Generalized Neutrosophic Set and Generalized Neutrosophic Topological Spaces

Abstract

In this paper we introduce definitions of generalized neutrosophic sets. After given the fundamental defin itions of generalized neutrosophic set operations, we obtain several properties, and discussed the relationship between generalized neutrosophic sets and others. Finally, we extend the concepts of neutrosophic topological space [9], intuition istic fuzzy topological space [5,6], and fu zzy topological space [4] to the case of generalized neutrosophic sets. Possible applicat ion to GIS topology rules are touched upon.

Generalization of Fuzzy C-Means based on Neutrosophic Logic

“…Salama et al in [2] [14][15] [19], provide a foundation for mathematically treating the neutrosophic phenomena which exist pervasively in our real world and for building new branches of neutrosophic mathematics.…”

Neutrosophic Crisp Open Set and Neutrosophic Crisp Continuity via Neutrosophic Crisp Ideals

“…We recollect some relevant basic preliminaries, and in particular, the work of Smarandache in [16,17,18], and Salama et al [4,5,6,7,8,9,10,11,12,13,14,15].…”

“…Smarandache [16,17,18] defined the notion of neutrosophic sets, which is a generalization of Zadeh's fuzzy set and Atanassov's intuitionistic fuzzy set. Neutrosophic sets have been investigated by Salama et al [4,5,6,7,8,9,10,11,12,13,14,15]. In this paper is to introduce and study some new neutrosophic crisp notions via neutrosophic crisp ideals.…”

Generalized Neutrosophic Soft Set

“…One of these theories was the fuzzy set theory discovered by Lotfi, Zadeh in 1965 [1], Later several researches present a number of results using different direction of fuzzy set such as: interval fuzzy set [12], generalized fuzzy set by Atanassov [2]..., all these are successful to some extent in dealing with the problems arising due to the vagueness present in the real world ,but there are also cases where these theories failed to give satisfactory results, possibly due to indeterminate and inconsistent information which exist in belief system, then in 1995, Smarandache [3] initiated the theory of neutrosophic set as new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. Several researchers dealing with the concept of neutrosophic set such as M. Bhowmik and M.Pal in [13], A.A.Salama in [7], and H.Wang in [14]. Furthermore, In 1999, a Russian mathematician (Molodtsov [4]) introduce a new mathematical tool for dealing with uncertainties, called "soft set theory".…”

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In this paper we present a new concept called "generalized neutrosophic soft set". This concept incorporates the beneficial properties of both generalized neutrosophic set introduced by A.A.Salama [7] and soft set techniques proposed by Molodtsov [4]. We also study some properties of this concept.

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