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Soft set theory is considered as one of the best effective tool which provides parameterization approach to tackle the inadequacy of fuzzy set. So far, it has been applied to different mathematical concepts such as set operations, algebraic structure (e.g., group and ring theory) and topological spaces. Many researchers have studied classical concept of convex and concave set under fuzzy-like, soft-like and fuzzy soft-like environments. In this paper, new notions of (m; n)-convex and (m; n)-concave fuzzy soft sets are developed first and then their versions for first and second senses are established. Further some known classical results and properties are generalized under fuzzy soft set environment. Moreover, special cases of (m; n)-convexity on fuzzy soft sets are established. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Uncertainty is a human instinct that prevails on the mind of a person while making an important decision. Decision making is the most integral part of human life which has a potential to change an entire life of a man. Soft set theory is an important tool which deals with uncertainty and helps to make the appropriate decision. This paper covers the generalization of soft sets including double framed and triple framed soft sets and discusses its extension to N-framed soft sets. By defining significant aggregative operations including union, intersection, not set, complement, relative complement, difference of double framed, triple framed and in general N-framed soft sets and some other laws, this paper provides an imperative insight for studying N-framed soft sets. [ABSTRACT FROM AUTHOR]

The purpose of MCDM is to determine the best option amongst all the probable options. Due to linguistic assessments, the traditional crisp techniques are not good to solve MCDM problems. This paper deals with the generalization of TOPSIS for neutrosophic hypersoft set primarily based issues explained in section 3. In section 4, the proposed technique is implemented. The proposed technique is easy to implement, and precise and sensible for fixing the MCDM problem with multiple-valued neutrosophic data. In the end, the applicability of the developed method, the problem of parking on which decision maker has normally vague and imprecise knowledge is used. It seems that the outcomes of these examinations are terrific. [ABSTRACT FROM AUTHOR]