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What is Soft Set

Let U be an initial universe set and E be the set of parameters. Let P ( U ) denote the power set of U and let A be a non-empty subset of E . A pair ( F,A ) is called soft set over U , where F is mapping given by F : A ? P ( U ) .
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)
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.
More Results
soft set was introduced by Molodtsov(1999) . Let U is a classical set of elements, the pair (U, E) is called the universe and E be a set of parameters often regarded as a soft universe. Members of the universe and the parameter set are generally denoted by x and e respectively. A soft set over the soft universe (U, E) is denoted by (F, A), where F : A ? P ( U ), where A is a subset of E and P (U) is the power set of U which comprises of all the subsets of U.