A New Study Based on Fuzzy Bi-Γ-Ideals in Ordered-Γ-Semigroups

G. Muhiuddin; A. Mahboob; Mohamed E. A. Elnair

doi:10.47852/bonviewJCCE19919205514

Authors

G. Muhiuddin Department of Mathematics, University of Tabuk, Saudi Arabia
A. Mahboob Department of Mathematics, Madanapalle Institute of Technology & Science Madanapalle, India
Mohamed E. A. Elnair Department of Mathematics, University of Tabuk, Saudi Arabia and Department of Mathematics and Physics, Gezira University, Sudan

DOI:

https://doi.org/10.47852/bonviewJCCE19919205514

Keywords:

ordered Γ-semigroups, fuzzy subsets, (∈, ∈ ∨(κ∗ , qκ))-fuzzy bi-Γ-ideals

Abstract

In this paper, using the notion of (k^∗ , q)-quasi-coincident of an ordered fuzzy point with a fuzzy set of the support, the concept of (∈, ∈ ∨(κ^∗ , q_k))-fuzzy bi-Γ-ideals in ordered Γ-semigroups is defined. We prove that intersection of (∈, ∈ ∨(κ^∗ , q_k))-fuzzy bi-Γ-ideals of S is an (∈, ∈ ∨(κ^∗ , q_k))-fuzzy bi-Γ-ideal but the statement does not hold for union, and in this aim an example is provided. Moreover, we present correspondence between bi-Γ-ideals and (∈, ∈ ∨(κ^∗ , q_k))-fuzzy bi-Γ-ideals of ordered Γ-semigroups based on level subset and (∈ ∨(κ^∗ , q_κ))-level subset of fuzzy sets.