Approximation approaches for rough hypersoft sets based on hesitant bipolar-valued fuzzy hypersoft relations on semigroups

Abstract

In the hybrid context of hesitant bipolar-valued fuzzy hypersoft relations, the modern notion of extended roughness is constructed to rough approximations of hypersoft sets and fuzzy sets based on such context in this research. Then, corresponding examples are proposed, and further verified in connections between the hesitant bipolar-valued fuzzy hypersoft relations and the upper (resp., lower) rough approximations of hypersoft sets and fuzzy sets. Specifically, relationships are shown between the non-rough hypersoft sets (resp., non-rough fuzzy sets) and hesitant bipolar-valued fuzzy hypersoft reflexive relations together with hesitant bipolar-valued fuzzy hypersoft antisymmetric relations. To find the optimal multi-parameter of a hypersoft set such that the best choice exists, the notion of the set-valued measurement issues and decision-making algorithm for such objective is developed in the terms of rough set theory. Associated with the aforementioned accomplishments, the notion of novel models has been used to semigroups. Subsequently, the argumentation within relationships concerning the upper (resp., lower) rough approximations of hypersoft quasi-ideals and fuzzy quasi-ideals are proved under hypersoft homomorphism problems.