)
operator, 2-tuple linguistic neutrosophic dual Hamy mean (2TLNDHM) operator, and 2-tuple
linguistic neutrosophic weighted dual Hamy mean (2TLNWDHM) operator. Then, the multiple
attribute decision-making (MADM) methods are proposed with these operators. Finally, we utilize an applicable example in risk assessment for construction engineering projects to prove the proposed methods.

**Category:** General Mathematics

[2819] **viXra:1808.0468 [pdf]**
*submitted on 2018-08-22 02:59:05*

**Authors:** Jing-JingWang, Zhong-Hua Miao, Feng-Bao Cui, Hu-Chen Liu

**Comments:** 18 Pages.

Nowadays robots have been commonly adopted in various manufacturing industries to improve product quality and productivity. The selection of the best robot to suit a specific production
setting is a difficult decision making task for manufacturers because of the increase in complexity and number of robot systems.

**Category:** General Mathematics

[2818] **viXra:1808.0467 [pdf]**
*submitted on 2018-08-22 03:00:45*

**Authors:** Farhan Dakhil Shyaa

**Comments:** 5 Pages.

In this paper, we define the concept of a smarandache anti fuzzy M-semigroup (S-Anti Fuzzy M-Semigroup) and some elementary properties about this concept are discussed.

**Category:** General Mathematics

[2817] **viXra:1808.0465 [pdf]**
*submitted on 2018-08-22 03:42:13*

**Authors:** Muhammad Azhar Iqbal, Ehsan Ellahi Khawaja

**Comments:** 61 Pages.

Scientific Inquiry and Review publishes articles in the fields of mathematics,
biology, chemistry, physics and other miscellaneous areas of pure and applied sciences. Manuscripts are categorized into broader areas of pure and applied sciences and may be published as full length articles, short communications/letters, review articles, letter to editor etc. Contributors are encouraged to contact directly to the Chief Editor or editorial team to avoid any conflict about forthcoming publications.

**Category:** General Mathematics

[2816] **viXra:1808.0462 [pdf]**
*submitted on 2018-08-22 03:45:39*

**Authors:** Andrey Kostin, Natalya Kostina, Aleksandr Minkin, Ellina Anisimova

**Comments:** 7 Pages.

Issues of simulation modeling are currently being given more and more attention in training specialists from different fields. In particular, in pedagogical universities it can be actively used during classes in teaching methods of various subjects. Simulation modeling involves the replacement of a real process by its model, reflecting the most significant characteristics of a real process from the point of view of the goals set.

**Category:** General Mathematics

[2815] **viXra:1808.0459 [pdf]**
*submitted on 2018-08-22 04:18:37*

**Authors:** Edward Samuel.A, Narmadhagnanam r.

**Comments:** 5 Pages.

In this paper, sine logarithmic distance among neutrosophic refined sets is proposed and some of its properties are discussed herein. The
concept of the above method is an essential tool for dealing with uncertainties and shortcomings that affect the existing methods. Implementation
of medical diagnosis is presented to find out the disease impacting the patient.

**Category:** General Mathematics

[2814] **viXra:1808.0458 [pdf]**
*submitted on 2018-08-22 04:19:44*

**Authors:** Durga Banerjee, Surapati Pramanik

**Comments:** 16 Pages.

This paper deals with single-objective linear goal programming problem with neutrosophic numbers. The
coefficients of objective function and the constraints are considered as neutrosophic numbers of the form (p +qI), where p, q are real numbers and I denotes indeterminacy. In the solution process, the neutrosophic numbers are transformed into interval numbers.

**Category:** General Mathematics

[2813] **viXra:1808.0457 [pdf]**
*submitted on 2018-08-22 04:21:19*

**Authors:** Qiaoyan Li, Yingcang Ma, Shuangwu Zhu

**Comments:** 12 Pages.

Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. Neutrosophic set, which is extension of fuzzy set, has received extensive attention in solving many real life problems of uncertainty, inaccuracy, incompleteness, inconsistency and uncertainty.

**Category:** General Mathematics

[2812] **viXra:1808.0456 [pdf]**
*submitted on 2018-08-22 04:22:28*

**Authors:** Muhammad Akram, Sundas Shahzadi, A.borumand Saeid

**Comments:** 14 Pages.

We introduce certain concepts, including single-valued neutrosophic hypergraph, line graph of single-valued neutrosophic hypergraph, dual single-valued neutrosophic hypergraph and transversal single-valued neutrosophic hypergraph.

**Category:** General Mathematics

[2811] **viXra:1808.0454 [pdf]**
*submitted on 2018-08-22 04:24:44*

**Authors:** Orhan EcemiŞ, Memet Şahin, Abdullah Kargin

**Comments:** 14 Pages.

Neutrosophy is a branch of philosophy. Neutrosophy is based on neutrosophic logic, neutrosophic
probability and neutrosophic set. Neutrosophic triplet theory is new structure in neutrosophic set theory. In this study; we introduced notion of generalized neutrosophic triplet group. We defined contrary element for generalized neutrosophic triplet group.

**Category:** General Mathematics

[2810] **viXra:1808.0453 [pdf]**
*submitted on 2018-08-22 04:26:36*

**Authors:** J. H. Kim, P. K. Lim, J. G. Lee, K. Hur

**Comments:** 21 Pages.

We introduce the concept of a single valued neutrosophic reFLexive, symmetric and transitive relation. And we study single valued neutrosophic analogues of many results concerning relationships between ordinary reflexive, symmetric and transitive relations. Next, we dene the concepts of a single valued neutrosophic equivalence class and a single valued neutrosophic partition, and we prove that the set of all single valued neutrosophic
equivalence classes is a single valued neutrosophic partition and the single valued neutrosophic equivalence relation is induced by a single valued neutrosophic partition.

**Category:** General Mathematics

[2809] **viXra:1808.0452 [pdf]**
*submitted on 2018-08-22 04:27:23*

**Authors:** Tanju Kahraman

**Comments:** 6 Pages.

In this paper, we define Smarandache curves of null quaternionic curves in the semi-Euclidean space 31E and obtaine that curvatures of null quaternionic curves have some relations for Smarandache curves

**Category:** General Mathematics

[2808] **viXra:1808.0450 [pdf]**
*submitted on 2018-08-22 04:30:15*

**Authors:** Yushui Geng, Xingang Wang, Xuemei Li, Kun Yu, Peide Liu

**Comments:** 23 Pages.

There are many practical decision-making problems in people’s lives, but the information given by decision makers (DMs) is often unclear and how to describe this information is of critical importance.

**Category:** General Mathematics

[2807] **viXra:1808.0449 [pdf]**
*submitted on 2018-08-22 04:31:18*

**Authors:** Peide Liu, Xinli You

**Comments:** 26 Pages.

Linguistic neutrosophic numbers (LNNs) can easily describe the incomplete and indeterminate
information by the truth, indeterminacy, and falsity linguistic variables (LVs), and the
Hamy mean (HM) operator is a good tool to deal with multiple attribute group decision making
(MAGDM) problems because it can capture the interrelationship among the multi-input
arguments.

**Category:** General Mathematics

[2806] **viXra:1808.0448 [pdf]**
*submitted on 2018-08-22 04:32:10*

**Authors:** V. Krishnaraj, R. Vikramaprasad

**Comments:** 11 Pages.

In this paper, we introduce the concepts of Bi-Magic labeling in single valued neutrosophic graphs. We investigate some properties of single valued neutrosophic bi-magic labeling on path, cycle and star graphs.

**Category:** General Mathematics

[2805] **viXra:1808.0447 [pdf]**
*submitted on 2018-08-22 04:33:12*

**Authors:** Subramanian Visweswaran, Jaydeep Parejiya

**Comments:** 15 Pages.

The rings considered in this article are commutative with identity which admit at least two maximal ideals. Let R be a ring such that R admits at least two maximal ideals.

**Category:** General Mathematics

[2804] **viXra:1808.0446 [pdf]**
*submitted on 2018-08-22 04:34:19*

**Authors:** Tevk Sahin, Merve Okur

**Comments:** 15 Pages.

In the present paper, we investigate special Smarandache curves with Darboux apparatus with respect to Frenet and Darboux frame of an arbitrary curve on a surface in the three-dimensional Galilean space G3.

**Category:** General Mathematics

[2803] **viXra:1808.0444 [pdf]**
*submitted on 2018-08-22 04:36:20*

**Authors:** Jiangbo Feng, Min Li, Yansong Li

**Comments:** 21 Pages.

Rooftop distributed photovoltaic projects have been quickly proposed in China because
of policy promotion. Before, the rooftops of the shopping mall had not been occupied, and it was
urged to have a decision-making framework to select suitable shopping mall photovoltaic plans.

**Category:** General Mathematics

[2802] **viXra:1808.0443 [pdf]**
*submitted on 2018-08-22 04:37:27*

**Authors:** Gülnur ŞAFFAK ATALAY

**Comments:** 11 Pages.

In this paper, we analyzed surfaces family possessing a Mannheim partner curve of a
given curve as a geodesic. Using the Frenet frame of the curve in Euclidean 3-space, we
express the family of surfaces as a linear combination of the components of this frame
and derive the necessary and sufficient conditions for coefficients to satisfy both the geodesic and isoparametric requirements. The extension to ruled surfaces is also outlined.
Finally, examples are given to show the family of surfaces with common Mannheim geodesic curve.

**Category:** General Mathematics

[2801] **viXra:1808.0442 [pdf]**
*submitted on 2018-08-22 04:58:08*

**Authors:** Angyan Tu, Jun Ye, Bing Wang

**Comments:** 10 Pages.

A simplified neutrosophic set (containing interval and single-valued neutrosophic sets) can
be used for the expression and application in indeterminate decision-making problems because three elements in the simplified neutrosophic set (including interval and single valued neutrosophic sets)are characterized by its truth, falsity, and indeterminacy degrees.

**Category:** General Mathematics

[2800] **viXra:1808.0439 [pdf]**
*submitted on 2018-08-22 05:06:57*

**Authors:** Changxing Fanhangxing, En Fan, Jun Ye

**Comments:** 12 Pages.

Based on the multiplicity evaluation in some real situations, this paper firstly introduces
a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to
express the multiplicity information and the operational relations of SVNMs.

**Category:** General Mathematics

[2799] **viXra:1808.0438 [pdf]**
*submitted on 2018-08-22 05:07:54*

**Authors:** Sue Newell

**Comments:** 11 Pages.

The People's Republic of China (PRC) is
home to 25 per cent of the world's population.

**Category:** General Mathematics

[2798] **viXra:1808.0436 [pdf]**
*submitted on 2018-08-22 05:10:25*

**Authors:** Vu Dung, Luong Thu Thuy, Pham Quynh Mai, Nguyen Van Dan, Nguyen Thi Mai Lan

**Comments:** 8 Pages.

Personnel selection is one of the most critical strategies for companies to enhance the input quality of human resource their competitive strength in knowledge economy environment. Interval neutrosophic set (INS) is an adequate way for modeling uncertainty in decision making problems.

**Category:** General Mathematics

[2797] **viXra:1808.0435 [pdf]**
*submitted on 2018-08-22 05:11:20*

**Authors:** Debapriya Banik, Zahid Hasan

**Comments:** 12 Pages.

Red Tech. BD, an online based business company intended to spread their business over whole Rajshahi District. As there is no cost for manufacturing the only factor that can maximize the profit is the product transportation cost. Determination of the optimum & reliable transportation medium was the first challenge.

**Category:** General Mathematics

[2796] **viXra:1808.0434 [pdf]**
*submitted on 2018-08-22 05:12:23*

**Authors:** SumanMaity, Sujit Kumar De, Madhumangal Pal

**Comments:** 11 Pages.

In this article we develop an economic order quantity (EOQ) model with backlogging where the
decision is made jointly from two decision maker supposed to view one of them as the industrialist (developer) and the other one as the responsible manager.

**Category:** General Mathematics

[2795] **viXra:1808.0433 [pdf]**
*submitted on 2018-08-22 05:13:57*

**Authors:** T. Srinivasa Rao, B. Srinivasa Kumar, S. Hanumanth Rao

**Comments:** 8 Pages.

Molodtsov ‘s soft settheory has been considered an effecient Mathematical tool is conduct along
uncertainties. In our regular life, we frequently facing some real problems which need right decision making to get the best solution for these problems. Therefore, it is necessary to consider various parameters related to the best solution. In this paper, we applied Γ(Gamma)-Soft set theory in decision making problems.

**Category:** General Mathematics

[2794] **viXra:1808.0432 [pdf]**
*submitted on 2018-08-22 05:15:20*

**Authors:** Snežana Urošević, Dragiša Stanujkić, Darjan Karabašević, Pavle Brzaković

**Comments:** 17 Pages.

Natural beauties of Eastern Serbia combined with the culture, traditions, food specialties and music, can become a recognizable tourism brand, which could improve the image of this part of Serbia, and that is the reason why Eastern Serbia has been recently discovering its potential
for tourism development.

**Category:** General Mathematics

[2793] **viXra:1808.0431 [pdf]**
*submitted on 2018-08-21 06:56:32*

**Authors:** Mehmet Şahin, Irfan Deli, Vakkas Ulusay

**Comments:** 22 Pages.

In this paper, we first proposed the extension principles of neutrosophic multi-sets and cut sets which are a bridge between neutrosophic multi-sets and crisp sets. Then the representation theorem of neutrosophic multi-sets based on cut sets are studied. Finally, the addition, subtraction, multiplication and division operations over neutrosophic multi-sets are defined based on the extension principle.

**Category:** General Mathematics

[2792] **viXra:1808.0430 [pdf]**
*submitted on 2018-08-21 06:57:56*

**Authors:** Jianghong Zhu, Rui Wang, Yanlai Li

**Comments:** 24 Pages.

Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis.

**Category:** General Mathematics

[2791] **viXra:1808.0429 [pdf]**
*submitted on 2018-08-21 06:58:59*

**Authors:** Juanli Li, Jiacheng Xie, Zhaojian Yang, Junjie Li

**Comments:** 16 Pages.

To reduce the difficulty of acquiring and transmitting data in mining hoist fault diagnosis
systems and to mitigate the low efficiency and unreasonable reasoning process problems, a fault
diagnosis method for mine hoisting equipment based on the Internet of Things (IoT) is proposed
in this study.

**Category:** General Mathematics

[2790] **viXra:1808.0428 [pdf]**
*submitted on 2018-08-21 07:00:10*

**Authors:** Memet Şahin, Abdullah Kargın, Mehmet Ali Çoban

**Comments:** 7 Pages.

Neutrosphic triplet is a new theory in neutrosophy. In a neutrosophic triplet set, there is a neutral element and antielement for each element. In this study, the concept of neutrosophic triplet partial metric space (NTPMS) is given and the properties of NTPMS are studied.

**Category:** General Mathematics

[2789] **viXra:1808.0427 [pdf]**
*submitted on 2018-08-21 07:00:57*

**Authors:** P. Sudha, A. Murugan

**Comments:** 7 Pages.

The objective of this paper is to detect fire in the forest where some plants and trees are prone to fire very easily. The detection of forest fire preserves economic and environmental wealth of forest and defends human life.

**Category:** General Mathematics

[2788] **viXra:1808.0425 [pdf]**
*submitted on 2018-08-21 07:03:15*

**Authors:** Abdolreza Rashno, Student Member, Ieee, Dara D. Koozekanani, Member, Ieee, Paul M. Drayna, Behzad Nazari, Saeed Sadri, Hossein Rabbani

**Comments:** 13 Pages.

This paper presents a fully-automated algorithm to
segment fluid-associated (fluid-filled) and cyst regions in optical coherence tomography (OCT) retina images of subjects with diabetic macular edema (DME).

**Category:** General Mathematics

[2787] **viXra:1808.0423 [pdf]**
*submitted on 2018-08-21 07:05:54*

**Authors:** Tadeusz Pietkiewicz, Bronisław Wajszczyk

**Comments:** 13 Pages.

This paper presents a method of fusion of identification (attribute) information provided by ELINT – ESM sensors (Electronic Intelligence – Electronic Support Measures). In the first section the basic taxonomy of attribute identification in accordance with the standards of STANAG 1241 ed. 5 and STANAG 1241 ed. 6 (draft) is adopted. These standards provide the following basic values of the attributes of identification: FRIEND, HOSTILE, NEUTRAL, UNKNOWN and additional values: ASSUMED FRIEND and SUSPECT. The last values can be interpreted as a conjunction of basic values.

**Category:** General Mathematics

[2786] **viXra:1808.0421 [pdf]**
*submitted on 2018-08-21 07:09:16*

**Authors:** Aboul Ella HASSANIEN, Sameh H. BASHA, Areeg S. ABDALLA

**Comments:** 43 Pages.

This article presents a New Neutrosophic C-Means (NNCMs) method for clustering. It uses the neutrosophic logic (NL), to generalize the Fuzzy C-Means (FCM) clustering system. The NNCMs system assigns objects to clusters using three degrees of membership: a degree of truth, a degree of indeterminacy, and a degree of falsity, rather than only the truth degree used in the FCM.

**Category:** General Mathematics

[2785] **viXra:1808.0419 [pdf]**
*submitted on 2018-08-21 07:11:38*

**Authors:** Xin Li, Xiaohong Zhang, Choonkil Park

**Comments:** 17 Pages.

The interval neutrosophic set (INS) is a subclass of the neutrosophic set (NS) and a
generalization of the interval-valued intuitionistic fuzzy set (IVIFS), which can be used in real engineering and scientific applications.

**Category:** General Mathematics

[2784] **viXra:1808.0417 [pdf]**
*submitted on 2018-08-21 07:13:56*

**Authors:** Sameh H. Basha, Areeg S. Abdalla, Aboul Ella Hassanien

**Comments:** 6 Pages.

In this paper, we present a hybrid intelligent
system based on Neutrosophic Logic (NL). In conjunction with Genetic Algorithm(GA) for classification. The neutrosophic logic
is adapted for representing different forms of knowledge. GA is used to refine the generated neutrosophic rules.

**Category:** General Mathematics

[2783] **viXra:1808.0414 [pdf]**
*submitted on 2018-08-21 07:15:54*

**Authors:** Yongfeng Pang, Wei Yang

**Comments:** 20 Pages.

In this paper, the hesitant neutrosophic linguistic set is first defined by extending a hesitant fuzzy set to accommodate linguistic terms and neutrosophic fuzzy values. Some operational laws are defined for hesitant neutrosophic linguistic fuzzy information.

**Category:** General Mathematics

[2782] **viXra:1808.0412 [pdf]**
*submitted on 2018-08-21 07:17:05*

**Authors:** Dheeraj Kumar Joshi, Ismat Beg, Sanjay Kumar

**Comments:** 20 Pages.

Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of
possible values into hesitant fuzzy linguistic element (HFLE) and define hesitant probabilistic fuzzy linguistic set (HPFLS) for ill structured and complex decision making problem.

**Category:** General Mathematics

[2781] **viXra:1808.0411 [pdf]**
*submitted on 2018-08-21 07:17:59*

**Authors:** Wenhua Cui, Jun Ye

**Comments:** 12 Pages.

This work indicates the insufficiency of existing symmetry measures (SMs) between asymmetry measures of simplified neutrosophic sets (SNSs) and proposes the improved normalized SMs of SNSs, including the improved SMs and weighted SMs in single-valued and interval neutrosophic settings.

**Category:** General Mathematics

[2780] **viXra:1808.0410 [pdf]**
*submitted on 2018-08-21 07:18:46*

**Authors:** Mihaela-Gabriela Păun

**Comments:** 19 Pages.

The study is an application in the esthetic field of the neutrosophic theory of Florentin Smarandache.

**Category:** General Mathematics

[2779] **viXra:1808.0409 [pdf]**
*submitted on 2018-08-21 07:19:43*

**Authors:** Soumitra De, Jaydev Mishra

**Comments:** 5 Pages.

I have introduced a new approach for treatment of human disease using Neutrosophic logic and data. Any neutrosophic data is based on indeterminacy membership along with truth and false membership values which is not available in other fuzzy and vague data. I have focused to solve the real problem of a patient whether
suffering from blood cancer or not through the different laboratory report with neutrosophic data and applying same medicine on different patient.

**Category:** General Mathematics

[2778] **viXra:1808.0408 [pdf]**
*submitted on 2018-08-21 07:20:27*

**Authors:** Sergey Gorbachev

**Comments:** 9 Pages.

The article is devoted to description of structure and operation algorithms of a multilevel intellectual system for analysis and forecast of scientific-technological and innovative development of objects and territories based on expert methods, trainable models of fuzzy logic and fuzzy cognitive analysis. The article analyses distinctions and advantages of the system in making forecast evaluation and scenarios of the dynamics of multidimensional feature objects and processes. The authors have built a neutrosophic cognitive map for interaction of technologies based on the results of foresight studies.

**Category:** General Mathematics

[2777] **viXra:1808.0407 [pdf]**
*submitted on 2018-08-21 07:21:28*

**Authors:** Francisco Gallego Lupiáñez

**Comments:** 6 Pages.

In 2005, Smarandache generalized the Atanassov’s intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs),which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.

**Category:** General Mathematics

[2776] **viXra:1808.0406 [pdf]**
*submitted on 2018-08-21 07:23:06*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 8 Pages.

The notion of interval valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets, interval valued fuzzy sets, interval valued intuitionstic fuzzy sets and single valued neutrosophic sets. We apply for the first time the concept of interval valued neutrosophic sets, an instance of neutrosophic sets, to graph theory. We introduce certain types of interval valued neutrosophc graphs (IVNG) and investigate some of their properties with proofs and examples.

**Category:** General Mathematics

[2775] **viXra:1808.0405 [pdf]**
*submitted on 2018-08-21 07:24:18*

**Authors:** Cristhian Fabián MENÉNDEZ DELGADO, Pablo José MENÉNDEZ VERA, Nory Analidhia PINELA MORAN, Mba

**Comments:** 13 Pages.

En Ecuador, específicamente en el Cantón de Yaguachi, hay un enorme potencial en la
producción de arroz, que desafortunadamente no está siendo bien utilizada y dirigida por
estrategias de mercado. En este trabajo se desarrollaron estrategias de mercadeo que ayudan a sostener la actividad comercial del arroz en Yaguachi Cantón y sus alrededores. Las estrategias propuestas fueron analizadas y priorizadas usando SVN y distancia euclidiana para el tratamiento de las neutralidades. El trabajo termina con la conclusión y futura propuesta de trabajo para la aplicación de la neutrosofía a nuevas áreas de comercialización.

**Category:** General Mathematics

[2774] **viXra:1808.0403 [pdf]**
*submitted on 2018-08-21 07:33:25*

**Authors:** YumeiWang, Peide Liu

**Comments:** 35 Pages.

To solve the problems related to inhomogeneous connections among the attributes, we introduce a novel multiple attribute group decision-making (MAGDM) method based on the introduced linguistic neutrosophic generalized weighted partitioned Bonferroni mean operator (LNGWPBM) for linguistic neutrosophic numbers (LNNs).

**Category:** General Mathematics

[2773] **viXra:1808.0402 [pdf]**
*submitted on 2018-08-21 07:34:23*

**Authors:** Ashraf Al-Quran, Nasruddin Hassan

**Comments:** 11 Pages.

We introduce the mapping on complex neutrosophic soft expert sets. Further, we investigated the basic operations and other related properties of complex neutrosophic soft expert image and complex neutrosophic soft expert inverse image of
complex neutrosophic soft expert sets.

**Category:** General Mathematics

[2772] **viXra:1808.0401 [pdf]**
*submitted on 2018-08-21 07:35:29*

**Authors:** Chao Zhang, Deyu Li, Said Broumi, Arun Kumar Sangaiah

**Comments:** 16 Pages.

In real-world diagnostic procedures, due to the limitation of human cognitive competence,
a medical expert may not conveniently use some crisp numbers to express the diagnostic information,and plenty of research has indicated that generalized fuzzy numbers play a significant role in describing complex diagnostic information.

**Category:** General Mathematics

[2771] **viXra:1808.0400 [pdf]**
*submitted on 2018-08-21 07:36:36*

**Authors:** Yan Yang, Junhua Hu, Ruixiao Sun, Xiaohong Chen

**Comments:** 41 Pages.

Medical tourism has developed rapidly worldwide, especially in Asia, and one of the most
important problems facing the patient-tourists is the selection of the optimum destination. In this
paper, we present a novel multiple criteria group decision making (MCGDM) methodology to
evaluate and rank the medical tourism destinations vague based on vague information.

**Category:** General Mathematics

[2770] **viXra:1808.0399 [pdf]**
*submitted on 2018-08-21 07:39:37*

**Authors:** Yanhui Guo

**Comments:** 17 Pages.

A medical imaging system includes an imaging device configured to scan a region of interest to acquire at least one of afirst image including a first plurality of pixels and a secondimage including a second plurality of pixels, a processing unit configured to receive the first and second images, calculate
respective first neutrosophic similarity scores for each of thefirst plurality of pixels of the first image, calculate respective second neutrosophic similarity scores for each of the second plurality of pixels of the second image, perform a template matching algorithm based on differences between the respective first and second neutrosophic similarity scores for each of the first and second plurality, respectively, to determine one or more registration parameters, and register the first and second images using the one or more registration parameters, and a display output configured to allow the registered first and
second images to be displayed.

**Category:** General Mathematics

[2769] **viXra:1808.0398 [pdf]**
*submitted on 2018-08-21 07:40:34*

**Authors:** M. Kaliraja, S. Rumenaka

**Comments:** 8 Pages.

In this paper, we have discussed the concept of M-N anti fuzzy normal soft group, we then dene the M-N anti level subsets of a normal fuzzy soft subgroup and its some elementary properties are also discussed.

**Category:** General Mathematics

[2768] **viXra:1808.0397 [pdf]**
*submitted on 2018-08-21 07:42:10*

**Authors:** JieWang, Guiwu Wei, YuWei

**Comments:** 36 Pages.

In this paper, we extend the Bonferroni mean (BM) operator, generalized Bonferroni
mean (GBM) operator, dual generalized Bonferroni mean (DGBM) operator and dual generalized geometric Bonferroni mean (DGGBM) operator with 2-tuple linguistic neutrosophic numbers (2TLNNs) to propose 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean
(2TLNNWBM) operator, 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (2TLNNWGBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (G2TLNNWBM) operator, generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (G2TL NNWGBM) operator, dual generalized 2-tuple linguistic neutrosophic numbers weighted Bonferroni mean (DG2TLNNWBM) operator, and dual generalized 2-tuple linguistic neutrosophic numbers weighted geometric Bonferroni mean (DG2TLNNWGBM)
operator.

**Category:** General Mathematics

[2767] **viXra:1808.0395 [pdf]**
*submitted on 2018-08-21 07:45:00*

**Authors:** Harish Garg, Nancy

**Comments:** 25 Pages.

The aim of this paper is to introduce some new operators for aggregating single-valued
neutrosophic (SVN) information and to apply them to solve the multi-criteria decision-making
(MCDM) problems.

**Category:** General Mathematics

[2766] **viXra:1808.0394 [pdf]**
*submitted on 2018-08-21 07:45:52*

**Authors:** Peide Liu, Hui Gao

**Comments:** 25 Pages.

In multicriteria decision making (MCDM), multi-hesitant fuzzy linguistic term sets
(MHFLTSs) can eliminate the limitations of hesitant fuzzy linguistic term sets (HFLTSs) and hesitant fuzzy linguistic sets (HFLSs), and emphasize the importance of a repeated linguistic term (LT). Meanwhile, there is usually an interrelation between criteria.

**Category:** General Mathematics

[2765] **viXra:1808.0393 [pdf]**
*submitted on 2018-08-21 07:46:49*

**Authors:** Jian-QiangWang, Chu-Quan Tian, Xu Zhang, Hong-Yu Zhang, Tie-Li Wang

**Comments:** 23 Pages.

This study introduces simplified neutrosophic linguistic numbers (SNLNs) to describe
online consumer reviews in an appropriate manner. Considering the defects of studies on SNLNs
in handling linguistic information, the cloud model is used to convert linguistic terms in SNLNs
to three numerical characteristics.

**Category:** General Mathematics

[2764] **viXra:1808.0392 [pdf]**
*submitted on 2018-08-21 07:48:33*

**Authors:** Faruk Karaaslan

**Comments:** 21 Pages.

In this paper, we propose three similarity measure methods for single-valued neutrosophic refined sets and interval neutrosophic re¯ned sets based on Jaccard, Dice and Cosine similarity measures of single-valued neutrosophic sets and interval neutrosophic sets. Furthermore, we suggest two multi-criteria decision making methods under single-valued neutrosophic refined environment and
interval neutrosophic refined environment, and give applications of proposed multi-criteria decision making methods. Finally we suggest a consistency analysis method for proposed similarity measures between interval neutrosophic refined sets and give an application to demonstrate process of the method.

**Category:** General Mathematics

[2763] **viXra:1808.0391 [pdf]**
*submitted on 2018-08-21 07:49:42*

**Authors:** Angyan Tu, Jun Ye, Bing Wang

**Comments:** 11 Pages.

In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set
(NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be
applied in decision-making to present its partial indeterminate and partial determinate information.

**Category:** General Mathematics

[2762] **viXra:1808.0389 [pdf]**
*submitted on 2018-08-21 07:57:25*

**Authors:** Juan-juan Peng, Jian-qiang Wang, Xiao-hui Wu, Jing Wang, Xiao-hong Chen

**Comments:** 19 Pages.

In recent years, hesitant fuzzy sets (HFSs) and neutrosophic sets (NSs) have become a subject of great interest for researchers and have been widely applied to multi-criteria group decision-making (MCGDM) problems. In this paper, multi-valued neutrosophic sets (MVNSs) are introduced, which allow the truth-membership, indeterminacy membership and falsity-membership degree have a set of crisp values between zero and one, espectively.

**Category:** General Mathematics

[2761] **viXra:1808.0388 [pdf]**
*submitted on 2018-08-21 07:58:41*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Tapan Kumar Roy

**Comments:** 20 Pages.

Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval
10 neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both 11 the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly 12 defined, little research on the operations and applications of neutrosophic cubic sets appear in the 13 current literature.

**Category:** General Mathematics

[2760] **viXra:1808.0387 [pdf]**
*submitted on 2018-08-21 08:00:58*

**Authors:** S. N. Bocharova

**Comments:** 8 Pages.

Сборник подготовлен на основе материалов, представленных на IV Международном экономическом форуме «Экономическое развитие региона:управление, инновации, подготовка кадров», организованного и проведенно-
го в ФГБОУ ВО «Алтайский государственный университет» 8 июня 2017 года (г. Барнаул) при поддержке ФГБУ «Российский фонд фундаментальных исследований», проект № 17‑02‑14081 «IV Международный экономический форум
«Экономическое развитие региона: управление, инновации, подготовка кадров».

**Category:** General Mathematics

[2759] **viXra:1808.0385 [pdf]**
*submitted on 2018-08-21 08:02:09*

**Authors:** R. Dhavaseelan, S. Jafari, R. Narmada Devi, Md. Hanif Page

**Comments:** 4 Pages.

In this paper, we introduce the concept of neutrosophic Baire space and present some of its characterizations.

**Category:** General Mathematics

[2758] **viXra:1808.0384 [pdf]**
*submitted on 2018-08-20 05:29:18*

**Authors:** Mohamed Abdel-Basset, M. Gunasekaran, Mai Mohamed, Florentin Smarandache

**Comments:** 11 Pages.

The most widely used technique for solving and optimizing a real-life problem is linear programming (LP), due to its simplicity and efficiency. However, in order to handle the impreciseness in the data, the neutrosophic set theory plays a vital role which makes a simulation of the decision-making process of humans by considering all aspects of decision (i.e.,agree, not sure and disagree).

**Category:** General Mathematics

[2757] **viXra:1808.0383 [pdf]**
*submitted on 2018-08-20 05:30:42*

**Authors:** Abduallah Gamal, Mahmoud Ismail, Florentin Smarandache

**Comments:** 23 Pages.

In this research, the main objectives are to study the Analytic Network Process (ANP) technique in neutrosophic environment, to develop a new method for formulating the problem of Multi-Criteria
Decision-Making (MCDM) in network structure, and to present a way of checking and calculating consistency consensus degree of decision makers.

**Category:** General Mathematics

[2756] **viXra:1808.0382 [pdf]**
*submitted on 2018-08-20 05:33:12*

**Authors:** Yanhui Guo, Amira S. Ashour, Florentin Smarandache

**Comments:** 19 Pages.

This paper proposes novel skin lesion detection based on neutrosophic clustering and adaptive region growing algorithms applied to dermoscopic images, called NCARG. First, the dermoscopic images are mapped into a neutrosophic set domain using the shearlet transform results for the images.

**Category:** General Mathematics

[2755] **viXra:1808.0370 [pdf]**
*submitted on 2018-08-21 01:43:04*

**Authors:** V. Vladareanu, S. B. Cononovici, M. Migdalovici, H. Wang, Y. Feng, F. Smarandache

**Comments:** 4 Pages.

The paper presents the position and load reference generation for a motor stand simulating a mechatronic chain, in this case a three degree of freedom robot leg. The task is accomplished using three PLC controlled motors in position as the robot joint actuators coupled with three controlled in torque, simulating the load at each simulation time-step. The paper briefly discusses the mathematical model and presents the visual interface used in the simulation, which is then to be further integrated into a virtual environment robot control application.

**Category:** General Mathematics

[2754] **viXra:1808.0369 [pdf]**
*submitted on 2018-08-21 01:44:39*

**Authors:** Abduallah Gamal, Mahmoud Ismail, Florentin Smarandache

**Comments:** 15 Pages.

In this paper, we present a hybrid model of Neutrosophic-MOORA for supplier selection problems. Making a suitable model for
supplier selection is an important issue to amelioration competitiveness and capability of the organization, factory, project etc. selecting of the best supplier selection is not decrease delays in any organizations but also maximum profit and saving of material costs.

**Category:** General Mathematics

[2753] **viXra:1808.0368 [pdf]**
*submitted on 2018-08-21 01:47:20*

**Authors:** Muhammad Gulistan, Naveed Yaqoob, Zunaira Rashid, Florentin Smarandache, Hafiz Abdul Wahab

**Comments:** 22 Pages.

Neutrosophic cubic sets are the more generalized tool by which one can handle imprecise information in a more effective way as compared to fuzzy sets and all other versions of fuzzy sets. Neutrosophic cubic sets have the more flexibility, precision and compatibility to the system as compared to previous existing fuzzy models. On the other hand the graphs represent a problem physically in the form of diagrams, matrices etc. which is very easy to understand and handle.

**Category:** General Mathematics

[2752] **viXra:1808.0363 [pdf]**
*submitted on 2018-08-21 01:57:25*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Florentin Smarandache, Jun Ye

**Comments:** 25 Pages.

The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar
neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of
a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions.

**Category:** General Mathematics

[2751] **viXra:1808.0362 [pdf]**
*submitted on 2018-08-21 02:28:18*

**Authors:** Muhammad Akram, Nabeela Ishfaq, Sidra Sayed, Florentin Smarandache

**Comments:** 20 Pages.

Rough set theory and neutrosophic set theory are mathematical models to deal with
incomplete and vague information. These two theories can be combined into a framework for
modeling and processing incomplete information in information systems. Thus, the neutrosophic
rough set hybrid model gives more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. In this research study, we develop neutrosophic rough digraphs based on the neutrosophic rough hybrid model. Moreover, we discuss regular neutrosophic rough digraphs, and we solve decision-making problems by using our proposed hybrid model. Finally, we give a comparison analysis of two hybrid models, namely, neutrosophic rough digraphs and rough
neutrosophic digraphs.

**Category:** General Mathematics

[2750] **viXra:1808.0361 [pdf]**
*submitted on 2018-08-21 02:30:15*

**Authors:** Parimala Mani, Karthika Muthusamy, Saeid Jafari, Florentin Smarandache, Udhayakumar Ramalingam

**Comments:** 10 Pages.

The concept of interval neutrosophic sets has been studied and the introduction of a new kind of set in topological spaces called the interval valued neutrosophic support soft set has been suggested. We study some of its basic properties. The main purpose of this paper is to give the optimum solution to decision-making in real life problems the using interval valued neutrosophic support soft set.

**Category:** General Mathematics

[2749] **viXra:1808.0360 [pdf]**
*submitted on 2018-08-21 02:31:42*

**Authors:** Muhammad Akram, Shumaiza, Florentin Smarandache

**Comments:** 17 Pages.

Technique for the order of preference by similarity to ideal solution (TOPSIS) and elimination and choice translating reality (ELECTRE) are widely used methods to solve multi-criteria decision making problems. In this research article, we present bipolar neutrosophic TOPSIS method and bipolar
neutrosophic ELECTRE-I method to solve such problems. We use the revised closeness degree to rank the alternatives in our bipolar neutrosophic TOPSIS method. We describe bipolar neutrosophic TOPSIS method and bipolar neutrosophic ELECTRE-I method by flow charts. We solve numerical examples by proposed methods. We also give a comparison of these methods.

**Category:** General Mathematics

[2748] **viXra:1808.0353 [pdf]**
*submitted on 2018-08-21 02:50:48*

**Authors:** Mumtaz Ali, Luu Quoc Dat, Le Hoang Son, Florentin Smarandache

**Comments:** 16 Pages.

Neutrosophic set is a powerful general formal
framework which generalizes the concepts of classic set,fuzzy set, interval-valued fuzzy set, intuitionistic fuzzy set,etc. Recent studies have developed systems with complex fuzzy sets, for better designing and modeling real-life applications.

**Category:** General Mathematics

[2747] **viXra:1808.0352 [pdf]**
*submitted on 2018-08-21 02:52:00*

**Authors:** Young Bae Jun, Seon Jeong Kim, Florentin Smarandache

**Comments:** 13 Pages.

Intuitionistic fuzzy set, which is introduced by Atanassov, is a generalization of Zadeh’s
fuzzy sets,and consider both truth-membership and falsity-membership. Since the sum of degree
true, indeterminacy and false is one in intuitionistic fuzzy sets, incomplete information is handled in intuitionistic fuzzy sets.

**Category:** General Mathematics

[2746] **viXra:1808.0350 [pdf]**
*submitted on 2018-08-21 02:54:15*

**Authors:** Temitope Gbolahan Jaiyeola, Florentin Smarandache

**Comments:** 20 Pages.

A generalized group is an algebraic structure which has a deep physical background in the unified gauge theory and has direct relation with isotopies. Mathematicians and physicists have been trying to construct a suitable unified theory for twistor theory, isotopies theory, and so on. It was known that generalized groups are tools for constructions in unified geometric theory and electroweak theory.

**Category:** General Mathematics

[2745] **viXra:1808.0349 [pdf]**
*submitted on 2018-08-21 02:55:30*

**Authors:** Xiaohong Zhang, Xiaoying Wu, Florentin Smarandache, Minghao Hu

**Comments:** 18 Pages.

The new notion of a neutrosophic triplet group (NTG) is proposed by Florentin Smarandache; it is a new algebraic structure different from the classical group. The aim of this paper is to further expand this new concept and to study its application in related logic algebra
systems. Some new notions of left (right)-quasi neutrosophic triplet loops and left (right)-quasi neutrosophic triplet groups are introduced, and some properties are presented.

**Category:** General Mathematics

[2744] **viXra:1808.0348 [pdf]**
*submitted on 2018-08-21 02:56:37*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Vakkas Uluçay

**Comments:** 11 Pages.

In this paper, an algorithm for searching the minimum spanning tree (MST) in a network having trapezoidal fuzzy neutrosophic edge weight is
presented. The network is an undirected neutrosophic weighted connected graph (UNWCG). The proposed algorithm is based on matrix approach to design the MST of UNWCG. A numerical example is provided to check the validity of the proposed algorithm. Next, a comparison example is made with Mullai’s algorithm in neutrosophic graphs.

**Category:** General Mathematics

[2743] **viXra:1808.0347 [pdf]**
*submitted on 2018-08-21 02:57:41*

**Authors:** Maikel Leyva-Vázquez, Rebeca Escobar-Jara, Florentin Smarandache

**Comments:** 9 Pages.

In this work, elements related to mental models elicitation and analysis are addressed through causal models. Issues related to the need to include indeterminacy in causal relationships through neutrophic cognitive maps are discussed. A proposal for static analysis in neutrosophic cognitive maps is presented. The following activities are included in the proposal: Calculate, measures of centrality, Classify nodes, De-neutrosification, and Ranking nodes. As future works, the incorporation of new metrics of centrality in neutrosophic cognitive maps is proposed. The inclusion of scenario analysis to the proposal is another area of future work.

**Category:** General Mathematics

[2742] **viXra:1808.0345 [pdf]**
*submitted on 2018-08-21 02:59:59*

**Authors:** Muhammad Akram, Sundas Shahzadi, Florentin Smarandache

**Comments:** 24 Pages.

Soft sets (SSs), neutrosophic sets (NSs), and rough sets (RSs) are different mathematical
models for handling uncertainties, but they are mutually related. In this research paper, we introduce the notions of soft rough neutrosophic sets (SRNSs) and neutrosophic soft rough sets (NSRSs) as hybrid models for soft computing. We describe a mathematical approach to handle decision-making problems in view of NSRSs. We also present an efficient algorithm of our proposed hybrid model to solve decision-making problems.

**Category:** General Mathematics

[2741] **viXra:1808.0342 [pdf]**
*submitted on 2018-08-21 03:09:25*

**Authors:** Surapati Pramanik, Shyamal Dalapati, Shariful Alam, Florentin Smarandache, Tapan Kumar Roy

**Comments:** 26 Pages.

The objective of the paper is to introduce a new cross entropy measure in a neutrosophic
cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision-making (MADM) strategy based on a weighted NC-cross entropy measure. To show the feasibility and applicability of the proposed multi attribute decision-making strategy,we solve an illustrative example of the multi attribute decision-making problem.

**Category:** General Mathematics

[2740] **viXra:1808.0341 [pdf]**
*submitted on 2018-08-21 03:10:47*

**Authors:** Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache, Victor Chang

**Comments:** 19 Pages.

Big Data is a large-sized and complex dataset, which cannot be managed using traditional
data processing tools. Mining process of big data is the ability to extract valuable information from these large datasets. Association rule mining is a type of data mining process, which is indented to determine interesting associations between items and to establish a set of association rules whose support is greater than a specific threshold.

**Category:** General Mathematics

[2739] **viXra:1808.0340 [pdf]**
*submitted on 2018-08-21 03:12:09*

**Authors:** Xiaohong Zhang, Florentin Smarandache, Xingliang Liang

**Comments:** 16 Pages.

The notions of the neutrosophic triplet and neutrosophic duplet were introduced by
Florentin Smarandache. From the existing research results, the neutrosophic triplets and neutrosophic duplets are completely different from the classical algebra structures. In this paper, we further study neutrosophic duplet sets, neutrosophic duplet semi-groups, and cancellable neutrosophic triplet groups.
First, some new properties of neutrosophic duplet semi-groups are funded, and the following important result is proven: there is no finite neutrosophic duplet semi-group.

**Category:** General Mathematics

[2738] **viXra:1808.0339 [pdf]**
*submitted on 2018-08-21 03:13:39*

**Authors:** Ibrahim M. Hezam, Mohamed Abdel-Baset, Florentin Smarandache

**Comments:** 14 Pages.

In this chapter, the goal programming in neutrosophic environment is introduced. The degree of acceptance, indeterminacy and rejection of objectives is considered simultaneous. In the two proposed
models to solve Neutrosophic Goal Programming Problem (NGPP), our goal is to minimize the sum of the deviation in the model (I),
while in the model (II), the neutrosophic goal programming problem NGPP is transformed into the crisp programming model using truth
membership, indeterminacy membership, and falsity membership functions. Finally, the industrial design problem is given to illustrate the efficiency of the proposed models. The obtained results of Model
(I) and Model (II) are compared with other methods.

**Category:** General Mathematics

[2737] **viXra:1808.0338 [pdf]**
*submitted on 2018-08-21 03:14:57*

**Authors:** Songtao Shao, Xiaohong Zhang, Chunxin Bo, Florentin Smarandache

**Comments:** 19 Pages.

The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy
filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fuzzy subalgebras (filters) and hesitant fuzzy subalgebras (filters) is discussed. Five kinds of special sets are constructed by a neutrosophic
hesitant fuzzy set, and the conditions for the two kinds of sets to be filters are given. Moreover, the conditions for two kinds of special neutrosophic hesitant fuzzy sets to be neutrosophic hesitant fuzzy filters are proved.

**Category:** General Mathematics

[2736] **viXra:1808.0337 [pdf]**
*submitted on 2018-08-21 03:16:12*

**Authors:** Muhammad Akram, Sidra Sayed, Florentin Smarandache

**Comments:** 14 Pages.

In this research study, we introduce the notion of single-valued neutrosophic incidence
graphs. We describe certain concepts, including bridges, cut vertex and blocks in single-valued
neutrosophic incidence graphs.We present some properties of single-valued neutrosophic incidence graphs. We discuss the edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic incidence graphs. We also deal with a mathematical model of the situation of illegal migration from Pakistan to Europe.

**Category:** General Mathematics

[2735] **viXra:1808.0336 [pdf]**
*submitted on 2018-08-21 03:17:44*

**Authors:** Mohamed Abdel-Baset, Mai Mohamed, Abdel-Nasser Hessian, Florentin Smarandache

**Comments:** 13 Pages.

In this chapter, we introduce the integer programming in neutrosophic environment, by considering coefficients of problem as a triangular neutrosophic numbers. The degrees of acceptance,indeterminacy and rejection of objectives are simultaneously considered.

**Category:** General Mathematics

[2734] **viXra:1808.0334 [pdf]**
*submitted on 2018-08-21 03:20:07*

**Authors:** Abdel-Nasser Hussian, Mai Mohamed, Mohamed Abdel-Baset, Yongquan Zhou, Florentin Smarandache

**Comments:** 19 Pages.

In this chapter, a solution procedure is proposed to solve neutrosophic linear fractional programming (NLFP) problem where
cost of the objective function, the resources and the technological coefficients are triangular neutrosophic numbers. Here, the NLFP
problem is transformed into an equivalent crisp multi-objective linear fractional programming (MOLFP) problem. By using proposed approach, the transformed MOLFP problem is reduced to
a single objective linear programming (LP) problem which can be solved easily by suitable LP problem algorithm.

**Category:** General Mathematics

[2733] **viXra:1808.0333 [pdf]**
*submitted on 2018-08-21 03:21:44*

**Authors:** Abdel-Nasser Hessian, Mai Mohamed, Mohamed Abdel-Baset, Florentin Smarandache

**Comments:** 13 Pages.

Smarandache presented neutrosophic theory as a tool for handling undetermined information. Wang et al. introduced a single valued neutrosophic set that is a special neutrosophic sets and can be used expediently to deal with real-world problems, especially in decision support. In this paper, we propose linear programming problems based on neutrosophic environment.

**Category:** General Mathematics

[2732] **viXra:1808.0332 [pdf]**
*submitted on 2018-08-21 03:22:51*

**Authors:** M. Parimala, M. Karthika, S. Jafari, F. Smarandache, R. Udhayakumar

**Comments:** 11 Pages.

Neutrosophic nano topology and Nano ideal topological spaces induced the authors to propose this new concept. The aim of this paper is to introduce a new type of structural space called neutrosophic nano ideal topological spaces and investigate the relation between neutrosophic nano topological space and neutro-
sophic nano ideal topological spaces. We define some closed sets in these spaces to establish their relationships. Basic properties and characterizations related to these sets are given.

**Category:** General Mathematics

[2731] **viXra:1808.0331 [pdf]**
*submitted on 2018-08-21 03:24:57*

**Authors:** Young Bae Jun, Florentin Smarandache, Seok-Zun Song, Hashem Bordbar

**Comments:** 16 Pages.

The notions of neutrosophic permeable values are introduced, and related properties are
investigated. Conditions for the neutrosophic level sets to be energetic, right stable, and right vanished are discussed. Relations between neutrosophic permeable S- and I-values are considered.

**Category:** General Mathematics

[2730] **viXra:1808.0330 [pdf]**
*submitted on 2018-08-21 03:26:11*

**Authors:** Young Bae Jun, Seok-Zun Song, Florentin Smarandache, Hashem Bordbar

**Comments:** 16 Pages.

The notion of a neutrosophic quadruple BCK/BCI-number is considered, and a neutrosophic
quadruple BCK/BCI-algebra, which consists of neutrosophic quadruple BCK/BCI-numbers,
is constructed. Several properties are investigated, and a (positive implicative) ideal in a neutrosophic quadruple BCK-algebra and a closed ideal in a neutrosophic quadruple BCI-algebra are studied.

**Category:** General Mathematics

[2729] **viXra:1808.0325 [pdf]**
*submitted on 2018-08-21 03:32:39*

**Authors:** Sudan Jha, Raghvendra Kumar, Le Hoang Son, Jyotir Moy Chatterjee, Manju Khari, Navneet Yadav, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, we point out a major issue of stock market regarding trending scenario of trades where data exactness, accuracy
of expressing data and uncertainty of values (closing point of the day) are lacked. We use neutrosophic soft sets (NSS) consisting of three factors (True, Uncertainty and False) to deal with exact state of data in several directions. A new approach based on NSS is proposed for stock value prediction based on real data from last 7 years. It calculates the stock price based on the factors like “open”, “high”, “low” and “adjacent close”. The highest score value retrieved from the score function
is used to determine which opening price and high price decide the closing price from the above mentioned four factors.

**Category:** General Mathematics

[2728] **viXra:1808.0323 [pdf]**
*submitted on 2018-08-21 03:36:41*

**Authors:** Florentin Smarandache, Mehmet Sahin, Abdullah Kargın

**Comments:** 9 Pages.

In this study, the neutrosophic triplet G-module is introduced and the properties of neutrosophic triplet G-module are studied. Furthermore, reducible, irreducible, and completely reducible neutrosophic triplet G-modules are defined, and relationships of these structures with each other are examined. Also, it is shown that the neutrosophic triplet G-module is different from the G-module.

**Category:** General Mathematics

[2727] **viXra:1808.0322 [pdf]**
*submitted on 2018-08-21 03:37:36*

**Authors:** Florentin Smarandache, Mumtaz Ali

**Comments:** 7 Pages.

Groups are the most fundamental and rich
algebraic structure with respect to some binary operation in the study of algebra. In this paper, for the first time, we introduced the notion of neutrosophic triplet which is a group of three elements that satisfy certain properties with
some binary operation.

**Category:** General Mathematics

[2726] **viXra:1808.0321 [pdf]**
*submitted on 2018-08-21 03:39:45*

**Authors:** Muhammed Turhan, Dönüs Sengür, Songül Karabatak, Yanhui Guo, Florentin Smarandache

**Comments:** 11 Pages.

In the recent years, school administrators often come across various problems while
teaching, counseling, and promoting and providing other services which engender disagreements and interpersonal conflicts between students, the administrative staff, and others. Action learning is an effective way to train school administrators in order to improve their conflict-handling styles. In this
paper, a novel approach is used to determine the effectiveness of training in school administrators who attended an action learning course based on their conflict-handling styles.

**Category:** General Mathematics

[2725] **viXra:1808.0320 [pdf]**
*submitted on 2018-08-21 03:41:06*

**Authors:** Xiaohong Zhang, Chunxin Bo, Florentin Smarandache, Jianhua Dai

**Comments:** 11 Pages.

The main purpose of this paper is to study the inclusion relations of neutrosophic sets and some applications in multiple attribute decision making. At first, the existing two definitions of inclusion relation (called type-1 and type-2 inclusion relation, respectively) of neutrosophic sets are analyzed, and the deficiencies of type-1 and type-2 inclusion relations are illustrated by examples (in fact, they are actually two extreme cases).

**Category:** General Mathematics

[2724] **viXra:1808.0319 [pdf]**
*submitted on 2018-08-21 03:42:17*

**Authors:** Wadei Al-Omeri, Florentin Smarandache

**Comments:** 21 Pages.

In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy. The purpose of this chapter is to construct the basic concepts of the so-called "neutrosophic sets via neutrosophic topological spaces (NTs)".

**Category:** General Mathematics

[2723] **viXra:1808.0318 [pdf]**
*submitted on 2018-08-21 03:43:24*

**Authors:** Said Broumi, Kifayat Ullah, Assia Bakali, Mohamed Talea, Prem Kumar Singh, Tahir Mahmood, Florentin Smarandache, Ayoub Bahnasse, Santanu Kumar Patro, Angelo de Oliveira

**Comments:** 11 Pages.

Telephony is gaining momentum in the daily lives of individuals and in the activities of all companies. With the great trend towards telephony networks, whether analogue or digital known as Voice over IP (VoIP), the number of calls an individual can receive becomes considerably high.However, effective management of incoming calls to subscribers becomes a necessity. Recently,much attention has been paid towards applications of single-valued neutrosophic graphs in various research fields.

**Category:** General Mathematics

[2722] **viXra:1808.0317 [pdf]**
*submitted on 2018-08-21 03:44:18*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 5 Pages.

In this paper, we discuss Maxwell-Dirac isomorphism and quantum entanglement.

**Category:** General Mathematics

[2721] **viXra:1808.0316 [pdf]**
*submitted on 2018-08-21 04:01:22*

**Authors:** Mani Parimala, Florentin Smarandache, Saeid Jafari, Ramalingam Udhayakumar

**Comments:** 7 Pages.

The aim of this paper is to introduce the concept of closed sets in terms of neutrosophic
topological spaces. We also study some of the properties of neutrosophic closed sets. Further,
we introduce continuity and contra continuity for the introduced set. The two functions and their
relations are studied via a neutrosophic point set.

**Category:** General Mathematics

[2720] **viXra:1808.0314 [pdf]**
*submitted on 2018-08-21 04:03:50*

**Authors:** M. Kavitha, P. Murugadas, S. Sriram

**Comments:** 15 Pages.

In some real life applications, one has to consider not only the truth membership
supported by the evidence but also the falsity membership against the evidence, which is beyond the scope of fuzzy sets and IVFSs.

**Category:** General Mathematics

[2719] **viXra:1808.0313 [pdf]**
*submitted on 2018-08-21 04:09:45*

**Authors:** L. Vladareanu, V. Vladareanu, H. Yu, H. Wang, F. Smarandache

**Comments:** 5 Pages.

The paper presents a versatile, intelligent portable robot platform VIPRo, which involves
developing intelligent control interfaces by applying advanced control techniques adapted to
the robot environment such Robot Neutrosophic Control (RNC), Robot Extenics Control (eHFPC), Robot Haptic Control (RHC), human adaptive mechatronics, implemented by high speed processing IT&C techniques and real time communication for a high amount processing data.

**Category:** General Mathematics

[2718] **viXra:1808.0311 [pdf]**
*submitted on 2018-08-21 04:12:27*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, K. P. Krishnan Kishore, Rıdvan Şahin

**Comments:** 7 Pages.

This paper presents a study of neutrosophic shortest path with interval valued neutrosophic number on a network. A proposed algorithm also gives the shortest path length using ranking function from source node to destination node. Here each arc length is assigned to interval valued neutrosophic number. Finally, a numerical example has been provided for illustrating the proposed approach.

**Category:** General Mathematics

[2717] **viXra:1808.0310 [pdf]**
*submitted on 2018-08-21 04:13:35*

**Authors:** Mohammad Hamidi, Arsham Borumand Saeid, Florentin Smarandache

**Comments:** 7 Pages.

This paper introduces the concept of single–valued neutrosophic EQ–subalgebras, single–valued neutrosophic EQ–prefilters and single–valued neutrosophic EQ–filters. We study some properties of single–valued neutrosophic EQ–prefilters
and show how to construct single–valued neutrosophic EQ–filters. Finally, the relationship between single–valued neutrosophic EQ–filters and EQ–filters are studied.

**Category:** General Mathematics

[2716] **viXra:1808.0309 [pdf]**
*submitted on 2018-08-21 04:14:51*

**Authors:** Hafsa Masood Malik, Muhammad Akram, Florentin Smarandache

**Comments:** 37 Pages.

In this paper, we apply the notion of soft rough neutrosophic sets to graph theory. We develop certain new concepts, including soft rough neutrosophic graphs, soft rough neutrosophic influence graphs, soft rough neutrosophic influence cycles and soft rough neutrosophic influence trees. We illustrate these concepts with examples, and investigate some of their properties. We solve the decision-making problem by using our proposed algorithm.

**Category:** General Mathematics

[2715] **viXra:1808.0308 [pdf]**
*submitted on 2018-08-21 04:16:02*

**Authors:** Tèmítópé Gbóláhàn Jaíyéolá, Florentin Smarandache

**Comments:** 14 Pages.

This article is based on new developments on a neutrosophic triplet group (NTG) and
applications earlier introduced in 2016 by Smarandache and Ali.

**Category:** General Mathematics

[2714] **viXra:1808.0307 [pdf]**
*submitted on 2018-08-21 04:17:45*

**Authors:** Shio Gai Quek, Said Broumi, Ganeshsree Selvachandran, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 30 Pages.

Fuzzy graph theory plays an important role in the study of the symmetry and asymmetry properties of fuzzy graphs. With this in mind, in this paper, we introduce new neutrosophic graphs called complex neutrosophic graphs of type 1 (abbr. CNG1). We then present a matrix representation for it and study some properties of this new concept.

**Category:** General Mathematics

[2713] **viXra:1808.0306 [pdf]**
*submitted on 2018-08-21 04:19:35*

**Authors:** Saima Anis, Seok-Zun Song, Young Bae Jun, Florentin Smarandache

**Comments:** 9 Pages.

In this paper, we studied the action of Picard modular group PSL.

**Category:** General Mathematics

[2712] **viXra:1808.0305 [pdf]**
*submitted on 2018-08-21 04:21:10*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Arindam Dey, Le Hoang Son

**Comments:** 10 Pages.

Neutrosophic set and neutrosophic logic theory are renowned theories to deal with complex, not clearly explained and uncertain real life problems, in which classical fuzzy sets/models may fail to model properly. This paper introduces an algorithm for finding minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph (abbr. UNWCG) where the arc/edge lengths are represented by a single valued neutrosophic numbers. To build the MST of UNWCG, a new algorithm based on matrix approach has been introduced. The proposed algorithm is compared to other existing methods and finally a numerical example is provided.

**Category:** General Mathematics

[2711] **viXra:1808.0304 [pdf]**
*submitted on 2018-08-21 04:23:01*

**Authors:** Mumtaz Ali, Florentin Smarandache, Mohsin Khan

**Comments:** 10 Pages.

Rings and fields are significant algebraic structures in algebra and both of them are based on the group structure. In this paper, we attempt to extend the notion of a neutrosophic triplet group to a neutrosophic triplet ring and a neutrosophic triplet field. We introduce a neutrosophic triplet ring and study some of its basic properties. Further, we define the zero divisor, neutrosophic triplet subring, neutrosophic triplet ideal, nilpotent integral neutrosophic triplet domain, and neutrosophic
triplet ring homomorphism. Finally, we introduce a neutrosophic triplet field.

**Category:** General Mathematics

[2710] **viXra:1808.0302 [pdf]**
*submitted on 2018-08-21 04:26:59*

**Authors:** Mai Mohamed, Mohamed Abdel-Basset, Abdel-Nasser Hussien, Florentin Smarandache

**Comments:** 11 Pages.

Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain,
inconsistent and incomplete information about real world problems. Elements of neutrosophic set are characterized by a truthmembership, falsity-membership and indeterminacy membership
functions.

**Category:** General Mathematics

[2709] **viXra:1808.0301 [pdf]**
*submitted on 2018-08-21 04:27:45*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 5 Pages.

In this paper, we tried to draw a fair assessment on things which will take place soon with the coming era of IoT, 5G technology, global eavesdropping and all that. Nonetheless, we are aware that this article sounds quite gloomy. We are not techno-utopians (read Evvgeny Morozov’s WSJ article on digital dictatorship1), but we are not techno-pessimists either. Perhaps you can consider us as: "techno-realists."2 This paper was written in the same spirit of Jonathan L. Zittrain’s book The Future of Internet and how to stop it.

**Category:** General Mathematics

[2708] **viXra:1808.0300 [pdf]**
*submitted on 2018-08-21 04:29:50*

**Authors:** Ibrahim M. Hezam, Mohamed Abdel-Baset, Florentin Smarandache

**Comments:** 14 Pages.

In this chapter, Taylor series is used to solve neutrosophic multiobjective programming problem (NMOPP). In the proposed approach, the truth membership, indeterminacy membership, falsity membership functions associated with each objective of multiobjective programming problems are transformed into a single objective linear programming problem by using a first order Taylor
polynomial series.

**Category:** General Mathematics

[2707] **viXra:1808.0298 [pdf]**
*submitted on 2018-08-21 05:19:53*

**Authors:** M. Hamidi, A. Borumand Saeid

**Comments:** 31 Pages.

This is an unedited version of the accepted manuscript scheduled for publication. It has been uploaded in advance for the benefit of our customers. The manuscript will be copyedited, typeset and proofread before it is released in the final form.

**Category:** General Mathematics

[2706] **viXra:1808.0281 [pdf]**
*submitted on 2018-08-20 04:47:04*

**Authors:** Vasantha KandasamyW.B., Ilanthenral Kandasamy, Florentin Smarandache

**Comments:** 8 Pages.

Fuzzy set theory was introduced by Zadeh and was generalized to the Intuitionistic Fuzzy Set (IFS) by Atanassov. Real-world, uncertain, incomplete, indeterminate, and inconsistent data were presented philosophically as a neutrosophic set by Smarandache [3], who also studied the notion
of neutralities that exist in all problems.

**Category:** General Mathematics

[2705] **viXra:1808.0280 [pdf]**
*submitted on 2018-08-20 04:48:40*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Florentin Smarandache, Yongquan Zhou

**Comments:** 11 Pages.

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision
makers are only approximate, which gives rise of neutrosophic critical path problem.

**Category:** General Mathematics

[2704] **viXra:1808.0279 [pdf]**
*submitted on 2018-08-20 04:50:13*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Florentin Smarandache, Yongquan Zhou

**Comments:** 8 Pages.

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision
makers are only approximate, which gives rise of neutrosophic critical path problem.

**Category:** General Mathematics

[2703] **viXra:1808.0278 [pdf]**
*submitted on 2018-08-20 04:51:20*

**Authors:** Jack Allen, Housila P. Singh

**Comments:** 15 Pages.

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors.

**Category:** General Mathematics

[2702] **viXra:1808.0277 [pdf]**
*submitted on 2018-08-20 04:52:46*

**Authors:** Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache

**Comments:** 21 Pages.

One of the most significant competitive strategies for organizations is sustainable supply chain management (SSCM). The vital part in the administration of a sustainable supply chain is the sustainable supplier selection, which is a multi-criteria decision-making issue, including many conflicting criteria.

**Category:** General Mathematics

[2701] **viXra:1808.0272 [pdf]**
*submitted on 2018-08-20 05:12:26*

**Authors:** Arindam Dey, Said Broumi, Le Hoang Son, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, we discuss the minimum spanning tree (MST) problem of an undirected neutrosophic weighted connected graph in which a single-valued neutrosophic number, instead of a real number/fuzzy number, is assigned to each arc as its arc length.We define this type of MST as neutrosophic minimum spanning tree (NMST).

**Category:** General Mathematics

[2700] **viXra:1808.0271 [pdf]**
*submitted on 2018-08-20 05:15:45*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Kishore Kumar P K

**Comments:** 16 Pages.

In this chapter, we introduce a new algorithm for finding a minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph whose edge weights are represented by an interval valued neutrosophic number. In addition, we compute the cost of MST and compare the de- neutrosophied value with an equivalent MST having the detereministic weights. Finally, a numerical example is provided.

**Category:** General Mathematics

[2699] **viXra:1808.0269 [pdf]**
*submitted on 2018-08-20 05:18:04*

**Authors:** Ganeshsree Selvachandran, Shio Gai Quek, Florentin Smarandache, Said Broumi

**Comments:** 17 Pages.

A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is
characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model.

**Category:** General Mathematics

[2698] **viXra:1808.0267 [pdf]**
*submitted on 2018-08-20 05:20:59*

**Authors:** Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache

**Comments:** 18 Pages.

Every organization seeks to set strategies for its development and growth and to do this, it must take into account the factors that affect its success or failure. The most widely used
technique in strategic planning is SWOT analysis. SWOT examines strengths (S), weaknesses (W),opportunities (O) and threats (T), to select and implement the best strategy to achieve organizational goals.

**Category:** General Mathematics

[2697] **viXra:1808.0266 [pdf]**
*submitted on 2018-08-20 05:22:13*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 7 Pages.

In this research paper, we propose the graph of the bipolar single-valued neutrosophic set (BSVNS) model. This graph generalized the graphs of single-valued neutrosophic set models.

**Category:** General Mathematics

[2696] **viXra:1808.0265 [pdf]**
*submitted on 2018-08-20 05:23:23*

**Authors:** V Christianto, F Smarandache, Y Umniyati

**Comments:** 3 Pages.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework.

**Category:** General Mathematics

[2695] **viXra:1808.0226 [pdf]**
*submitted on 2018-08-17 00:25:54*

**Authors:** Toshiro Takami

**Comments:** 19 Pages.

I found a prime number theorem. All prime numbers except 2 and 3 are /sqrt(24a-23)=t .
(a =positive integer, t =prime number)
As an exception, 77 which is not a prime number comes up, but it seems to be treated as the only exception.

**Category:** General Mathematics

[2694] **viXra:1808.0191 [pdf]**
*submitted on 2018-08-14 07:38:32*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents an image related with the function f(z)=ln(2z+tan z).

**Category:** General Mathematics

[2693] **viXra:1808.0174 [pdf]**
*submitted on 2018-08-13 06:51:14*

**Authors:** Saikat Sarkar

**Comments:** 8 Pages.

Here i am representing some basic graphs of some known functions and their behaviour.

**Category:** General Mathematics

[2692] **viXra:1808.0105 [pdf]**
*submitted on 2018-08-08 20:22:13*

**Authors:** Travis Keraly

**Comments:** 1 Page. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Using a simple pattern, a linear chromatic scale is revealed, beginning and ending with a perfect octave.

**Category:** General Mathematics

[2691] **viXra:1808.0092 [pdf]**
*submitted on 2018-08-07 10:53:42*

**Authors:** Colin James III

**Comments:** 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com. (We instruct troll Mikko at Disqus to read the entire article twice before she starts typing.)

In superposition calculus, the property of translation invariance for A < B → XAY < XBY for all words A,B,X,Y as TCTT TCTT TCTT TTTT is not tautologous and hence refuted.

**Category:** General Mathematics

[2690] **viXra:1808.0005 [pdf]**
*submitted on 2018-08-01 01:53:32*

**Authors:** Janne Hakkarainen

**Comments:** 2 Pages.

Magic squares have interested (recreational) mathematicians for hundreds, if not thousands, of years. But what would happen if the grid of a magic square would be infinite?

**Category:** General Mathematics

[2689] **viXra:1807.0497 [pdf]**
*submitted on 2018-07-29 18:52:13*

**Authors:** James A. Smith

**Comments:** 12 Pages.

Because the Chain Rule can confuse students as much as it helps them solve real problems, we put ourselves in the shoes of the mathematicians who derived it, so that students may understand the motivation for the rule; its limitations; and why textbooks present it in its customary form. We begin by finding the derivative of sin2x without using the Chain Rule. That exercise, having shown that even a comparatively simple compound function can be bothersome to differentiate using the definition of the derivative as a limit, provides the motivation for developing our own formula for the derivative of the general compound function g[f(x)]. In the course of that development, we see why the function f must be continuous at any value of x to which the formula is applied. We finish by comparing our formula to that which is commonly given.

**Category:** General Mathematics

[2688] **viXra:1807.0477 [pdf]**
*submitted on 2018-07-28 17:20:43*

**Authors:** Waldemar Zieliński

**Comments:** 3 Pages.

This paper is a supplement to the previous "Union of two arithmetic sequences - Basic calculation formula (1)” (viXra:1712.0636). We will derive a simpler version of formula for the union of two arithmetics progressions.

**Category:** General Mathematics

[2687] **viXra:1807.0415 [pdf]**
*submitted on 2018-07-23 11:15:19*

**Authors:** Martin Peter Neuenhofen

**Comments:** 13 Pages. Proof of convergence for a direct transcription method for OCP

In the arXiv paper [arXiv:1712.07761] from December 2017 we presented a convergent direct transcription method for optimal control problems. In the present paper we present a significantly generalized convergence theory in succinct form. Therein, we replace strong assumptions that we had formerly made on local uniqueness of the solution, and on differentiability of a particular functional. These assumptions are removed now.

**Category:** General Mathematics

[2686] **viXra:1807.0399 [pdf]**
*submitted on 2018-07-24 08:41:02*

**Authors:** Edgar Valdebenito

**Comments:** 6 Pages.

This note presents some sequences related with the cosine fixed point constant.

**Category:** General Mathematics

[2685] **viXra:1807.0197 [pdf]**
*submitted on 2018-07-09 09:58:18*

**Authors:** Thinh D. Nguyen

**Comments:** 3 Pages.

In this work, we will take one problem, namely Packing Triangles as an example of combinatorial optimization problems. We show that if one has ever loved reading Prasolov’s books, then one should not try to ﬁnd efﬁcient algorithm for various restricted cases of this problem.

**Category:** General Mathematics

[2684] **viXra:1807.0125 [pdf]**
*submitted on 2018-07-05 14:59:41*

**Authors:** Thinh Nguyen

**Comments:** 19 Pages.

We prove that for every d≥2, deciding if a pure, d-dimensional, simplicial complex is
shellable is NP-hard, hence NP-complete. This resolves a question raised, e.g., by Danaraj
and Klee in 1978. Our reduction also yields that for every d≥2 and k≥0, deciding if a pure,
d-dimensional, simplicial complex is k-decomposable is NP-hard. For d≥ 3, both problems
remain NP-hard when restricted to contractible pure d-dimensional complexes. Another
simple corollary of our result is that it is NP-hard to decide whether a given poset is CL-
shellable.

**Category:** General Mathematics

[2683] **viXra:1807.0098 [pdf]**
*submitted on 2018-07-03 06:11:19*

**Authors:** Thinh Nguyen

**Comments:** 4 Pages.

The Erd ̋os-Szekeres theorem states that, for every $k$, there is a number $n_k$ such that every set of $n_k$ points in general position in the plane contains a subset of $k$ points in convex position. If we ask the same question for subsets whose convex hull does not contain any other point from the set, this is not true: as shown by Horton, there are sets of arbitrary size that do not contain an empty 7-gon.
These questions have also been studied extensively
from a computational point of view, and polynomial time algorithms for finding the largest (empty) convex set have been given for the planar case. In higher dimension, it is not known how to compute such a set efficiently. In this paper, we show that already in 3 dimensions no polynomial time algorithm exists for determining the largest (empty) convex set (unless $P$=$NP$), by proving that the corresponding decision problem is $NP$-hard. This answers a question by Dobkin, Edelsbrunner and Overmars from 1990.
As a corollary, we derive a similar result for the closely related problem of testing weak $ε$-nets in $R^3$ . Answering a question by Chazelle et al. from 1995, our reduction shows that the problem is $co-NP$-hard.
Finally, we make several suggestions for further research on the subject.

**Category:** General Mathematics

[2682] **viXra:1807.0031 [pdf]**
*submitted on 2018-07-01 16:07:27*

**Authors:** A. Lau

**Comments:** 6 Pages.

Abstract. Mathematics has been highly effective in its application of formalism to the real world. It spans from physical science to data science. Mathematical algorithm affects our everyday life. Mathematization (converting data to equations or mathematical forms) has been very successful. It has led to comments like “the unreasonable effectiveness of mathematics,” but we might have “unreasonable expectation of mathematics.”

**Category:** General Mathematics

[2681] **viXra:1806.0460 [pdf]**
*submitted on 2018-06-29 08:19:41*

**Authors:** Timothy W. Jones

**Comments:** 9 Pages.

We develop calculus from an experimental perspective. Using results from geometry and algebra, we generalize to other functions as a speculative act. Eventually formulas are created. This sequence reverses the usual hard things first approach of contemporary calculus text books.

**Category:** General Mathematics

[2680] **viXra:1806.0431 [pdf]**
*submitted on 2018-06-29 03:16:29*

**Authors:** Thinh Nguyen

**Comments:** 0 Pages.

The Marquis du Condorcet recognized 200 years ago that majority rule can produce intransitive group preferences if the domain of possible (transitive) individual preference orders is unrestricted. We present results on the cardinality and structure of those maximal sets of permutations for which majority rule produces transitive results (consistent sets). Consistent sets that contain a maximal chain in the Weak Bruhat Order inherit from it an upper semimodular sublattice structure. They are intrinsically related to a special class of hamiltonian graphs called persistent graphs. These graphs in turn have a clean geometric interpretation: they are precisely visibility graphs of staircase polygons. We highlight the main tools used to prove these connections and indicate possible social choice and computational research directions.

**Category:** General Mathematics

[2679] **viXra:1806.0339 [pdf]**
*submitted on 2018-06-22 06:21:33*

**Authors:** Thinh Nguyen

**Comments:** 3 Pages.

We survey some information about the clique problem - one of the cornerstone of the ﬁeld of research in theory of algorithms. A short note at the end of the paper should be read with care on the reader’s own.

**Category:** General Mathematics

[2678] **viXra:1806.0222 [pdf]**
*submitted on 2018-06-19 08:52:17*

**Authors:** Edgar Valdebenito

**Comments:** 8 Pages.

This note presents some numerical series

**Category:** General Mathematics

[2677] **viXra:1806.0220 [pdf]**
*submitted on 2018-06-19 08:54:52*

**Authors:** Edgar Valdebenito

**Comments:** 1 Page.

In this note we recall an identity given by Ramanujan.

**Category:** General Mathematics

[2676] **viXra:1806.0214 [pdf]**
*submitted on 2018-06-19 12:56:04*

**Authors:** Fenasi Kerim

**Comments:** 2 Pages.

In this paper I am proposing that we should find the general solution for every conceivable problem and how we can achieve such a triumph in mathematics.

**Category:** General Mathematics

[136] **viXra:1809.0187 [pdf]**
*replaced on 2018-09-10 17:05:00*

**Authors:** Toshiro Takami

**Comments:** 3 Pages.

Simulation of the nontrivial zero of Riemann's prediction succeeded in mimicking with rotational force alone. Although it is a simulation with only the rotational force, it is a very approximate value because the initial value was set as the first nonzero point of the Riemann zeta function. We adopted a method of placing a rotating force on the previous value and stacking it.
I could reproduce how the dragon climbs up the x = 0.5 axis.
The expressions a1, a2, a3, a4, a5, a6 ... are 1, 2, 3, 4, 5, 6 .......
In 1.0 of the interval of the nuclear energy, simulation did not hold and it was forced to take the value of 1.1.
At first, although it is out of the nonobvious point of Riemann's prediction, it gradually becomes an approximate value.
However, this may also be lower than the previous value, and it should be improved in the future.

**Category:** General Mathematics

[135] **viXra:1809.0187 [pdf]**
*replaced on 2018-09-09 16:26:38*

**Authors:** Toshiro Takami

**Comments:** 9 Pages.

We simulated the nontrivial zeros of Riemann's prediction. Looking at every other degree of increase, there is a maximum point of increase in every fourth, third or fifth place. For that reason, we did not only change one another but we looked at differences from two, three, four, five, six, seven and so on, but the degree of increase has changed variously Was observed.
This is reminiscent of the dragon which rises x = 0.5 while changing the degree of freedom freely while drawing a circle.
Initially we tried to simulate a nontrivial point with only the degree of increase of the circle, but we thought that it was impossible without increasing regularity and we adopted ln(x!). And averaged the increase. The average increase is 2πln(x!) = N (n is an integer starting from 1).
The expression of this increase degree is expressed as follows.
when ln(x!) = 1 Increase +2.31244
when ln(x!) = 2 Increase +3.16283
when ln(x!) = 3 Increase +3.88072
And so on.

**Category:** General Mathematics

[134] **viXra:1808.0684 [pdf]**
*replaced on 2018-09-01 16:01:06*

**Authors:** Armando M. Evangelista Jr.

**Comments:** I’ve made a mistake on the starting value for k in the double sum on pages 2 and 3, it should start at k =1.

The Riemann zeta-function is one of the most studied complex function in mathematics. Riemann in his 1859 paper On the Number of Prime Numbers less than a Given Quantity [1] claimed that the analytic continuation of the zeta-function extends its domain over the entire complex plane except at s = 1. But, as I’ve shown in my two papers: A Short Disproof of the Riemann Hypothesis [2] and Riemann’s Functional Equation is Not a Valid Function and Its Implication on the Riemann Hypothesis [3], the zeta-function is only defined on the right half-plane. It is the purpose of this present work to precisely locate the domain of this function on the right half-plane.

**Category:** General Mathematics

[133] **viXra:1807.0477 [pdf]**
*replaced on 2018-07-29 09:52:37*

**Authors:** Waldemar Zieliński

**Comments:** 3 Pages.

This paper is a supplement to the previous "Union of two arithmetic sequences - Basic calculation formula (1)” (viXra:1712.0636). We will derive a simpler version of formula for the union of two arithmetics progressions.

**Category:** General Mathematics

[132] **viXra:1807.0031 [pdf]**
*replaced on 2018-07-02 07:45:23*

**Authors:** August Lau

**Comments:** 6 Pages.

Mathematics has been highly effective in its application of formalism to the real world. It spans from physical science to data science. Mathematical algorithm affects our everyday life. Mathematization (converting data to equations or mathematical forms) has been very successful. It has led to comments like “the unreasonable effectiveness of mathematics,” but we might have “unreasonable expectation of mathematics.”

**Category:** General Mathematics