Abstract
Hypersoft set theory is an extension of soft set theory and is a new mathematical tool for dealing with fuzzy problems; however, it still suffers from the parametric tools’ inadequacies. In order to boost decision-making accuracy even more, a new mixed mathematical model called the bipolar hypersoft set is created by merging hypersoft sets and bipolarity. It is characterized by two hypersoft sets, one of which provides positive information and the other provides negative information. Moreover, some fundamental properties relative to it such as subset, superset, equal set, complement, difference, relative (absolute) null set and relative (absolute) whole set are defined. Furthermore, some set-theoretic operations such as the extended intersection, the restricted union, intersection, union, AND-operation and OR-operation of two bipolar hypersoft sets with their properties are discussed and supported by examples. Finally, tabular representations for the purposes of storing bipolar hypersoft sets in computer memory are used.
Highlights
A soft set is made up of two parts—a predicate and an approximate value set—and it provides an approximate description of the object under consideration
The OR-operation of two bipolar hypersoft sets (F1, G1, A ) and (F2, G2, B ) over a common universe U is a bipolar hypersoft set (H, I, C ), where C = A × B and the following is the case for all (α, β) ∈ C, α ∈ A, β ∈ B
Hypersoft sets are derived by transforming the approximate function in the structure of a soft set into a multi-attribute approximate function
Summary
A soft set is made up of two parts—a predicate and an approximate value set—and it provides an approximate description of the object under consideration. Properties, operations and a bipolar soft set application in decision-making problems were investigated in [11]. Aslam and Ullah [15] introduced the bipolar fuzzy soft set and studied its applications in the decision-making problem. Karaaslan and Çaǧman [16] pointed out the bipolar soft rough set and studied utilization in decision making. Malik and Shabir [22] successfully applied rough fuzzy bipolar soft sets in decision-making problems. By replacing the function F with a multi-argument function defined on the Cartesian product of n different sets of parameters, Smarandache [35] extended the notion of a soft set to the hypersoft set in 2018 This definition is more adaptable than the soft set and better suited for decision-making problems.
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