Abstract
The notion of fuzzy sets initiated to overcome the uncertainty of an object. Fuzzy topological space, in- tuitionistic fuzzy sets in topological structure space, vagueness in topological structure space, rough sets in topological space, theory of hesitancy and neutrosophic topological space, etc. are the extension of fuzzy sets. Soft set is a family of parameters which is also a set. Fuzzy soft topological space, intuitionistic fuzzy soft and neutrosophic soft topological space are obtained by incorporating soft sets with various topological structures. This motivates to write a review and study on various soft set concepts. This paper shows the detailed review of soft topological spaces in various sets like fuzzy, Intuitionistic fuzzy set and neutrosophy. Eventually, we compared some of the existing tools in the literature for easy understanding and exhibited their advantages and limitations.
Highlights
In the year 1999, Molodtsov[47] proposed the concept of soft sets (SS)
The first definition of soft spaces was introduced by the authors Shabir and Naz[70] and it is defined on the universe of discourse with a fixed set of parameters
Intuitionistic fuzzy set A(a) on the non-empty set X is defined by A = {(a, μA(a), νA(a)) : a ∈ X}, where μA denotes truth value and νA denote the falsehood and the map of truth value and falsehood from the universal set X to the interval [0, 1] and satisfying the constraint that sum of truth and falsehood value is lies between 0 and 1, for each a ∈ X
Summary
In the year 1999, Molodtsov[47] proposed the concept of soft sets (SS). This concept developed to overcome the difficulty to fix membership for each case. The first definition of soft spaces was introduced by the authors Shabir and Naz[70] and it is defined on the universe of discourse with a fixed set of parameters. They proved that a soft topological space provides a parameterized family of topological spaces. Many complex problems in statistics, in graph theory when relationship between the object have acceptance, rejection and indeterminacy, physics, image processing, networking and in decision making which can’t be solved by existing classical methods The generalisation of this notion exist in the literature, namely neutrosophic soft topology, neutrosophic nano topology, neutrosophic nano ideals topology, neutrosophic support soft set,[56] neutrosophic soft supra topological spaces in various sets, etc. Comparison table of classical soft topological space, FSTS, IFSTS, NSTS are presented
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