Abstract
Hypersoft set is a generalization of soft sets, which takes into account a multiargument function. The main objective of this work is to introduce fuzzy semiopen and closed hypersoft sets and study some of their characterizations and also to present neutrosophic semiopen and closed hypersoft sets, an extension of fuzzy hypersoft sets, along with few basic properties. We propose two algorithms based on neutrosophic hypersoft open sets and topology to obtain optimal decisions in MAGDM. The efficiency of the algorithms proposed is demonstrated by applying them to the current COVID-19 scenario.
Highlights
Fuzzy set theory [1] is an important tool for dealing with vagueness and incomplete data and is much more evolving and applied in different fields
Wang et al [4] proposed the concept of single-valued neutrosophic sets, a generalization of intuitionistic sets and a subclass of neutrosophic sets, which comprise elements with three membership functions which they belong to interval [0, 1]
A comparison analysis is performed for this method with two examples [6], and the developed singlevalued neutrosophic TOPSIS extension is demonstrated on a numerical illustration of the evaluation and selection of e-commerce development strategies [7]
Summary
Fuzzy set theory [1] is an important tool for dealing with vagueness and incomplete data and is much more evolving and applied in different fields. Wang et al [4] proposed the concept of single-valued neutrosophic sets, a generalization of intuitionistic sets and a subclass of neutrosophic sets, which comprise elements with three membership functions which they belong to interval [0, 1] Under this neutrosophic environment, many researchers have worked on their extensions and developed many applications and results. Separation axioms, compactness, and connectedness on intuitionistic fuzzy soft topological spaces were defined along with some base theorems [32], some important properties of intuitionistic fuzzy soft topological spaces and intuitionistic fuzzy soft closure and interior of an intuitionistic fuzzy soft set were introduced, and an intuitionistic fuzzy soft continuous mapping with structural characteristics was studied [33]. We define the idea of semiopen sets in fuzzy hypersoft topological spaces with their characterization and extend to semiopen sets in intuitionistic and neutrosophic hypersoft topological spaces.
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