Ordered Semigroups Based on ∈,∈∨qkδ-Fuzzy Ideals

Abstract

A new trend of using fuzzy algebraic structures in various applied sciences is becoming a central focus due to the accuracy and nondecoding nature. The aim of the present paper is to develop a new type of fuzzy subsystem of an ordered semigroup . This new type of fuzzy subsystem will overcome the difficulties faced in fuzzy ideal theory of an ordered semigroup up to some extent. More precisely, we introduce (∈, ∈ ∨ )-fuzzy left (resp., right, quasi-) ideals of . These concepts are elaborated through appropriate examples. Further, we are bridging ordinary ideals and (∈, ∈ ∨ )-fuzzy ideals of an ordered semigroup through level subset and characteristic function. Finally, we characterize regular ordered semigroups in terms of (∈, ∈ ∨ )-fuzzy left (resp., right, quasi-) ideals.

Characterizations of Regular Ordered Semigroups by (∈,∈∨(k∗,qk))-Fuzzy Quasi-Ideals

“…For more details on fuzzy ideals and their related notions in ordered semigroups, the reader is referred to [26][27][28][29][30][31][32].…”

The largest family of generalized fuzzy subhypergroups

“…Jun et al (2016) introduced a new generalization for (∈, ∈ ∨q)-fuzzy subgroups, called (∈, ∈ ∨q δ )-fuzzy subgroups. After that, (∈, ∈ ∨q δ k )fuzzy ideals of ordered semigroups were defined in Khan et al (2018). Motivated by it, now, we define new generalizations of (∈, ∈ ∨q)-fuzzy subhypergroups and also (∈, ∈ ∨q k )-fuzzy subhypergroups of hypergroups which are said to be (∈, ∈ ∨q δ )-fuzzy subhypergroups and (∈, ∈ ∨q δ k )-fuzzy subhypergroups of H , respectively.…”