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Regular and intra-regular semirings in terms of bipolar fuzzy ideals

Research paper by Muhammad Shabir, Saba Liaquat, Shahida Bashir

Indexed on: 26 Feb '21Published on: 16 Oct '19Published in: Computational and Applied Mathematics



Abstract

Using the concept of belongingness and quasi-coincidence of a bipolar fuzzy point with a bipolar fuzzy set, the concepts of \((\alpha ,\beta )\)-bipolar fuzzy subsemiring, \((\alpha ,\beta )\)-bipolar fuzzy ideal and \((\alpha ,\beta )\)-bipolar fuzzy bi-ideal in semiring are introduced. We emphasized more on \((\in ,\in \vee q)\)-bipolar fuzzy ideals and \((\in ,\in \vee q)\)-bipolar fuzzy bi-ideals. Characterizations of regular and intra-regular semirings by using \((\in ,\in \vee q)\)-bipolar fuzzy ideals and \((\in ,\in \vee q)\)-bipolar fuzzy bi-ideals are presented.