Neutrosophic hesitant fuzzy set is the generalization of neutrosophic set and the hesitant fuzzy set, which can easily express the uncertain, incomplete and inconsistent information in cognitive activity, and the VIKOR (from Serbian:VIseKriterijumska Optimizacija I Kompromisno Resenje) method is an effective decision making tool which can select the optimal alternative by the maximum ‘‘group ut...

Single-valued neutrosophic hesitant fuzzy set (SVNHFS) is a combination of single-valued neutrosophic set and hesitant fuzzy set, and its aggregation tools play an important role in the multiple criteria decision-making (MCDM) process. This paper investigates the MCDM problems in which the criteria under SVNHF environment are in different priority levels. First, the generalized single-valued ne...

Molodtsov [35] initiated the soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Maji [30] defined the concept of neutrosophic soft set which is based on a combination of the neutrosophic set and soft set models. In this paper, we give the notion of neutrosophic soft set with a new style and present some algebraic properties. We define several distanc...

This paper introduces the concept of fuzzy neutrosophic equivalence relations and discuss some of their properties. define fuzzy neutrosophic transitive closure and investigate their properties.

In this paper we extend the neutrosophic group and subgroup to soft neutrosophic group and soft neutrosophic subgroup respectively. Properties and theorems related to them are proved and many examples are given.

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) ...

In this paper we introduced mapping on neutrosophic soft expert sets through which we can study the images and inverse images of neutrosophic soft expert sets. Further, we investigatedthe basic operations and other related properties of mapping on neutrosophic soft expert sets in this paper.

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, c...

Recently, F.Smarandache generalized the Atanassov’s intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, this author de…ned the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.

Department of Mathematics and Computer Science, Faculty of Sciences, Port Said University, Egypt * [email protected] **Department of Computer Science, Port Said University, Egypt [email protected] ***Department of Mathematics, University of New Mexico Gallup, NM, USA [email protected] Abstract: In this paper we introduce the notion of ideals on neutrosophic set which is considered as a gen...