Semihypergroups Characterized by Generalized Fuzzy Bi-Hyperideals

Abstract

In this paper, we introduce the notion of interval valued (α, β)-fuzzy bi-hyperideal in semihypergroups. The obtained concept is a generalized form of fuzzy bi-hyperideal and (α, β)-fuzzy bi-hyperideal in semihypergroups, where α, β ∈ {∈, q, ∈ ∨q, ∈ ∧q} with α =∈ ∧q. So, we can easily construct twelve different types of interval valued fuzzy left (right) hyperideals of semihypergroups. Combining the notion of an interval valued fuzzy point and an interval valued fuzzy set, we introduce the notion of a generalized interval valued fuzzy bi-hyperideal in semihypergroups and some useful characterization theorems are provided. We give some special attention to interval valued (∈, ∈ ∨q)-fuzzy bi-hyperideals.