Characterizations of regular ordered semigroups by generalized fuzzy ideals

Abstract

Let S be an ordered semigroup. In this paper we first introduce the concepts of (∈, ∈ ∨ q_k)-fuzzy ideals, (∈, ∈ ∨ q_k)-fuzzy bi-ideals and (∈, ∈ ∨ q_k)-fuzzy generalized bi-ideals of an ordered semigroup S by the ordered fuzzy points of S, and investigate their related properties. Furthermore, characterizations of regular ordered semigroups by the properties of (∈, ∈ ∨ q_k)-fuzzy left ideals, (∈, ∈ ∨ q_k)-fuzzy right ideals and (∈, ∈ ∨ q_k)-fuzzy (generalized) bi-ideals are given.

Keywords

Regular ordered semigroup intra-regular ordered semigroup strongly convex fuzzy subset $(\in,\in \vee q_k)$-fuzzy left (right) ideal $(\in,\in \vee q_k)$-fuzzy (generalized) bi-ideal