An element x of U is called significant with respect to neutrosophic set A of U if the degree of truth-membership or falsity-membership or indeterminacy-membership value, i.e.,T A(x) or F A(x) or I A(x) = 0.5. Otherwise, we call it insignificant. Also, for neutrosophic set the truth-membership, indeterminacy-membership and falsity-membership all can not be significant. We define an intuitionistic neutrosophic set by A = {< x: T A(x), I A(x), F A(x) >,x ? U},wheremin { T A(x), F A(x) } = 0.5, min { T A(x) , I A(x) } = 0.5, min { F A(x) , I A(x) } = 0.5, for all x ?U, with the condition 0 = T A(x) + I A(x) + F A(x) = 2.
Published in Chapter:
Neutrosophic Soft Sets and Their Properties
Mumtaz Ali (Quaid-i-azam University Islamabad, Pakistan) and
Florentin Smarandache (University of New Mexico, USA)
Copyright: © 2016
|Pages: 28
DOI: 10.4018/978-1-4666-9798-0.ch014
Abstract
Soft set plays an important role in the theory of approximations, as parameterized family of subsets in the universe of discourse. On the other hand, neutrosophic set is based on the neutrosophic philosophy, which states that: Every idea A has an opposite anti(A) and its neutral neut(A). This is the main theme of neutrosophic sets and logics. This chapter is about the hybrid structure called neutrosophic soft set, i.e. a soft set defined over a neutrosophic set. This chapter begins with the introduction of soft sets and neutrosophic sets. The notions of neutrosophic soft sets are defined and their properties studied. Then the algebraic structures associated with neutrosophic soft sets are debated. After that, the mappings on soft classes are studied with some of their properties. Finally, the notion of intuitionistic neutrosophic soft sets is taken into consideration.