On weakly bi-ideals in ordered semigroups and their fuzzifications

Volume 30, Issue 2, pp 165--172 https://doi.org/10.22436/jmcs.030.02.07

Publication Date: December 25, 2022 Submission Date: October 08, 2022 Revision Date: November 14, 2022 Accteptance Date: November 28, 2022

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Authors

N. Lekkoksung - Division of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand. W. Nakkhasen - Department of Mathematics, Faculty of Science, Mahasarakham University, Maha Sarakham 44150, Thailand.

Abstract

The concept of bi-ideals in ordered semigroups is a subuniverse of ordered semigroups with certain conditions. It can be used to characterize ordered semigroups. In this paper, we extend the concept of bi-ideals to a general way, so-called weakly bi-ideals. We consider the primitive and semiprimitive of weakly bi-ideals. Some connections between prime (semiprime) weakly bi-ideals and fuzzy prime (semiprime) weakly bi-ideals is established.

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Keywords

• Weakly bi-ideal
• fuzzy weakly bi-ideal
• ordered semigroup

MSC

•  08A72
•  06F05
•  20M12

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