Ordered semigroups characterized by interval valued (ε, ε $\vee$ q)-fuzzy bi-ideals

Abstract

In this article, we first introduce the concept of quasi-coincidence of an interval valued fuzzy point with an interval valued fuzzy subset. This concept is a generalization of the concept of quasi-coincidence of a fuzzy point within a fuzzy subset. By using this new idea, we introduce the concept of an interval valued (α, β)-fuzzy bi-ideals in ordered semigroups. Which is a generalization of the idea of an (α, β)-fuzzy bi-ideals in ordered semigroups. Some interesting results of the algebraic ordered semigroups in terms of interval valued (α, β)-fuzzy bi-ideals are given. By using interval valued (∈, ∈ ∨q)-fuzzy bi-ideals some interesting results are obtained.

A New View of Fuzzy Ordered Semigroups

“…We refer the reader to (18) for more details on operations on two interval-valued fuzzy sets of . Note that since every is in correspondence with the interval , hence a fuzzy set is a particular case of the interval valued fuzzy sets.…”

Semihypergroups Characterized by Generalized Fuzzy Bi-Hyperideals

“…initiated the notion of an (α, β)-fuzzy bi-ideal in ordered semigroups and some useful theorems are studied (cf. [29][30][31]). See also [32][33][34][35].…”

Characterizations of Ordered Semigroups by New Type of Interval Valued Fuzzy Quasi-Ideals

“…The theory of fuzzy sets on ordered semigroups has been recently developed (see [22][23][24][25][26][27][28][29][30]). Recently, Khan et al [31] introduced the concept of interval valued ( , )-fuzzy biideals of ordered semigroups by using the idea of a quasicoincidence of an interval valued fuzzy point with an interval valued fuzzy set. In particular, they studied the properties of interval valued (∈, ∈ ∨ )-fuzzy biideals in detail.…”