[53] **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

[52] **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

[51] **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

[50] **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

[49] **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

[48] **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

[47] **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

[46] **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

[45] **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

[44] **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

[43] **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

[42] **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

[41] **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

[40] **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

[39] **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

[38] **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

[37] **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

[36] **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

[35] **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

[34] **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

[33] **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

[32] **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

[31] **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

[30] **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

[29] **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

[28] **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

[27] **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

[26] **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

[25] **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

[24] **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

[23] **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

[22] **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

[21] **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

[20] **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

[19] **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

[18] **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

[17] **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

[16] **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

[15] **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

[14] **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

[13] **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

[12] **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

[11] **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

[10] **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

[9] **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

[8] **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

[7] **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

[6] **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

[5] **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

[4] **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

[3] **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

[2] **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

[1] **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