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Any replacements are listed further down

[2246] **viXra:1708.0205 [pdf]**
*submitted on 2017-08-17 05:20:01*

**Authors:** Mohsen Soori, Behrooz Arezoo, Mohsen Habibi

**Comments:** 14 Pages.

Accuracy of produced parts in machining process is influenced by many errors such as tool deflection as well as geometrical deviations of machine tool structure. To increase accuracy
and productivity in part manufacturing, the errors are modelled by using mathematical concepts. This paper presents an application for the virtual machining systems to analyse accuracy in modelling of tool deflection error. A virtual machining system is used to create actual parts in
virtual environments. Then, a comparison for different methods of tool deflection error such as
cantilever beam model of the cutting tool, Finite Element Method (FEM) of the cutting tool and
workpiece and geometrical model of the cutting tool effects on the workpiece is presented to
show accuracy and reliability of the methods in prediction of milled surfaces. So, capabilities and difficulties of the methods in the error modelling are presented to increase accuracy and
efficiency in part manufacturing.

**Category:** General Mathematics

[2245] **viXra:1708.0102 [pdf]**
*submitted on 2017-08-09 13:30:28*

**Authors:** Edgar Valdebenito

**Comments:** 15 Pages.

This note presents some results related with fractals,polynomials and number pi.

**Category:** General Mathematics

[2244] **viXra:1707.0287 [pdf]**
*submitted on 2017-07-21 14:03:43*

**Authors:** Dmitri Martila

**Comments:** 17 Pages.

Proposed solution to the Clay Institute Millennium Prize Problems.

**Category:** General Mathematics

[2243] **viXra:1706.0559 [pdf]**
*submitted on 2017-06-29 13:12:24*

**Authors:** Edgar Valdebenito

**Comments:** 7 Pages.

In this note we briefly explore the sequence: z(n+1)=(2+sqrt(3)+i)exp(-z(n)),z(1)=0,i=sqrt(-1),n natural number.

**Category:** General Mathematics

[2242] **viXra:1706.0542 [pdf]**
*submitted on 2017-06-29 01:01:09*

**Authors:** Kohji Suzuki

**Comments:** 12 Pages.

We solve a Berkeley problem in several ways.

**Category:** General Mathematics

[2241] **viXra:1706.0400 [pdf]**
*submitted on 2017-06-19 13:18:30*

**Authors:** Edgar Valdebenito

**Comments:** 14 Pages.

Some formulas and fractals related with the number s.

**Category:** General Mathematics

[2240] **viXra:1706.0361 [pdf]**
*submitted on 2017-06-12 00:54:28*

**Authors:** I. Arockiarani

**Comments:** 5 Pages.

The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

**Category:** General Mathematics

[2239] **viXra:1706.0360 [pdf]**
*submitted on 2017-06-12 00:55:59*

**Authors:** Rui Yong, Jun Ye, Qi-Feng Liang, Man Huang, Shi-Gui Du

**Comments:** 15 Pages.

Accurate determination of joint roughness coefﬁcient (JRC) of rock joints is essential for evaluating the inﬂuence of surface roughness on the shear behavior of rock joints. The JRC values of rock joints are typically measured by visual comparison against Barton’s standard JRC proﬁles. However, its accuracy is strongly affected by personal bias. In the present study, a new comparison method is proposed for JRC evaluation to overcome the drawback of conventional visual comparison methods based on vector similarity measures (VSMs). The feature vectors are obtained by analyzing the angular variation of line segments of both standard JRC proﬁles and test proﬁles obtained from three kinds of natural rocks with a sampling interval of 0.5 mm.

**Category:** General Mathematics

[2238] **viXra:1706.0359 [pdf]**
*submitted on 2017-06-12 00:58:09*

**Authors:** Simon Carladous, Jean-Marc Tacnet, Jean Dezert, Deqiang Han, Mireiile Batton-Hubert

**Comments:** 8 Pages.

Decision-Aid Methods (DAMs) such as the CostBeneﬁt Analysis (CBA) and the Analytical Hierarchy Process (AHP) help decision-makers to rank alternatives or to choose the best one among several potential ones. The new Belief Function based Technique for Order Preference by Similarity to Ideal Solution (BF-TOPSIS) methods have been recently developed for Multi-Criteria Decision-Making problems. In this paper, we compare CBA, AHP and BF-TOPSIS methods through an actual application case to natural risks in mountains. The CBA is the most used approach but is limited. Classical Multi-Criteria Decision-Aid methods (MCDAs) such as the AHP help to go further. The BF-TOPSIS methods notably show a robustness to rank reversal problems in the problem under concern, with a tractable complexity. Moreover, some steps of these new methods can be included in other MCDAs developed under the belief function theory framework.

**Category:** General Mathematics

[2237] **viXra:1706.0358 [pdf]**
*submitted on 2017-06-12 00:59:00*

**Authors:** Jun Ye

**Comments:** 18 Pages.

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems.

**Category:** General Mathematics

[2236] **viXra:1706.0356 [pdf]**
*submitted on 2017-06-12 01:19:15*

**Authors:** Yan-Ling Liu, Hai-Long Yang

**Comments:** 21 Pages.

Neutrosophic sets (NSs), as a new mathematical tool for dealing with problems involving incomplete, indeterminant and inconsistent knowledge, were proposed by Smarandache. By simplifying NSs, Wang et al. proposed the concept of single valued neutrosophic sets (SVNSs) and studied some properties of SVNSs. In this paper, we mainly investigate the topological structures of single valued neutrosophic rough sets which is constructed by combining SVNSs and rough sets. Firstly, we introduce the concept of single valued neutrosophic topological spaces.

**Category:** General Mathematics

[2235] **viXra:1706.0346 [pdf]**
*submitted on 2017-06-12 01:38:39*

**Authors:** R.Uma, P. Murugadas, S.Sriram

**Comments:** 16 Pages.

Aim of this article is to ﬁnd the maximum and minimum solution of the fuzzy neutrosophic soft relational equation = and = , where and are fuzzy neutrosophic soft vector and is a fuzzy neutrosophic soft matrix.

**Category:** General Mathematics

[2234] **viXra:1706.0345 [pdf]**
*submitted on 2017-06-12 01:39:34*

**Authors:** A. Hassan, M. A. Malik

**Comments:** 9 Pages.

The generalization of the concept of single valued neutrosophic hypergraph (SVNHG), strong SVNHG by considering SVN-Vertex instead of crisp vertex set and interrelations between SVN-Vertices and family of SVN-Edges are introduced here. A few properties and operations of such graphs are established here.

**Category:** General Mathematics

[2233] **viXra:1706.0342 [pdf]**
*submitted on 2017-06-12 02:00:44*

**Authors:** Uwe Mönks, Helene Dörksen, Volker Lohweg, Michael Hübner

**Comments:** 37 Pages.

Sensors, and also actuators or external sources such as databases, serve as data sources in order to realise condition monitoring of industrial applications or the acquisition of characteristic parameters like production speed or reject rate. Modern facilities create such a large amount of complex data that a machine operator is unable to comprehend and process the information contained in the data.

**Category:** General Mathematics

[2232] **viXra:1706.0340 [pdf]**
*submitted on 2017-06-12 02:14:15*

**Authors:** Peide Liu, Xinli You

**Comments:** 32 Pages.

In recent years, neutrosophic sets (NSs) have attracted widespread attentions and been widely applied to multiple attribute decision-making (MADM). The interval neutrosophic set (INS) is an extension of NS, in which the truth-membership, indeterminacy-membership and falsity-membership degree are expressed by interval values, respectively. Obviously, INS can conveniently describe complex information.

**Category:** General Mathematics

[2231] **viXra:1706.0339 [pdf]**
*submitted on 2017-06-12 02:15:06*

**Authors:** Tahir Mahmood, Qaisar Khan

**Comments:** 16 Pages.

In this paper we introduced the concept of interval neutrosophic ﬁnite state machine, interval neutrosophic ﬁnite switchboard state machine using the notion of interval neutrosophic set. We also introduced the concept of homomorphism and strong homomorphism of interval neutrosophic ﬁnite state machine.

**Category:** General Mathematics

[2230] **viXra:1706.0338 [pdf]**
*submitted on 2017-06-12 02:16:12*

**Authors:** Chenchen Liu

**Comments:** 7 Pages.

For the stochastic multi-criteria decision-making problem, in which the information on criteria's weights is incomplete and the indices value of alternatives are in the form of interval neutrosophic fuzzy numbers, an interval neutrosophic random decision-making approach based on WYCIN certainty factor and prospect theory is proposed. According to the score function of interval neutrosophic fuzzy numbers and prospect theory, the MYCIN certainty factors of different alternatives in different indices are obtained. And the trust degrees of different indices are determined by using the grey incidence analysis. Then, the certainty factor fusion method in different indices is deduced to get the optimal alternative. And the best alternative is got by using the method. Finally, an example shows the feasibility and validity of this method.

**Category:** General Mathematics

[2229] **viXra:1706.0336 [pdf]**
*submitted on 2017-06-12 02:17:06*

**Authors:** Muhammad Akram, Maryam Nasir

**Comments:** 18 Pages.

We ﬁrst introduce the concept of interval-valued neutrosophic competition graphs. We then discuss certain types, including k-competition interval-valued neutrosophic graphs, p-competition interval-valued neutrosophic graphs and m-step interval-valued neutrosophic competition graphs. Moreover, we present the concept of m-step interval-valued neutrosophic neighbouhood graphs.

**Category:** General Mathematics

[2228] **viXra:1706.0335 [pdf]**
*submitted on 2017-06-12 02:17:58*

**Authors:** Fatma Adam, Nasruddin Hassan

**Comments:** 21 Pages.

Molodtsov’s soft set theory is a newly emerging mathematical tool for handling uncertainty. However, classical multiparameterized soft sets are not appropriate for imprecise and Q-fuzzy parameters.

**Category:** General Mathematics

[2227] **viXra:1706.0334 [pdf]**
*submitted on 2017-06-12 02:20:10*

**Authors:** S. A. Akinleye, E .O. Adeleke, A. A. A. Agboola

**Comments:** 14 Pages.

The objective of this paper is to introduce the concept of neutrosophic nearrings. The concept of neutrosophic N-group of a neutrosophic nearring is introduced. We study neutrosophic subnearrings of neutrosophic nearrings and also neutrosophic N-subgroups of neutrosophic N- groups. The notions of neutrosophic ideals in neutrosophic nearrings and neutrosophic N-groups are introduced and their elementary properties are presented. In addition, we introduce the concepts of neutrosophic homomorphisms of neutrosophic nearrings and neutrosophic N-homomorphisms of neutrosophic N-groups and also, we present neutrosophic quotient nearrings and quotient N-groups.

**Category:** General Mathematics

[2226] **viXra:1706.0333 [pdf]**
*submitted on 2017-06-12 02:30:08*

**Authors:** Mehmet Şahin, İrfan Deli, Vakkas Uluçay

**Comments:** 8 Pages.

The main aim of this study is to present a novel method based on multi-criteria decision making for bipolar neutrosophic sets. Therefore, Jaccard vector similarity and weighted Jaccard vector similarity measure is defined to develop the bipolar neutrosophic decision making method. In addition, the method is applied to a numerical example in order to confirm the practicality and accuracy of the proposed method.

**Category:** General Mathematics

[2225] **viXra:1706.0330 [pdf]**
*submitted on 2017-06-12 02:34:39*

**Authors:** Faouzi Sebbak, Farid Benhammadi

**Comments:** 15 Pages.

Nowadays, tremendous growth of Internet of Things (IoT) applications is seen in smart environments such as medical remote care applications which are crucial due to the general aging of the population.

**Category:** General Mathematics

[2224] **viXra:1706.0329 [pdf]**
*submitted on 2017-06-12 02:36:25*

**Authors:** Jiawei Zou, Yong Deng, Yong Hu, Ge Lin

**Comments:** 8 Pages.

Due to the efﬁciency to handle uncertainty information, the single valued neutrosophic set is widely used in multicriteria decision-making. In MCDM, it is inevitable to measure the distance between two single valued neutrosophic sets. In this paper, an evidence distance for neutrosophic sets is proposed. There are two main contributions of this work. One is a new method to transform the single valued neutrosophic set into basic probability assignment. The other is evidence distance function between two single valued neutrosophic sets. The application in MCDM is illustrated the efﬁciency of the proposed distance.

**Category:** General Mathematics

[2223] **viXra:1706.0324 [pdf]**
*submitted on 2017-06-12 03:36:52*

**Authors:** Zhang-peng Tian, Jing Wang, Hong-yu Zhang, Jian-qiang Wang

**Comments:** 17 Pages.

A simpliﬁed neutrosophic uncertain linguistic set that integrates quantitative and qualitative evaluation can serve as an extension of both an uncertain linguistic variable and a simpliﬁed neutrosophic set. It can describe the real preferences of decision-makers and reﬂect their uncertainty, incompleteness and inconsistency.

**Category:** General Mathematics

[2222] **viXra:1706.0313 [pdf]**
*submitted on 2017-06-12 08:50:34*

**Authors:** Changrong Ye，Guojun Li, Yang Bao, Jinliang Qiao, Deping Zhang

**Comments:** 10 Pages.

T-Wave alternans (TWA) is a cardiac phenomenon regarded as an index of high risk of sudden cardiac death (SCD). Although a number of methods have been proposed for TWA detection, their final decision always fully depends on one single lead which is usually picked out for its strongest TWA detection result among all the other leads. That is to say that lots of useful information have been unused and wasted. To our best knowledge, no method that fuses TWA detection results independently obtained by each lead to do comprehensive decision has been introduced. In this paper, a novel multi-lead method for TWA fusion detection is proposed.

**Category:** General Mathematics

[2221] **viXra:1706.0311 [pdf]**
*submitted on 2017-06-12 08:53:27*

**Authors:** Yan Gao

**Comments:** 7 Pages.

Based on the interval neutrosophic numbers, a new multi-objective optimal model of two-sided matching is researched. Through integrating interval neutrosophic information of each subject, the relative closeness degree
of uncertainty evaluation information and positive and negative ideal is calculated by the approximate method, which can be expected as the satisfaction of the matching subjects. According to these, a multi-objective optimal
model of two-sided matching is constructed, and applied to the leisure industry technology demand and supply. Finally a numerical example is given to illustrate the feasibility and validity of the proposed method.

**Category:** General Mathematics

[2220] **viXra:1706.0305 [pdf]**
*submitted on 2017-06-12 09:23:32*

**Authors:** Nouran M. Radwan, M. Badr Senousy, Alaa El Din M. Riad

**Comments:** 11 Pages.

Learning management systems (LMSs) are used today to assist in the designing, delivery and
management of learning resources for learners. There are hundreds of LMS available in the marketplace. Selecting the most suitable LMS that meets specific requirements is a problem of decision making. Many studies in learning management system selection are implemented under complete information, while in the
real world many uncertainty aspects do exist. As these systems were described by decision makers with vague, imprecise, ambiguous and inconsistent terms, it is understandable that traditional multi criteria decision making methods may not be effective.

**Category:** General Mathematics

[2219] **viXra:1706.0299 [pdf]**
*submitted on 2017-06-12 09:35:41*

**Authors:** Kalyan Mondal, Surapati Pramanik

**Comments:** 11 Pages.

In this paper, cotangent similarity measure of neutrosophic refined set is proposed and some of its properties are studied. Finally, using this refined cotangent similarity measure of single valued neutrosophic set, an application on educational stream selection is presented.

**Category:** General Mathematics

[2218] **viXra:1706.0298 [pdf]**
*submitted on 2017-06-12 09:36:42*

**Authors:** P. Iswarya, K. Bageerathi

**Comments:** 10 Pages.

The purpose of this paper is to define the product related neutrosophic topological space and proved some theorems based on this. We introduce the concept of neutrosophic semi-open sets and neutrosophic semi-closed sets in neutrosophic topological spaces and derive some of their characterization. Finally, we analyze neutrosophic semi-interior and neutrosophic semi-closure operators also.

**Category:** General Mathematics

[2217] **viXra:1706.0282 [pdf]**
*submitted on 2017-06-12 12:18:33*

**Authors:** A. Borumand Saeid, Young Bae Jun

**Comments:** 10 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

[2216] **viXra:1706.0275 [pdf]**
*submitted on 2017-06-13 00:01:46*

**Authors:** Nancy, Harish Garg

**Comments:** 15 Pages.

Uncertainties play a dominant role during the aggregation process and hence their corresponding decisions are made fuzzier. Single-value neutrosophic numbers (SVNNs) contain the three ranges: truth, indeterminacy, and falsity membership degrees, and are very useful for describing and handling the uncertainties in the day-to-day life situations. In this study, some operations of SVNNs such as sum, product, and scalar multiplication are defined under Frank norm
operations and, based on it, some averaging and geometric aggregation operators have been developed. We further establish some of its properties. Moreover, a decision-making method based on the proposed operators is established and illustrated with a numerical example.

**Category:** General Mathematics

[2215] **viXra:1706.0271 [pdf]**
*submitted on 2017-06-13 00:42:22*

**Authors:** P. Jeya Puvaneswari, Dr.K.Bageerathi

**Comments:** 8 Pages.

The focus of this paper is to introduce the
concept of Neutrosophic point, Neutrosophic quasi coincident, Neutrosophic feebly open sets and Neutrosophic feebly closed sets in Neutrosophic Topological spaces. Also we analyse their characterizations and investigate their properties. This concept is the generalization of intuitionistic topological spaces and fuzzy topological spaces. Using this neutrosophic feebly open sets and neutrosophic feebly closed sets, we define a new class of functions namely neutrosophic feebly
continuous functions. Further, relationships between this new class and the other classes of functions are established.

**Category:** General Mathematics

[2214] **viXra:1706.0269 [pdf]**
*submitted on 2017-06-13 00:44:55*

**Authors:** Vakkas Uluçay, Mehmet Sahin, Necati Olgun, Adem Kilicman

**Comments:** 10 Pages.

In this study, using the neutrosophic soft definitions, we define some new concept such as the neutrosophic soft lattice, neutrosophic soft sublattice, complete neutrosophic soft lattice, modular neutrosophic soft lattice, distributive neutrosophic soft lattice, neutrosophic soft chain then we study the relationship and observe some common properties.

**Category:** General Mathematics

[2213] **viXra:1706.0267 [pdf]**
*submitted on 2017-06-13 00:47:43*

**Authors:** Yousef Al-Qudah, Nasruddin Hassan

**Comments:** 17 Pages.

In this paper, we introduce the concept of complex multi-fuzzy sets (CMkFSs) as a generalization of the concept of multi-fuzzy sets by adding the phase term to the definition of multi-fuzzy sets. In other words, we extend the range of multi-membership function from the interval [0,1] to unit circle in the complex
plane. The novelty of CMkFSs lies in the ability of complex multi- membership functions to achieve more range of values while handling uncertainty of data that is
periodic in nature. The basic operations on CMkFSs, namely complement, union, intersection, product and Cartesian product are studied along with accompanying examples. Properties of these operations are derived. Finally, we introduce the intuitive definition of the distance measure between two complex multi-fuzzy sets
which are used to define δ-equalities of complex multi-fuzzy sets.

**Category:** General Mathematics

[2212] **viXra:1706.0266 [pdf]**
*submitted on 2017-06-13 00:49:16*

**Authors:** Muhammad Akram, Gulfam Shahzadi

**Comments:** 26 Pages.

The concept of neutrosophic sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of single-valued neutrosophic sets to graphs. We introduce the notion of single-valued neutrosophic graphs, and present some fundamental operations on single-valued neutrosophic graphs. We explore some interesting properties of single-valued
neutrosophic graphs by level graphs. We highlight some flaws in the definitions of Broumi et al. [10] and Shah-Hussain [18]. We also present an application of single-valued neutrosophic graphs in social network.

**Category:** General Mathematics

[2211] **viXra:1706.0265 [pdf]**
*submitted on 2017-06-13 00:50:25*

**Authors:** Zheng Wang, Lin Liu

**Comments:** 9 Pages.

New energy storage alternative selection is a hot research issue that involves multiple-criteria decision-making process. In view of the existing deficiencies of multiple-criteria decision-making methods, an optimized method of PROMETHEE was proposed based on interval neutrosophic sets that has the advantage in describing fuzzy decision-making information.

**Category:** General Mathematics

[2210] **viXra:1706.0264 [pdf]**
*submitted on 2017-06-13 00:53:04*

**Authors:** J. Dezert, A. Tchamova, L. Bojilov, P. Konstantinova

**Comments:** 5 Pages.

The main objective of this paper is to
investigate the impact of the quality of attribute data source on the performance of a target tracking algorithm. An array of dense scenarios arranged according to the distance between closely spaced targets is studied by different confusion matrices. The used
algorithm is Generalized Data Association (GDA-MTT) algorithm for multiple target tracking processing kinematic as well as attribute data. The fusion rule for attribute data is based on Dezert-Smarandache Theory (DSmT). Besides the main goal a comparison is made between the cited above algorithm and an algorithm with Kinematic based only Data Association (KDAMTT).
The measures of performance are evaluated
using intensive Monte Carlo simulation.

**Category:** General Mathematics

[2209] **viXra:1706.0260 [pdf]**
*submitted on 2017-06-13 00:59:56*

**Authors:** Chunfang Liu, Yuesheng Luo

**Comments:** 10 Pages.

The simplified neutrosophic set (SNS) is a useful generalization of the fuzzy set that is designed for some practical situations in which each element has different truth membership
function, indeterminacy membership function and falsity membership function. In this paper, we develop a series of power aggregation operators called simplified neutrosophic number power
weighted averaging (SNNPWA) operator, simplified neutrosophic number power weighted geometric (SNNPWG) operator, simplified
neutrosophic number power ordered weighted averaging (SNNPOWA) operator and simplified neutrosophic number power ordered weighted geometric (SNNPOWG) operator.

**Category:** General Mathematics

[2208] **viXra:1706.0259 [pdf]**
*submitted on 2017-06-13 01:01:25*

**Authors:** José Luis Usó-Doménech, Josué Antonio Nescolarde-Selva, Lorena Segura-Abad

**Comments:** 11 Pages.

Classical logic is typically concerned with abstract analysis. The problem for a synthetic
logic is to transcend and unify available data to reconstruct the object as a totality. Three rules are proposed to pass from classic logic to synthetic logic. We present the category logic of qualitative opposition using examples from various sciences. This logic has been defined to include the neuter as part of qualitative opposition. The application of these rules to qualitative opposition, and, in
particular, its neuter, demonstrated that a synthetic logic allows the truth of some contradictions. This synthetic logic is dialectical with a multi-valued logic, which gives every proposition a truth value
in the interval [0,1] that is the square of the modulus of a complex number. In this dialectical logic, contradictions of the neuter of an opposition may be true.

**Category:** General Mathematics

[2207] **viXra:1706.0254 [pdf]**
*submitted on 2017-06-13 01:20:03*

**Authors:** Muhammad Akram, Sundas Shahzadi

**Comments:** 23 Pages.

The concept of intuitionistic neutrosophic soft sets can be utilized as a mathematical tool to deal with imprecise and unspecified information. In this paper, we apply the concept of intuitionistic neutrosophic soft
sets to graphs. We introduce the concept of intuitionistic neutrosophic soft graphs, and present applications of intuitionistic neutrosophic soft graphs in multiple-attribute decision-making problems. We also present an algorithm of our proposed method.

**Category:** General Mathematics

[2206] **viXra:1706.0252 [pdf]**
*submitted on 2017-06-13 01:22:50*

**Authors:** Irshad Ahmad Ansari, Millie Pant, Chang Wook Ahn

**Comments:** 12 Pages.

Watermarking is used to protect the copyrighted materials from being misused and help us to know the lawful ownership. The security of any watermarking scheme is always a prime concern for the developer.

**Category:** General Mathematics

[2205] **viXra:1706.0250 [pdf]**
*submitted on 2017-06-13 01:26:07*

**Authors:** I. Arockiarani, C. Antony Crispin Sweety

**Comments:** 7 Pages.

In this paper, we examine the relationship between rough fuzzy neutrosophic sets and lattice theory. We introduce the notion of Rough fuzzy neutrosophic set and Rough fuzzy neutrosophic lattice (resp Rough fuzzy neutrosophic ideals). Further, we discuss about fuzzy neutrosophic rough set corresponding to a rough set and define the terms and conditions for fuzzy neutrosophic rough lattice.

**Category:** General Mathematics

[2204] **viXra:1706.0245 [pdf]**
*submitted on 2017-06-13 01:49:46*

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

**Comments:** 10 Pages.

Algebraic Neutrosophic theory is an abstract branch of modern mathematics that originated from classical algebra through the composition of Neutrosophic theory. Its development started few years ago, and now a days Neutrosophic analytic methods and results are important in various fields of engineering science and applied mathematics with its applications.

**Category:** General Mathematics

[2203] **viXra:1706.0242 [pdf]**
*submitted on 2017-06-13 01:55:36*

**Authors:** Zhang-peng Tian, Jing Wang, Jian-qiang Wang, Hong-yu Zhang

**Comments:** 31 Pages.

For many companies, green product development has become a key strategic consideration due to regulatory requirements and market trends. In this paper, the life cycle assessment technique is used to develop an innovative multi-criteria group decision-making approach that incorporates power aggregation operators and a TOPSIS-based QUALIFLEX method in order to solve green product design selection problems using neutrosophic linguistic information.

**Category:** General Mathematics

[2202] **viXra:1706.0241 [pdf]**
*submitted on 2017-06-13 01:56:50*

**Authors:** Muhammad Akram

**Comments:** 11 Pages.

We apply the concept of single-valued neutrosophic sets to multigraphs, planar graphs and dual graphs. We introduce the notions of single-valued neutrosophic multigraphs, single-valued neutrosophic planar graphs, and single-valued neutrosophic dual graphs. We illustrate these concepts with examples. We also investigate some of their properties.

**Category:** General Mathematics

[2201] **viXra:1706.0239 [pdf]**
*submitted on 2017-06-13 01:58:57*

**Authors:** Seema Mehra, Manjeet Singh

**Comments:** 4 Pages.

Motivated by the notion of single valued neutrosophic graphs defined by Broumi, Talea, Bakali and Smarandache[2] and notion of intuitionistic fuzzy signed graphs defined by Mishra and Pal[8], we introduce the concept of single valued neutrosophic signed graphs and examine the properties of this new concept and examples.

**Category:** General Mathematics

[2200] **viXra:1706.0237 [pdf]**
*submitted on 2017-06-13 02:01:12*

**Authors:** Peide Liu, Fei Teng

**Comments:** 41 Pages.

Interval-valued neutrosophic hesitant fuzzy uncertain linguistic set (IVNHFULS) has the
advantages of both neutrosophic numbers and interval-valued hesitant fuzzy uncertain linguistic variable. In this paper, we firstly introduce the definition, the operational laws, and the score function of IVNHFULS.

**Category:** General Mathematics

[2199] **viXra:1706.0234 [pdf]**
*submitted on 2017-06-13 02:03:21*

**Authors:** M. A. Malik, A. Hassan

**Comments:** 13 Pages.

Neutrosophic theory has many applications in graph theory, interval valued neutrosophic graph (IVNG) is the generalization of fuzzy graph, intuitionistic fuzzy graph and single valued neutrosophic graph. In this paper, we introduced some types of IVNGs, which are subdivision IVNGs, middle IVNGs, total IVNGs and interval valued neutrosophic line graphs (IVNLGs), also discussed the isomorphism, co weak isomorphism and weak isomorphism properties of subdivision IVNGs, middle IVNGs, total IVNGs and IVNLGs.

**Category:** General Mathematics

[2198] **viXra:1706.0231 [pdf]**
*submitted on 2017-06-13 02:07:07*

**Authors:** Anjan Mukherjee, Sadhan Sarkar

**Comments:** 8 Pages.

F. Smarandache introduced the concept of neutrosophic set in 1995 and P. K. Maji introduced the notion of neutrosophic soft set in 2013, which is a hybridization of neutrosophic set and soft set. Irfan Deli
introduced the concept of interval valued neutrosophic soft sets. Interval valued neutrosophic soft sets are most efficient tools to deals with problems that contain uncertainty such as problem in social, economic system,
medical diagnosis, pattern recognition, game theory, coding theory and so on. In this article we introduce similarity measure between two interval valued neutrosophic soft sets and study some basic properties of similarity measure. An algorithm is developed in interval valued neutrosophic soft set setting using similarity measure. Using this algorithm a model is constructed for supervised pattern recognition problem using similarity measure.

**Category:** General Mathematics

[2197] **viXra:1706.0230 [pdf]**
*submitted on 2017-06-13 02:08:19*

**Authors:** Priyanka Deshpande, A.N.Banubakode

**Comments:** 5 Pages.

It is studied in this paper that the arrangement of inadequate examples is an extremely testing
assignment in light of the fact that the article (inadequate example) with distinctive feasible estimations of missing qualities may yield particular arrangement results. The insecurity (equivocalness) of grouping is for the most part brought about by the absence of data of the missing information.

**Category:** General Mathematics

[2196] **viXra:1706.0229 [pdf]**
*submitted on 2017-06-13 02:09:20*

**Authors:** D.PonJenifer, Y.R.Packia Dhas

**Comments:** 4 Pages.

Aircraft recognition plays an important role in
image processing. Recognition processor is used to extract the shape of aircraft. Recognition is done using various algorithms. In this paper eight types of recognition algorithm are discussed.

**Category:** General Mathematics

[2195] **viXra:1706.0226 [pdf]**
*submitted on 2017-06-13 02:13:36*

**Authors:** Edmundas Kazimieras Zavadskas, Romualdas Bausys, Arturas Kaklauskas, Ieva Ubarte, Agne Kuzminske, Neringa Gudiene

**Comments:** 14 Pages.

Traditionally, the real estate asset assessment is performed by experienced valuators, who take into
account its economic, social, physical and locational aspects. Nowadays, the construction industry is becoming more and more influenced by the sustainability requirements. Therefore, the inclusion of the sustainability evaluation into real estate asset valuation is of utmost importance.

**Category:** General Mathematics

[2194] **viXra:1706.0224 [pdf]**
*submitted on 2017-06-13 02:15:51*

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

**Comments:** 12 Pages.

We introduce the category NCSet consisting of neutrosophic crisp sets and morphisms between them. And we study NCSet in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category consisting of ordinary sets and
ordinary mappings between them.

**Category:** General Mathematics

[2193] **viXra:1706.0220 [pdf]**
*submitted on 2017-06-13 02:20:44*

**Authors:** Wu Hao, Tian Guohui, Pan Chunwei, Wang Xin, Yu Jinshan

**Comments:** 8 Pages.

When service robots carry on mission planning and execution, they not only need structural information about the environment to navigation and localization, but also need to possess deeper knowledge to endow a robot with higher degrees of autonomy and intelligence.

**Category:** General Mathematics

[2192] **viXra:1706.0216 [pdf]**
*submitted on 2017-06-13 02:25:24*

**Authors:** ZHAO Yu-xin, JIA Ren-feng, LIU Chang, SHEN Zhi-feng

**Comments:** 7 Pages.

To slove the problem in the transformation of basic probability assignment to decision-making
probability, this paper proposed a novel transformation method based on correlation degree.

**Category:** General Mathematics

[2191] **viXra:1706.0215 [pdf]**
*submitted on 2017-06-13 02:26:26*

**Authors:** Mariana Man, Maria Ciurea

**Comments:** 21 Pages.

One of the key factors affecting the efficient use of resources, the increase of shareholders confidence in the managers of the company, the success in achieving objectives and economic efficiency is the system of corporate governance by which a company is managed and controlled.

**Category:** General Mathematics

[2190] **viXra:1706.0212 [pdf]**
*submitted on 2017-06-13 02:29:56*

**Authors:** Mayank Vatsa, Richa Singh, Afzel Noore

**Comments:** 12 Pages.

This paper formulates an evidence-theoretic multimodal unification approach using belief functions that takes into account the variability in biometric image characteristics. While processing non-ideal images the variation in the quality of features at different levels of abstraction may cause individual classifiers to generate conflicting genuine-impostor decisions.

**Category:** General Mathematics

[2189] **viXra:1706.0211 [pdf]**
*submitted on 2017-06-13 02:31:16*

**Authors:** Srijit Biswas, FIE Sonal Bhugra

**Comments:** 7 Pages.

In this study we present a methodology of neutrosophic logic in defining river water quality of Yamuna, one of the most important river of Delhi. The laboratory test results of water quality parameters are not always found to be same in all locations of the river rather varies with wide range of interval daily, monthly and seasonally. For an engineer it is very difficult to define the water quality with degree of certainty.

**Category:** General Mathematics

[2188] **viXra:1706.0210 [pdf]**
*submitted on 2017-06-13 05:25:56*

**Authors:** Andrej Liptaj

**Comments:** 19 Pages.

If several independent algorithms for a computer-calculated quantity exist, then one can expect their results (which differ because of numerical errors) to follow approximately Gaussian distribution. The mean of this distribution, interpreted as the value of the quantity of interest, can be determined with better precision than what is the precision provided by a single algorithm. Often, with lack of enough independent algorithms, one can proceed differently: many practical algorithms introduce a bias using a parameter, e.g. a small but finite number to compute a limit or a large but finite number (cutoff) to approximate infinity. One may vary such parameter of a single algorithm and interpret the resulting numbers as generated by several algorithms. A numerical evidence for the validity of this approach is shown for differentiation.

**Category:** General Mathematics

[2187] **viXra:1706.0185 [pdf]**
*submitted on 2017-06-11 11:14:01*

**Authors:** Selim ERASLAN, Naim ÇAĞMAN

**Comments:** 12 Pages.

In this study, we first introduce the fuzzy sets, soft sets, fuzzy soft sets and their related properties. We then present the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) that is one of classical Multiple Attribute Decision Making (MADM) methods. We also present the Grey Relation Method. In the main part of this study, we extend the TOPSIS method on the fuzzy soft set theory to construct a decision
making method to deal with problems that contain uncertainties. To make it we combine the TOPSIS and The Grey Relational Analysis (GRA) under fuzzy soft sets. We finally give an illustrative application for drug selection.

**Category:** General Mathematics

[2186] **viXra:1706.0184 [pdf]**
*submitted on 2017-06-11 11:16:34*

**Authors:** Xi Chen, Jing Li, Yunfei Zhang, Liangliang Tao, Wei Shen

**Comments:** 4 Pages.

This paper proposes a framework of change detection with multi-source remote sensing images through collaboration of multiple operators. Firstly, pre-processed images are distributed to different operators. Then the images are classified by the operators independently. Finally, with uploaded classification results, change detection result can be derived through evidential fusion based on PCR5 rule in the server. By making use of complementary and redundant information in the images, the framework can solve the problems of information loss, imprecision, inconformity or conflict in multi-source data.

**Category:** General Mathematics

[2185] **viXra:1706.0183 [pdf]**
*submitted on 2017-06-11 11:17:57*

**Authors:** Jun Ye

**Comments:** 11 Pages.

Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties.

**Category:** General Mathematics

[2184] **viXra:1706.0181 [pdf]**
*submitted on 2017-06-11 11:21:03*

**Authors:** Zhiquan Liu, Jianfeng Ma, Zhongyuan Jiang, Yinbin Miao

**Comments:** 22 Pages.

In the mobile distributed environment, an entity may move across domains with great frequency. How to utilize the trust information in the previous domains and quickly establish trust relationships with others in the current domain remains a challenging issue. The classic trust models do not support cross-domain and the existing cross-domain trust models are not in a fully distributed way. This paper improves the outstanding Certified Reputation (CR) model and proposes a Lightweight Cross-domain Trust (LCT) model for the mobile distributed environment in a fully distributed way.

**Category:** General Mathematics

[2183] **viXra:1706.0180 [pdf]**
*submitted on 2017-06-11 11:22:58*

**Authors:** Shengqun CHEN, Yingming WANG, Hailiu SHI, Meijing ZHANG, Yang LIN

**Comments:** 39 Pages.

In the evidential reasoning approach of decision theory, different evidence weights can generate different combined results. Consequently, evidence weights can significantly influence solutions. In terms of the “psychology of economic man,” decision-makers may tend to seek similar pieces of evidence to support their own evidence and thereby form alliances.

**Category:** General Mathematics

[2182] **viXra:1706.0179 [pdf]**
*submitted on 2017-06-11 11:25:17*

**Authors:** WenBo Zhu, Huicheng Yang, Yi Jin, andBingyou Liu

**Comments:** 10 Pages.

This study proposes a method based on Dempster-Shafer theory (DST) and fuzzy neural network (FNN) to improve the reliability of recognizing fatigue driving.

**Category:** General Mathematics

[2181] **viXra:1706.0174 [pdf]**
*submitted on 2017-06-11 11:34:03*

**Authors:** Juan-juan Peng, Jian-qiang Wang, Wu-E.Yang

**Comments:** 11 Pages.

In this paper, multi-criteria decision-making (MCDM) problems based on the qualitative flexible multiple criteria method (QUALIFLEX), in which the criteria values are expressed by multi-valued neutrosophic information, are investigated. First,multi-valued neutrosophic sets(MVNSs),which allow the truth-membership function,indeterminacy-membership function and falsity-membership function to have a set of crisp values between zeroand one, are introduced.

**Category:** General Mathematics

[2180] **viXra:1706.0172 [pdf]**
*submitted on 2017-06-11 11:36:53*

**Authors:** Dayong Ye, Qiang He, Yanchun Wang, Yun Yang

**Comments:** 13 Pages.

Service composition is an important research problem in service computing systems, which combines simple and individual services into composite services to fulﬁll users’ complex requirements. Service composition usually consists of four stages, i.e., service discovery, candidate selection, service negotiation and task execution. In self-organising systems, there is the ﬁfth stage of service composition: self-evolution.

**Category:** General Mathematics

[2179] **viXra:1706.0158 [pdf]**
*submitted on 2017-06-11 12:25:59*

**Authors:** Eser Sert

**Comments:** 17 Pages.

Segmentation is paramount to 3D video systems
employing multi-view video-plus-depth data (MVD) to implement free-viewpoint navigation
and comfortable 3D viewing, modeling, and
comprehension.

**Category:** General Mathematics

[2178] **viXra:1706.0155 [pdf]**
*submitted on 2017-06-11 12:31:29*

**Authors:** Rui Hu, Mengjin Wei, Hongchun Sun

**Comments:** 7 Pages.

In this paper, a new simplified neutrosophic weighted average operator is presented, which is named as the simplified Neutrosophic Weighted Maclaurin Mean (NWMM). At the same time, the aggregated formula of NWMM is also established and showed in detail, and some properties of NWMM are researched. Finally, a practical application in E-commerce of the developed method is given.

**Category:** General Mathematics

[2177] **viXra:1706.0152 [pdf]**
*submitted on 2017-06-11 12:35:24*

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

**Comments:** 12 Pages.

In this paper, an extension Elimination and Choice Translating Reality (ELECTRE) method is introduced to handle multi-valued neutrosophic multi-criteria decision-making (MCDM) problems.

**Category:** General Mathematics

[2176] **viXra:1706.0149 [pdf]**
*submitted on 2017-06-11 12:40:02*

**Authors:** Nancy, Harish Garg

**Comments:** 9 Pages.

The neutrosophic set (NS) is a more general platform which generalizes the concept of crisp, fuzzy, and intuitionistic fuzzy sets to describe the membership functions in terms of truth, indeterminacy, and false degree. Under this environment, the present paper proposes an improved score function for ranking the single as well as interval-valued NSs by incorporating the idea of hesitation degree between the truth and false degrees. Shortcomings of the existing function have been highlighted in it. Further, the decision-making method has been presented based on proposed function and illustrates it with a numerical example to demonstrate its practicality and effectiveness.

**Category:** General Mathematics

[2175] **viXra:1706.0147 [pdf]**
*submitted on 2017-06-11 12:45:31*

**Authors:** Chao Zhang, Deyu Li, Yimin Mu, Dong Song

**Comments:** 12 Pages.

In the ﬁeld of mechanical engineering, steam
turbine fault diagnosis is a diﬃcult task
for mechanical engineers who are confronted
with challenges in dealing with copious amounts
of uncertain information.

**Category:** General Mathematics

[2174] **viXra:1706.0146 [pdf]**
*submitted on 2017-06-11 12:46:33*

**Authors:** Y. Veereswari

**Comments:** 6 Pages.

In this paper we introduce fuzzy neutrosophic topological spaces and its some properties. Also we provide fuzzy continuous and fuzzy compactness of fuzzy neutrosophic topological space and its some properties and examples.

**Category:** General Mathematics

[2173] **viXra:1706.0090 [pdf]**
*submitted on 2017-06-06 00:33:27*

**Authors:** Temotope Gbolahan Jayeola

**Comments:** 9 Pages.

By studying the holomorphic structure of automorphic inverse property quasigroups
and loops[AIPQ and (AIPL)] and cross inverse property quasigroups and loops[CIPQ and (CIPL)], it is established that the holomorph of a loop is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop if and only if its Smarandache automorphism group is trivial and the loop is itself is a Smarandache; AIPL, CIPL, K-loop, Bruck-loop or Kikkawa-loop.

**Category:** General Mathematics

[2172] **viXra:1706.0089 [pdf]**
*submitted on 2017-06-06 00:34:47*

**Authors:** Temotope Gbolahan Jayeola

**Comments:** 10 Pages.

The isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal
have been found to be isotopic invariant relative to a special type of isotopism or the
other. Presently, there are two outstanding open problems on universality of loops: semi automorphic inverse property loops(1999) and Osborn loops(2005). Smarandache isotopism(S-isotopism) was originally introduced by Vasantha Kandasamy in 2002.

**Category:** General Mathematics

[2171] **viXra:1706.0080 [pdf]**
*submitted on 2017-06-06 00:47:27*

**Authors:** Hee Sik Kim, J Neggers, Keum Sook So

**Comments:** 10 Pages.

In this paper, we introduce the notion of generalized Fibonacci sequences over a groupoid and discuss it in particular for the case where the groupoid contains idempotents and pre-idempotents. Using the notion of Smarandache-type P-algebra, we obtain several relations on groupoids which are derived from generalized
Fibonacci sequences.

**Category:** General Mathematics

[2170] **viXra:1706.0078 [pdf]**
*submitted on 2017-06-06 00:49:39*

**Authors:** Linfan Mao

**Comments:** 35 Pages.

The universality of contradiction and connection of things in nature implies that a thing is nothing else but a labeled topological graph GL with a labeling map L.

**Category:** General Mathematics

[2169] **viXra:1706.0075 [pdf]**
*submitted on 2017-06-06 00:53:01*

**Authors:** Leo G. Sapogin, V. A. Dzhanibekov, Yu. A. Ryabov

**Comments:** 65 Pages.

The present article discuses the problems of new Unitary Quantum Theory in its applications to the different aspects of the reality. There are
spectacular examples of such applications. The Modern science cannot explain origin of life's.

**Category:** General Mathematics

[2168] **viXra:1706.0067 [pdf]**
*submitted on 2017-06-06 01:02:44*

**Authors:** Ogaba Philip Obande

**Comments:** 9 Pages.

Light is investigated with simple harmonic motion formalism; the procedure reveals the photon’s physicalcharacteristics but fails to provide its exact identity.

**Category:** General Mathematics

[2167] **viXra:1706.0066 [pdf]**
*submitted on 2017-06-06 01:04:16*

**Authors:** Zhengang Wu, Jianghua Li, Han Zhang

**Comments:** 8 Pages.

The main purpose of this paper is, using the elementary method and the properties of the third-order linear recurrence sequence, to unify the above results by proving the following theorem.

**Category:** General Mathematics

[2166] **viXra:1706.0065 [pdf]**
*submitted on 2017-06-06 01:06:41*

**Authors:** Temotope Gbolahan Jayeola

**Comments:** 15 Pages.

A Smarandache quasigroup(loop) is shown to be universal if all its f; g-principal isotopes are Smarandache f; g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f; g-principal isotopes are Smarandache f; g-principal isotopes.

**Category:** General Mathematics

[2165] **viXra:1706.0062 [pdf]**
*submitted on 2017-06-06 01:10:09*

**Authors:** Leo G. Sapogin, Dzhanibekov V A, Yu. A. Ryabov

**Comments:** 29 Pages.

The present article discuses the problems of new Unitary Quantum Theory in its applications to the different aspects of the reality. There are spectacular examples of such applications. The Modern science cannot explain origin of life's.

**Category:** General Mathematics

[2164] **viXra:1706.0061 [pdf]**
*submitted on 2017-06-06 01:11:10*

**Authors:** Edjard de S. Mota, Yan B. Diniz

**Comments:** 11 Pages.

This paper presents a new neural-symbolic reasoning approach based on a sharing of neural multi-space representation for coded fractions of first-order logic. A multi-space is the union of spaces with different dimensions, each one for a different set of distinct features.

**Category:** General Mathematics

[2163] **viXra:1706.0056 [pdf]**
*submitted on 2017-06-06 01:23:26*

**Authors:** Temotope Gbolahan Jayeola

**Comments:** 14 Pages.

The study of the Smarandache concept in groupoids was initiated by W. B. Vasantha Kandasamy. In her book and first paper on Smarandache concept in loops,she defined a Smarandache loop(S-loop) as a loop with at least a subloop which forms a
subgroup under the binary operation of the loop.

**Category:** General Mathematics

[2162] **viXra:1706.0049 [pdf]**
*submitted on 2017-06-06 01:32:12*

**Authors:** Sayak Chakrabarty

**Comments:** 8 Pages.

We found this problem in a paper by Florentin Smarandache. This is the 18th unsolved problem in his paper.

**Category:** General Mathematics

[2161] **viXra:1706.0047 [pdf]**
*submitted on 2017-06-06 01:34:57*

**Authors:** Murat SAVAS, Atakan Tugkan YAKUT, Tugba TAMIRCI

**Comments:** 9 Pages.

In this study, we give special Smarandache curves according to the Sabban frame in hyperbolic space and new Smarandache partners in de Sitter space. The existence of duality between Smarandache curves in hyperbolic and de Sitter space is obtained. We also describe how we can depict picture of Smarandache partners in de Sitter space of a curve in hyperbolic space. Finally, two examples are given to illustrate our main results.

**Category:** General Mathematics

[2160] **viXra:1705.0448 [pdf]**
*submitted on 2017-05-29 08:31:20*

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

**Comments:** 7 Pages.

In this study, we propose an approach to determine the shortest path length between a pair of specified nodes s and t on a network whose edge weights are represented by trapezoidal neutrosophic numbers. Finally, an illustrative example is provided to show the applicability and effectiveness of the proposed approach.

**Category:** General Mathematics

[2159] **viXra:1705.0446 [pdf]**
*submitted on 2017-05-29 08:33:21*

**Authors:** Florentin Smarandache

**Comments:** 17 Pages.

This paper introduces two new fusion rules for combining quantitative basic belief assignments.
These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

**Category:** General Mathematics

[2158] **viXra:1705.0437 [pdf]**
*submitted on 2017-05-29 08:48:19*

**Authors:** Akbar Rezaei, Arsham Borumand Saeid, Florentin Smarandache

**Comments:** 15 Pages.

In this paper, we introduce the notion of (implicative) neutrosophic filters in BE-algebras. The relation between implicative neutrosophic filters and neutrosophic filters is investigated and we show that in self distributive BEalgebras
these notions are equivalent.

**Category:** General Mathematics

[2157] **viXra:1705.0434 [pdf]**
*submitted on 2017-05-29 08:53:23*

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

**Comments:** 6 Pages.

In this work, a neutrosophic network method is
proposed for finding the shortest path length with single valued trapezoidal neutrosophic number. The proposed algorithm gives the shortest path length using score function from source node to destination node. Here the weights of the edges are considered to be single valued trapezoidal neutrosophic number. Finally, a numerical example is used to illustrate the efficiency of the proposed approach.

**Category:** General Mathematics

[2156] **viXra:1705.0432 [pdf]**
*submitted on 2017-05-29 08:56:53*

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

**Comments:** 8 Pages.

In this paper, we first define the concept of bipolar single neutrosophic graphs as the
generalization of bipolar fuzzy graphs, N-graphs, intuitionistic fuzzy graph, single valued
neutrosophic graphs and bipolar intuitionistic fuzzy graphs.

**Category:** General Mathematics

[2155] **viXra:1705.0431 [pdf]**
*submitted on 2017-05-29 08:57:42*

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

**Comments:** 6 Pages.

In this paper, the authors propose an extended
version of Dijkstra’ algorithm for finding the shortest path on a network where the edge weights are characterized by an interval valued neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.

**Category:** General Mathematics

[2154] **viXra:1705.0430 [pdf]**
*submitted on 2017-05-29 08:58:40*

**Authors:** Ilanthenral Kandasamy, Florentin Smarandache

**Comments:** 8 Pages.

Personality tests are most commonly objective type, where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A
person may not be in general capable to judge his/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved.

**Category:** General Mathematics

[2153] **viXra:1705.0428 [pdf]**
*submitted on 2017-05-29 09:00:23*

**Authors:** Florentin Smarandache

**Comments:** 10 Pages.

During the process of adaptation of a being (plant, animal, or human), to a new
environment or conditions, the being partially evolves, partially devolves (degenerates),
and partially is indeterminate {i.e. neither evolving nor devolving, therefore unchanged
(neutral), or the change is unclear, ambiguous, vague}, as in neutrosophic logic. Thank to
adaptation, one therefore has: evolution, involution, and indeterminacy (or neutrality),
each one of these three neutrosophic components in some degree.

**Category:** General Mathematics

[2152] **viXra:1705.0426 [pdf]**
*submitted on 2017-05-29 09:02:36*

**Authors:** Dragisa STANUJKIC, Edmundas Kazimieras ZAVADSKAS, Florentin SMARANDACHE, Willem K.M. BRAUERS, Darjan KARABASEVIC

**Comments:** 12 Pages.

The aim of this manuscript is to propose a new extension of theMULTIMOORA method adapted for usage with a neutrosophic set. By using single valued neutrosophic sets, the MULTIMOORA method can be more efficient for solving complex problems whose solving requires assessment and prediction, i.e. those problems associated with inaccurate and unreliable data. The suitability of the proposed approach is presented through an example.

**Category:** General Mathematics

[2151] **viXra:1705.0425 [pdf]**
*submitted on 2017-05-29 09:04:39*

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

**Comments:** 6 Pages.

Smarandache presented neutrosophic theory as a tool for handling undetermined information, and together with Wang et al. introduced single valued neutrosophic sets that is a special neutrosophic set 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. Neutrosophic sets characterized by three independent parameters, namely truth-membership degree (T), indeterminacy-membership degree (I) and falsity-membership degree (F), which is more capable to handle imprecise parameters. We also transform the neutrosophic linear programming problem into a crisp programming model by using neutrosophic set parameters. To measure the efficiency of our proposed model we solved several numerical examples.

**Category:** General Mathematics

[2150] **viXra:1705.0423 [pdf]**
*submitted on 2017-05-29 09:11:42*

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

**Comments:** 19 Pages.

In this article, we combine the concept of bipolar neutrosophic set and graph theory. We introduce the notions of bipolar single valued neutrosophic graphs, strong bipolar single valued neutrosophic graphs, complete bipolar single valued neutrosophic graphs, regular bipolar single valued neutrosophic graphs and investigate some of their related properties.

**Category:** General Mathematics

[2149] **viXra:1705.0420 [pdf]**
*submitted on 2017-05-29 09:15:33*

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

**Comments:** 16 Pages.

The notion of single valued neutrosophic sets is a generalization of fuzzy sets, intuitionistic fuzzy sets. We apply the concept of single valued neutrosophic sets, an instance of neutrosophic sets, to graphs. We introduce certain types of single valued neutrosophic graphs (SVNG) and investigate some of their properties with proofs and examples.

**Category:** General Mathematics

[2148] **viXra:1705.0418 [pdf]**
*submitted on 2017-05-29 09:17:27*

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

**Comments:** 8 Pages.

In this article, we extend the neutrosophic
graph-based multicriteria decision making method (NGMCDM) introduced by Sahin [49] for the case of interval valued neutrosophic graph theory. We also give an algorithm to solve decision making problems by using interval valued neutrosophic graphs. Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing methods, to verify the feasibility and effectiveness of the
developed approach.

**Category:** General Mathematics

[2147] **viXra:1705.0414 [pdf]**
*submitted on 2017-05-29 09:22:13*

**Authors:** Kenta Takay, Toshinori Asai, Valeri Kroumov, Florentin Smarandache

**Comments:** 6 Pages.

In the process of development a control strategy for mobile robots, simulation is important for testing the software components, robot behavior and control algorithms in different surrounding environments. In this paper we introduce a simulation environment for mobile robots based on ROS and Gazebo.
We show that after properly creating the robot models under Gazebo, the code developed for the simulation process can be directly implemented in the real robot without modifications.
In this paper autonomous navigation tasks and 3D-mapping simulation using control programs under ROS are presented. Both the simulation and experimental results agree very well
and show the usability of the developed environment.

**Category:** General Mathematics

[2146] **viXra:1705.0411 [pdf]**
*submitted on 2017-05-29 09:25:08*

**Authors:** Victor Christianto, Florentin Smarandache, Yunita Umniyati

**Comments:** 12 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 abundant. However, such an acoustic model of cosmology is rarely developed fully into a complete framework from the notion of space up to the sky.

**Category:** General Mathematics

[2145] **viXra:1705.0088 [pdf]**
*submitted on 2017-05-04 00:59:50*

**Authors:** Memet Sahin, Necati Olgun, Vakkas Uluçay, Abdullah Kargın, Florentin Smarandache

**Comments:** 18 Pages.

In this paper, we propose some transformations based on the centroid points between single valued neutrosophic numbers. We introduce these transformations according to truth, indeterminacy and falsity value of single valued neutrosophic numbers. We propose a new similarity measure based on falsity value between single valued neutrosophic sets.

**Category:** General Mathematics

[2144] **viXra:1705.0086 [pdf]**
*submitted on 2017-05-04 01:02:46*

**Authors:** Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri, Florentin Smarandache

**Comments:** 10 Pages.

Bipolar neutrosophic sets are the extension of neutrosophic sets and are based on the idea of positive and negative preferences of information. Projection measure is a useful apparatus for modelling real life decision making problems. In the paper, we define projection, bidirectional projection and hybrid projection measures between bipolar neutrosophic sets.

**Category:** General Mathematics

[2143] **viXra:1705.0084 [pdf]**
*submitted on 2017-05-04 01:05:13*

**Authors:** Durga Banerjee, Bibhas C. Giri, Surapati Pramanik, Florentin Smarandache

**Comments:** 10 Pages.

In this paper, multi attribute decision making problem based on grey relational analysis in neutrosophic cubic set environment is investigated. In the decision making situation, the attribute weights are considered as single valued neutrosophic sets. The neutrosophic weights are converted into crisp weights. Both positve and negative GRA coefficients, and weighted GRA coefficients are determined.

**Category:** General Mathematics

[2142] **viXra:1705.0083 [pdf]**
*submitted on 2017-05-04 01:06:12*

**Authors:** Florentin Smarandache

**Comments:** 6 Pages.

During the process of adaptation of a being (plant, animal, or human), to a new environment or conditions, the being partially evolves, partially devolves (degenerates), and partially is indeterminate i.e. neither evolving nor devolving, therefore unchanged (neutral), or the change is unclear, ambiguous, vague, as in neutrosophic logic.

**Category:** General Mathematics

[2141] **viXra:1705.0082 [pdf]**
*submitted on 2017-05-04 01:07:43*

**Authors:** Muhammad Aslam Malik, Ali Hassan, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 24 Pages.

In this paper, we introduce the homomorphism, the weak isomorphism, the co-weak isomorphism, and the isomorphism of the bipolar single valued neutrosophic hypergraphs. The properties of order, size and degree of vertices are discussed. The equivalence relation of the isomorphism of the bipolar single valued neutrosophic hypergraphs and the weak isomorphism of bipolar single valued neutrosophic hypergraphs, together with their partial order relation, is also verified.

**Category:** General Mathematics

[2140] **viXra:1705.0081 [pdf]**
*submitted on 2017-05-04 01:08:50*

**Authors:** Muhammad Aslam Malik, Ali Hassan, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 26 Pages.

In this paper, we introduce the homomorphism, weak isomorphism, co-weak isomorphism and isomorphism of interval valued neutrosophic hypergraphs. The properties of order, size and degree of vertices, along with isomorphism, are included. The isomorphism of interval valued neutrosophic hypergraphs equivalence relation and weak isomorphism of interval valued neutrosophic hypergraphs partial order relation are also verified.

**Category:** General Mathematics

[2139] **viXra:1705.0080 [pdf]**
*submitted on 2017-05-04 01:10:24*

**Authors:** Muhammad Aslam Malik, Ali Hassan, Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 22 Pages.

In this paper, we introduce the homomorphism, weak isomorphism, co-weak isomorphism, and isomorphism of single valued neutrosophic hypergraphs. The properties of order, size and degree of vertices, along with isomorphism, are included. The isomorphism of single valued neutrosophic hypergraphs equivalence relation and of weak isomorphism of single valued neutrosophic hypergraphs partial order relation is also verified.

**Category:** General Mathematics

[2138] **viXra:1705.0079 [pdf]**
*submitted on 2017-05-04 01:11:52*

**Authors:** W.B. Vasantha Kandasamy, K. Ilanthenral, Florentin Smarandache

**Comments:** 3 Pages.

The Collatz conjecture was proposed by Lothar Collatz in 1937. Till date this conjecture remains open.

**Category:** General Mathematics

[2137] **viXra:1705.0078 [pdf]**
*submitted on 2017-05-04 01:13:10*

**Authors:** Kalyan Mondal, Surapati Pramanik, Florentin Smarandache

**Comments:** 15 Pages.

The purpose of this study is to propose new similarity measures namely rough variational coefficient similarity measure under the rough neutrosophic environment. The weighted rough variational coefficient similarity measure has been also defined.

**Category:** General Mathematics

[2136] **viXra:1705.0077 [pdf]**
*submitted on 2017-05-04 01:14:19*

**Authors:** Dragisa Stanujkic, Florentin Smarandache, Edmundas Kazimieras Zavadskas, Darjan Karabasevic

**Comments:** 4 Pages.

Gathering the attitudes of the examined respondents would be very significant in some evaluation models. Therefore, a multiple criteria approach based on the use of the neutrosophic set is considered in this paper.

**Category:** General Mathematics

[2135] **viXra:1705.0076 [pdf]**
*submitted on 2017-05-04 01:15:33*

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

**Comments:** 5 Pages.

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

**Category:** General Mathematics

[2134] **viXra:1705.0072 [pdf]**
*submitted on 2017-05-04 01:21:37*

**Authors:** Ali Hassan, Muhammad Aslam Malik, Florentin Smarandache

**Comments:** 14 Pages.

In this paper, we define the regular and the totally regular interval valued neutrosophic hypergraphs, and discuss the order and size along with properties of the regular and the totally regular single valued neutrosophic hypergraphs. We extend work to completeness of interval valued neutrosophic hypergraphs.

**Category:** General Mathematics

[2133] **viXra:1705.0071 [pdf]**
*submitted on 2017-05-04 01:23:01*

**Authors:** Muhammad Aslam Malik, Ali Hassan, Said Broumi, F. Smarandache

**Comments:** 6 Pages.

In this paper, we define the regular and totally regular bipolar single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular bipolar single valued neutrosophic hypergraphs. We extend work on completeness of bipolar single valued neutrosophic hypergraphs.

**Category:** General Mathematics

[2132] **viXra:1705.0070 [pdf]**
*submitted on 2017-05-04 01:24:41*

**Authors:** Muhammad Aslam Malik, Ali Hassan, Said Broumi, Florentin Smarandache

**Comments:** 6 Pages.

In this paper, we define the regular and totally regular single valued neutrosophic hypergraphs, and discuss the order and size along with properties of regular and totally regular single valued neutrosophic hypergraphs. We also extend work on completeness of single valued neutrosophic hypergraphs.

**Category:** General Mathematics

[2131] **viXra:1705.0069 [pdf]**
*submitted on 2017-05-04 01:25:54*

**Authors:** Kalyan Mondal, Surapati Pramanik, Florentin Smarandache

**Comments:** 16 Pages.

This paper presents multi-attribute decision making based on rough neutrosophic hyper-complex sets with rough neutrosophic hyper-complex attribute values. The concept of neutrosophic hyper-complex set is a powerful mathematical tool to deal with incomplete, indeterminate and inconsistent information. We extend the concept of neutrosophic hyper-complex set to rough neutrosophic hyper-complex environ-ment. The ratings of all alternatives are expressed in terms of the upper / lower approximations and pairs of neutrosophic hyper-complex sets, which are characterized by two hyper-complex functions and an indeterminacy component.

**Category:** General Mathematics

[2130] **viXra:1705.0068 [pdf]**
*submitted on 2017-05-04 01:27:01*

**Authors:** Kalyan Mondal, Surapati Pramanik, Florentin Smarandache

**Comments:** 13 Pages.

This paper is devoted to present Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method for multi-attribute group decision making under rough neutrosophic environment. The concept of rough neutrosophic set is a powerful mathematical tool to deal with uncertainty, indeterminacy and inconsistency.

**Category:** General Mathematics

[2129] **viXra:1705.0062 [pdf]**
*submitted on 2017-05-04 01:33:21*

**Authors:** Florentin Smarandache

**Comments:** 8 Pages.

In this paper, we define the subtraction and the division of neutrosophic single-valued numbers. The restrictions for these operations are presented for neutrosophic singlevalued numbers and neutrosophic single-valued overnumbers / undernumbers / offnumbers. Afterwards, several numeral examples are presented.

**Category:** General Mathematics

[2128] **viXra:1705.0059 [pdf]**
*submitted on 2017-05-04 01:43:17*

**Authors:** Mona Gamal Gafar, Ibrahim El-Henawy

**Comments:** 10 Pages.

Uncertainty and indeterminacy are two major problems in data analysis these days. Neutrosophy is a generalization of the fuzzy theory. Neutrosophic system is based on indeterminism and falsity of concepts in addition to truth degrees.

**Category:** General Mathematics

[2127] **viXra:1705.0058 [pdf]**
*submitted on 2017-05-04 01:44:57*

**Authors:** Rajashi Chatterjee, Pinaki Majumdar, Syamal Kumar Samanta

**Comments:** 9 Pages.

The theory of quadripartitioned single valued neutrosophic sets was proposed very recently as an extension to the existing theory of single valued neutrosophic sets.

**Category:** General Mathematics

[2126] **viXra:1705.0057 [pdf]**
*submitted on 2017-05-04 01:46:22*

**Authors:** Tuhin Bera, Nirmal Kumar Mahapatra

**Comments:** 10 Pages.

The notion of neutrosophic soft group is introduced, together with several related properties. Its structural characteristics are investigated with suitable examples.

**Category:** General Mathematics

[2125] **viXra:1705.0056 [pdf]**
*submitted on 2017-05-04 01:48:04*

**Authors:** Nasir Shah, Said Broumi

**Comments:** 9 Pages.

The concepts of neighbourly irregular neutrosophic graphs, neighbourly totally irregular neutrosophic graphs, highly irregular neutrosophic graphs and highly totally irregular neutrosophic graphs are introduced. A criteria for neighbourly irregular and highly irregular neutrosophic graphs to be equivalent is discussed.

**Category:** General Mathematics

[2124] **viXra:1705.0055 [pdf]**
*submitted on 2017-05-04 01:50:31*

**Authors:** Pablo José Menéndez Vera, Cristhian Fabián Menéndez Delgado, Miriam Peña Gónzalez, Maikel Leyva Vázquez

**Comments:** 9 Pages.

In Ecuador, specifically in the Yaguachi Canton, there is an enormous potential in the rice production, which unfortunately is not being well used and driven by marketing strategies. In this work, marketing strategies were developed that help to sustain the commercial activity of rice in Yaguachi Canton and its surroundings.

**Category:** General Mathematics

[2123] **viXra:1705.0054 [pdf]**
*submitted on 2017-05-04 01:51:47*

**Authors:** Tanushree Mitra Basu, Shyamal Kumar Mondal

**Comments:** 11 Pages.

In this paper, we have introduced a new concept of multi-dimensional neutrosophic soft sets together with various operations, properties and theorems on them.

**Category:** General Mathematics

[2122] **viXra:1705.0053 [pdf]**
*submitted on 2017-05-04 01:53:03*

**Authors:** Mridula Sarkar, Samir Dey, Tapan Kumar Roy

**Comments:** 10 Pages.

This paper develops a multi-objective Neutrosophic Goal Optimization (NSGO) technique for optimizing the design of three bar truss structure with multiple objectives subject to a specified set of constraints. In this optimum design formulation, the objective functions are weight and deflection; the design variables are the cross-sections of the bar; the constraints are the stress in member.

**Category:** General Mathematics

[2121] **viXra:1705.0052 [pdf]**
*submitted on 2017-05-04 01:54:28*

**Authors:** Wadei Al-Omeri

**Comments:** 9 Pages.

In this paper, the structure of some classes of neutrosophic crisp nearly open sets are investigated via topology, and some applications are given. Finally, we generalize the crisp topological and neutrosophic crisp studies to the notion of neutrosophic crisp set.

**Category:** General Mathematics

[2120] **viXra:1705.0051 [pdf]**
*submitted on 2017-05-04 02:05:20*

**Authors:** Rakib Iqbal, Sohail Zafar, Muhammad Shoaib Sardar

**Comments:** 14 Pages.

The objective of this paper is to introduced the concept of neutrosophic cubic set to subalgebras, ideals and closed ideals of B-algebra. Links among neutrosophic cubic subalgebra with neutrosophic cubic ideals and neutrosophic closed ideals of B-algebras as well as some related properties will be investigated.

**Category:** General Mathematics

[2119] **viXra:1705.0049 [pdf]**
*submitted on 2017-05-04 02:07:35*

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

**Comments:** 9 Pages.

Most of the real world problems in the fields of philosophy, physics, statistics, finance, robotics, design theory, coding theory, knot theory, engineering, and information science contain subtle uncertainty and inconsistent, which causes complexity and difficulty in solving these problems.

**Category:** General Mathematics

[2118] **viXra:1705.0048 [pdf]**
*submitted on 2017-05-04 02:09:32*

**Authors:** Serkan Karatas, Cemil Kuru

**Comments:** 6 Pages.

In this paper, we redefine the neutrosophic set operations and, by using them, we introduce neutrosophic topology and investigate some related properties such as neutrosophic closure, neutrosophic interior, neutrosophic exterior, neutrosophic boundary and neutrosophic subspace.

**Category:** General Mathematics

[2117] **viXra:1705.0047 [pdf]**
*submitted on 2017-05-04 02:10:33*

**Authors:** Harish Garg, Nancy

**Comments:** 8 Pages.

Entropy is one of the measures which is used for measuring the fuzziness of the set. In this article, we have presented an entropy measure of order α under the single-valued neutrosophic set environment by considering the pair of their membership functions as well as the hesitation degree between them

**Category:** General Mathematics

[2116] **viXra:1705.0046 [pdf]**
*submitted on 2017-05-04 02:11:38*

**Authors:** Wenzhong Jiang, Jun Ye

**Comments:** 5 Pages.

This paper defines basic operations of neutrosophic numbers and neutrosophic number functions for objective functions and constraints in optimization models. Then, we propose a general neutrosophic number optimization model for the optimal design of truss structures.

**Category:** General Mathematics

[2115] **viXra:1705.0045 [pdf]**
*submitted on 2017-05-04 02:13:04*

**Authors:** Naga Raju I, Rajeswara Reddy P, Diwakar Reddy V, Krishnaiah G.

**Comments:** 9 Pages.

In real life scientific and engineering problems decision making is common practice. Decision making include single decision maker or group of decision makers. Decision maker’s expressions consists imprecise, inconsistent and indeterminate information.

**Category:** General Mathematics

[2114] **viXra:1705.0044 [pdf]**
*submitted on 2017-05-04 02:14:35*

**Authors:** Pablo José Menéndez Vera, Cristhian Fabián Menéndez Delgado, Susana Paola Carrillo Vera, Milton Villegas Alava, Miriam Peña Gónzales

**Comments:** 4 Pages.

Static analysis is developed in neutrosophic cognitive maps to define the importance of each node based on centrality measures. In this paper a framework static analysis of neutrosophic cognitive maps is presented.

**Category:** General Mathematics

[2113] **viXra:1705.0043 [pdf]**
*submitted on 2017-05-04 02:16:06*

**Authors:** Kul Hur, Pyung Ki Lim, Jeong Gon Lee, Junhui Kim

**Comments:** 9 Pages.

We introduce the category NSet(H) consisting of neutrosophic H-sets and morphisms between them. And we study NSet(H) in the sense of a topological universe and prove that it is Cartesian closed over Set, where Set denotes the category con
sisting of ordinary sets and ordinary mappings between them. Furthermore, we investigate some relationships between two categories ISet(H) and NSet(H).

**Category:** General Mathematics

[2112] **viXra:1705.0042 [pdf]**
*submitted on 2017-05-04 02:17:47*

**Authors:** A.A. Salama, Hewayda, ElGhawalby, Shimaa Fathi Ali

**Comments:** 4 Pages.

In this paper, we introduce and study a neutrosophic crisp manifold as a new topological structure of manifold via neutrosophic crisp set. Therefore, we study some new topological concepts and some metric distances on a neutrosophic crisp manifold.

**Category:** General Mathematics

[2111] **viXra:1705.0041 [pdf]**
*submitted on 2017-05-04 02:19:06*

**Authors:** Sujit Kumar De, Ismat Beg

**Comments:** 14 Pages.

In this study, we introduce the concept of denser property in fuzzy membership function used in neutrosophic sets. We present several new definitions and study their properties.

**Category:** General Mathematics

[2110] **viXra:1705.0040 [pdf]**
*submitted on 2017-05-04 02:20:20*

**Authors:** Mridula Sarkar, Samir Dey, Tapan Kumar Roy

**Comments:** 8 Pages.

In this paper, we develop a neutrosophic optimization (NSO) approach for optimizing the design of plane truss structure with single objective subject to a specified set of constraints. In this optimum design formulation, the objective functions are the weight of the truss and the deflection of loaded joint; the design variables are the crosssections of the truss members; the constraints are the stresses in members.

**Category:** General Mathematics

[2109] **viXra:1705.0032 [pdf]**
*submitted on 2017-05-02 13:21:02*

**Authors:** Omar Abu Arqub; Shaher Momani; Ma'mon Abu Hammad; Ahmed Alsaedi

**Comments:** 13 Pages.

In this article, a residual power series technique for the power series solution of systems of initial value problems is introduced. The new approach provides the solution in the form of a rapidly convergent series with easily computable components using symbolic computation software. The proposed technique obtains Taylor expansion of the solution of a system and reproduces the exact solution when the solution is polynomial. Numerical examples are included to demonstrate the efficiency, accuracy, and applicability of the presented technique. The results reveal that the technique is very effective, straightforward, and simple.

**Category:** General Mathematics

[2108] **viXra:1704.0354 [pdf]**
*submitted on 2017-04-26 11:52:19*

**Authors:** Le Fay Yvann

**Comments:** 4 Pages.

We generalize a simple formula for constructing the multinomial function f which interpolates a set of (d+1) points in IR^N. We also provide an example of application of this method.

**Category:** General Mathematics

[2107] **viXra:1704.0329 [pdf]**
*submitted on 2017-04-25 03:19:00*

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

**Comments:** 14 Pages.

The interval valued neutrosophic graphs are generalizations of the fuzzy graphs,
interval fuzzy graphs, interval valued intuitionstic fuzzy graphs, and single valued
neutrosophic graphs. Previously, several results have been proved on the isolated
graphs and the complete graphs. In this paper, a necessary and sufficient condition
for an interval valued neutrosophic graph to be an isolated interval valued
neutrosophic graph is proved.

**Category:** General Mathematics

[2106] **viXra:1704.0327 [pdf]**
*submitted on 2017-04-25 03:22:04*

**Authors:** Abdel Nasser H. Zaied, Hagar M. Naguib

**Comments:** 9 Pages.

In daily life, decision makers around the world
are seeking for the appropriate decisions while facing many challenges due to conflicting criteria and the presence of many alternatives.

**Category:** General Mathematics

[2105] **viXra:1704.0325 [pdf]**
*submitted on 2017-04-25 03:25:49*

**Authors:** W.b. Vasantha Kandasamy, Ilanthenral Kandasamy, Florentin Smarandache

**Comments:** 6 Pages.

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n 1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried.

**Category:** General Mathematics

[2104] **viXra:1704.0323 [pdf]**
*submitted on 2017-04-25 03:52:27*

**Authors:** Salah Bouzina

**Comments:** 6 Pages.

The goal of this research is first to show how
different, thorough, widespread and effective are the operations logic of the neutrosophic logic compared to the fuzzy logic’s operations logical. The second aim is to observe how a fully new logic, the neutrosophic logic, is
established starting by changing the previous logical perspective fuzzy logic, and by changing that, we mean changing the truth values from the truth and falsity degrees membership in fuzzy logic, to the truth, falsity and indeterminacy degrees membership in neutrosophic logic; and thirdly, to observe that there is no limit to the logical discoveries.

**Category:** General Mathematics

[2103] **viXra:1704.0322 [pdf]**
*submitted on 2017-04-25 03:53:42*

**Authors:** Nguyen Xuan Thao, Bui Cong Cuong, Florentin Smarandache

**Comments:** 11 Pages.

A rough fuzzy set is the result of approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets, standard neutrosophic information system and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.

**Category:** General Mathematics

[2102] **viXra:1704.0321 [pdf]**
*submitted on 2017-04-25 03:55:07*

**Authors:** Tahir Mahmood, Florentin Smarandache, Kifayat Ullah, Qaisar Khan

**Comments:** 8 Pages.

In this article we define some aggregation operators for bipolar-valued hesitant fuzzy sets. These operations include bipolar-valued hesitant fuzzy ordered weighted averaging (BPVHFOWA) operator, bipolar-valued hesitant fuzzy ordered weighted geometric (BPVHFOWG) operator and their generalized forms. We also define hybrid aggregation operators and their generalized forms and solved a decision-making problem on these operation.

**Category:** General Mathematics

[2101] **viXra:1704.0299 [pdf]**
*submitted on 2017-04-22 16:51:50*

**Authors:** Surapati Pramanik, Rumi Roy, Tapan Kumar Roy

**Comments:** 15 Pages.

In this paper, we define projection and bidirectional projection measures between rough neutrosophic sets. Then two new multi criteria decision making methods are proposed based on neutrosophic projection and bidirectional projection measures respectively. Then the proposed methods are applied for solving multiple criteria group decision making problems. Finally, two numerical examples are provided to demonstrate the applicability and effectiveness of the proposed methods.

**Category:** General Mathematics

[2100] **viXra:1704.0292 [pdf]**
*submitted on 2017-04-23 05:21:47*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

In this research investigation, the author has detailed two models of One Step Forecasting

**Category:** General Mathematics

[2099] **viXra:1704.0257 [pdf]**
*submitted on 2017-04-20 08:14:31*

**Authors:** Edgar Valdebenito

**Comments:** 5 Pages.

this note presents some representations for the real root of the equation: x^5+x^4+x-1=0.

**Category:** General Mathematics

[2098] **viXra:1704.0241 [pdf]**
*submitted on 2017-04-19 11:32:41*

**Authors:** Andrej Liptaj

**Comments:** 10 Pages.

Full analogy to the Lagrange form of the interpolation polynomial is constructed for Fourier series. As a straightforward consequence one gets the ability to extend an existing trigonometric interpolation to additional data point(s).

**Category:** General Mathematics

[82] **viXra:1705.0309 [pdf]**
*replaced on 2017-05-23 15:24:32*

**Authors:** Roman Vinokur

**Comments:** 4 Pages. Replaced.

The human factor is very important if the high-level R&D skills are needed (“Intellectuals solve problems, geniuses prevent them.” - Albert Einstein). Many people believe more in the power of teamwork than in “myths” of the lone genius. However, if a project goal can be successfully achieved just by one high-skilled professional, it is not wise to delegate this duty to a group of low-skilled persons (“A great engineer is worth 100 average engineers.” - Facebook CEO Mark Zuckerberg. Generally, the dilemma “ordinary team or single expert” is of frequent interest for R&D organizations.
In this paper, an approximate mathematical approach has been developed to estimate the critical (minimum) size of an ordinary R&D team that can be more successful than a single expert. As a result, this method could help to resolve the “hire or not hire” issue.

**Category:** General Mathematics

[81] **viXra:1704.0354 [pdf]**
*replaced on 2017-04-28 14:41:46*

**Authors:** Yvann Le Fay

**Comments:** 4 Pages.

We generalize a simple formula for constructing the multinomial function f which interpolates a set of (d+1) points in IR^N. We also provide an example of application of this method.

**Category:** General Mathematics