The chapter aims to give computational algorithm to solve a multiobjective non-linear programming problem using Neutrosophic geometric programming technique. As the Neutrosophic optimization technique utilizes degrees of truth-membership, falsity-membership and indeterminacy-membership functions, we made a study of correspondence among those membership functions to see its impact on optimizatio...

In this paper, we will define a new class of sets, called fuzzy neutrosophic weakly- generalized closed then proved some theorems related to definition. After that, studied relations between weakly-generalized sets and α regular pre semi sets.

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies. 1. Definition of the Neutrosophic Logic/Set: Let T, I, F be real standard or non-standard subsets of ]0, 1[, with sup T = t_sup, inf T = t_inf, sup I = i_sup, inf...

A simplified neutrosophic set (SNS) is a subclass of neutrosophic set and contains a single-valued neutrosophic set (SVNS) and an interval neutrosophic set (INS). It was proposed as a generalization of an intuitionistic fuzzy set (IFS) and an interval-valued intuitionistic fuzzy set (IVIFS) in order to deal with indeterminate and inconsistent information. The paper proposes another form of the ...

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. Keywords—trapezoidal fuzzy neutrosophic sets; score function; Shortest path pro...

Triple Refined Indeterminate Neutrosophic Set (TRINS) which is a case of the refined neutrosophic set was introduced in [27]. It provides the additional possibility to represent with sensitivity and accuracy the uncertain, imprecise, incomplete, and inconsistent information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) ...

This paper introduces a novel soft computing technique, called the complex neutrosophic soft expert relation (CNSER), to evaluate the degree of interaction between two hybrid models called complex neutrosophic soft expert sets (CNSESs). CNSESs are used to represent two-dimensional data that are imprecise, uncertain, incomplete and indeterminate. Moreover, it has a mechanism to incorporate the p...

In this paper a new branch of philosophy is presented, called neutrosophy, which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. The Fundamental Thesis: Any idea is T% true, I% indeterminate, and F% false, where T, I, F are standard or non-standard subsets included in the non-standard unit interval K 0, 1 M. The Fundame...

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 fuzz...