The largest family of generalized fuzzy subhypergroups

Abstract

In this paper, we introduce the largest family of generalized fuzzy subhypergroups based on concepts of belongingness and quasi-coincidence of a fuzzy point to a fuzzy subset. In this regards, (∈, ∈ ∨q δ)-fuzzy subhypergroups and (∈, ∈ ∨q δ k)-fuzzy subhypergroups of hypergroups are defined as a generalization of fuzzy subhypergroups, (∈, ∈ ∨q)-fuzzy subhypergroups and (∈, ∈ ∨q k)-fuzzy subhypergroups of hypergroups. Some properties of them are investigated and their differences with other types are studied.