A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings-Reference-Cited by-同舟云学术

A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings

Published:2023-06-24 Issue:7 Volume:12 Page:626
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Muhiuddin Ghulam¹^ORCID,Abughazalah Nabilah²^ORCID,Mahboob Ahsan³,Al-Kadi Deena⁴

Affiliation:

1. Department of Mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia

2. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

3. Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle 517325, India

4. Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia

Abstract

In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is established. We prove that (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (∈,∈∨(κ*,qκ))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are presented. Moreover, the (κ*,κ)-lower part of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (∈,∈∨(κ*,qκ))-fuzzy bi-simple.

Funder

Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Link

https://www.mdpi.com/2075-1680/12/7/626/pdf

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