Affiliations: [a] Department of Mathematics, Abdul Wali Khan University, Mardan, KPK, Pakistan
| [b] Department of Mathematics, Yazd University, Yazd, Iran
Correspondence:
[*]
Corresponding author. Muhammad Ibrar, Department of Mathematics, Abdul Wali Khan University, Mardan, KPK,
Pakistan. Tel.: +923449397758; E-mail: [email protected].
Abstract: In this paper, we introduce the concept of (α, β)-bipolar fuzzy generalized bi-ideal in ordered semigroup, which is a generalization of bipolar-fuzzy generalized bi-ideal in ordered semigroup. Using this concept, we provide some characterization theorems. We prove that in regular ordered semigroup, the concept of (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideal and (∈, ∈ ∨q)-bipolar fuzzy bi-ideal coincide. We also introduce the upper/lower parts of (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideals and characterize the regular ordered semigroups in terms of lower part of (∈, ∈ ∨q)-bipolar fuzzy left (resp. right or two sided) ideals and (∈, ∈ ∨q)-bipolar fuzzy generalized bi-ideals.
