Multipolar (m,n)-Fuzzy Set and its Applications to Semihypergroups

This paper introduces a new hybrid structure called a multipolar $(m, n)$-fuzzy set, which is an extension of multipolar fuzzy sets and $(m, n)$-fuzzy sets. The concept of a multipolar $(m,n)$-fuzzy set has been applied to the study of semihypergroups. In particular, we introduce the notions of multipolar $(m, n)$-fuzzy sub-semihypergroups, multipolar $(m, n)$-fuzzy hyperideals, multipolar $(m, n)$-fuzzy bi-hyperideals, multipolar $(m, n)$-fuzzy quasi-hyperideals, and multipolar $(m, n)$-fuzzy (1, 2)-hyperideals of semihypergroups, and investigate some of their properties. Additionally, we characterised regular semihypergroups in terms of various types of multipolar $(m, n)$-F-hyperideals.