Development of Hybrids of Hypersoft Set with Complex Fuzzy Set, Complex Intuitionistic Fuzzy set and Complex Neutrosophic Set

Abstract

 The complex fuzzy soft set and its generalized hybrids are such effective structures which not only
minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulfill all the
parametric requirements of soft sets. This feature makes it a completely new mathematical tool for solving
problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set
as it transforms the single attribute function into a multi-attribute function. This generalization demands an
extension of complex fuzzy soft-like structures to hypersoft structure for more precise results. In this study,
hybrids of hypersoft set with complex fuzzy set and its generalized structures i.e. complex intuitionistic fuzzy
set and complex neutrosophic set, are developed along with illustrative examples to address the demand of
literature. Moreover, some of their fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic
operations i.e. compliment, union, intersection etc. are discussed.