[14] **viXra:1605.0231 [pdf]**
*submitted on 2016-05-22 20:23:04*

**Authors:** Philip Druck

**Comments:** 27 Pages.

A totally ordered set is identified with cardinality strictly between natural (N) and real (R) numbers. This set, denoted DS, is essentially an experimental finding, identified in unrelated patented research on nonuniform data sampling and self-stabilizing computer arithmetic. Its theoretical validation here will provide concrete proof that the Continuum Hypothesis (CH) is false. Note that this is distinct from determining whether CH can or cannot be proven from current axioms of set theory, which is settled. Also note that the Generalized Continuum Hypothesis is not addressed. First, Cantor diagonalization is applied isomorphically to prove that DS has strictly more than Cardinality(N) points. Then three (3) distinct proofs are provided to show that DS contains strictly fewer than Cardinality(R) elements. Each proof relies on a distinct property of primes. It is surmised that the considerable research efforts to-date on CH missed this result due to over-generalization, by considering all Alephi sets, i=0.., ∞. Those efforts thereby missed the impact of primes specifically on Aleph0/Aleph1 sets.

**Category:** Set Theory and Logic

[13] **viXra:1605.0052 [pdf]**
*submitted on 2016-05-04 05:05:38*

**Authors:** J. Martina Jency, I. Arockiarani

**Comments:** 9 Pages.

In this paper, we design a model based on adjustable and mean potentiality approach to single valued neutrosophic level soft sets. Further, we introduce the notion of weighted single valued neutrosophic soft set and investigate its application in decision making.

**Category:** Set Theory and Logic

[12] **viXra:1605.0051 [pdf]**
*submitted on 2016-05-04 05:07:03*

**Authors:** Chunfang Liu, YueSheng Luo

**Comments:** 4 Pages.

Interval-valued neutrosophic set (INS) is a
generalization of fuzzy set (FS) that is designed for some practical situations in which each element has different truth membership function, indeterminacy membership function and falsity membership function and permits the membership degrees to be expressed by interval values.

**Category:** Set Theory and Logic

[11] **viXra:1605.0050 [pdf]**
*submitted on 2016-05-04 05:08:47*

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

**Comments:** 10 Pages.

This paper investigates an extended grey relational analysis method for multiple attribute decision making problems under interval neutrosophic uncertain linguistic environment. Interval neutrosophic uncertain
linguistic variables are hybridization of uncertain linguistic variables and interval neutrosophic sets and they can easily express the imprecise, indeterminate and inconsistent
information which normally exist in real life situations.

**Category:** Set Theory and Logic

[10] **viXra:1605.0049 [pdf]**
*submitted on 2016-05-04 05:09:58*

**Authors:** Florentin Smarandache

**Comments:** 3 Pages.

We have introduced for the first time the
degree of dependence (and consequently the degree of independence) between the components of the fuzzy set, and also between the components of the neutrosophic set in our 2006 book’s fifth edition. Now we extend it for the first time to the refined neutrosophic set considering the degree of dependence or independence of subcomponets.

**Category:** Set Theory and Logic

[9] **viXra:1605.0048 [pdf]**
*submitted on 2016-05-04 05:11:04*

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

**Comments:** 5 Pages.

Many results have been obtained on isolated
graphs and complete graphs. In this paper, a necessary and sufficient condition will be proved for a single valued neutrosophic graph to be an isolated single valued neutrosophic graph.

**Category:** Set Theory and Logic

[8] **viXra:1605.0047 [pdf]**
*submitted on 2016-05-04 05:12:42*

**Authors:** Gaurav, Megha Kumar, Kanika Bhutani, Swati Aggarwal

**Comments:** 12 Pages.

This paper employs a new soft computing based
methodology for identifying and analyzing the relationships among the causes and implications of the two challenging problems in India: unbalanced sex ratio and poverty.

**Category:** Set Theory and Logic

[7] **viXra:1605.0046 [pdf]**
*submitted on 2016-05-04 05:13:56*

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

**Comments:** 5 Pages.

This paper reviews some of the multivalued
logic models which are fuzzy set, intuitionistic
fuzzy set, and suggests a new approach which is neutrosophic set for handling uncertainty in expert systems to derive decisions. The paper highlights, compares and clarifies the differences of these models in terms of the application area of problem solving.

**Category:** Set Theory and Logic

[6] **viXra:1605.0045 [pdf]**
*submitted on 2016-05-04 05:15:14*

**Authors:** Madad Khan, Florentin Smarandache, Sania Afzal

**Comments:** 16 Pages.

In this paper we have defined neutrosophic ideals,
neutrosophic interior ideals, netrosophic quasi-ideals and neutrosophic bi-ideals (neutrosophic generalized bi-ideals) and proved some results related to them.

**Category:** Set Theory and Logic

[5] **viXra:1605.0044 [pdf]**
*submitted on 2016-05-04 05:16:41*

**Authors:** Nasir Shah, Asim Hussain

**Comments:** 14 Pages.

The aim of this paper is to propose a new type of
graph called neutrosophic soft graphs. We have established a link between graphs and neutrosophic soft sets. Basic operations of neutrosophic soft graphs such as union, intersection and complement are defined here. The concept of strong neutrosophic soft graphs is also discussed in this paper.

**Category:** Set Theory and Logic

[4] **viXra:1605.0043 [pdf]**
*submitted on 2016-05-04 05:18:07*

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

**Comments:** 9 Pages.

The present paper proposes neutrosophic soft
multi-attribute decision making based on grey relational projection method. Neutrosophic soft sets is a combination of neutrosophic sets and soft sets and it is a new mathematical apparatus to deal with realistic problems in the fields of medical sciences, economics, engineering, etc.

**Category:** Set Theory and Logic

[3] **viXra:1605.0041 [pdf]**
*submitted on 2016-05-04 05:21:11*

**Authors:** Vasile Patrascu

**Comments:** 10 Pages.

In this article, starting from primary representation of neutrosophic information, namely the triplet (μ, ω, ν) made up of the degree of truth μ, degree of indeterminacy
ω and degree of falsity ν, we define a refined representation in a penta-valued fuzzy space, described by the index of truth t, index of falsity f, index of ignorance u, index of contradiction c and index of hesitation h. In
the proposed penta-valued refined representation the indeterminacy was split into three sub-indeterminacies such as ignorance, contradiction and hesitation.

**Category:** Set Theory and Logic

[2] **viXra:1605.0040 [pdf]**
*submitted on 2016-05-04 05:22:55*

**Authors:** Huda E. Khalid

**Comments:** 5 Pages.

This article sheds light on the possibility of finding the minimum solution set of neutrosophic relational geometric programming with (max, min) composition. This work examines the privacy enjoyed by both neutrosophic logic and geometric programming, and how it affects the minimum solutions. It is the first attempt to solve this type of problems.

**Category:** Set Theory and Logic

[1] **viXra:1605.0020 [pdf]**
*submitted on 2016-05-03 01:19:33*

**Authors:** Florentin Smarandache - Editor-in-Chief

**Comments:** 113 Pages.

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics
that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc.

**Category:** Set Theory and Logic