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

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.