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

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∗ , qk))-fuzzy bi-Γ-ideals in ordered Γ-semigroups is defined. We prove that intersection of (∈, ∈ ∨(κ∗ , qk))-fuzzy bi-Γ-ideals of S is an (∈, ∈ ∨(κ∗ , qk))-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∗ , qk))-fuzzy bi-Γ-ideals of ordered Γ-semigroups based on level subset and (∈ ∨(κ∗ , qκ))-level subset of fuzzy sets.

 

Received: 3 January 2022 | Revised: 11 February 2022 | Accepted: 13 February 2022

 

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.


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Published

2022-02-17

Issue

Vol. 1 No. 1 (2022)

Section

Research Articles

License

Copyright (c) 2022 Authors

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Muhiuddin, G., Mahboob, A., & E. A. Elnair, M. (2022). A New Study Based on Fuzzy Bi-Γ-Ideals in Ordered-Γ-Semigroups. Journal of Computational and Cognitive Engineering, 1(1), 42-46. https://doi.org/10.47852/bonviewJCCE19919205514