Regular ternary semirings in terms of bipolar fuzzy ideals

Abstract

The central objective of this paper is to introduce $$\left( {\alpha ,\beta } \right)$$ -bipolar fuzzy ideals (left, lateral and right) and bi-ideals in ternary semirings by applying the definitions of belongingness $$\left( \in \right)$$ and quasi-coincidence ( $$q$$ ) of a bipolar fuzzy point with a bipolar fuzzy set. In this work, upper parts and lower parts of bipolar fuzzy set in ternary semirings are also discussed. Regular and intra-regular ternary semirings in terms of $$\left( { \in, \in \vee q} \right)$$ -bipolar fuzzy (left, lateral and right) ideals and $$\left( { \in, \in \vee q} \right)$$ -bipolar fuzzy bi-ideals are characterized.