Regular ternary semirings in terms of bipolar fuzzy ideals (Q2027661)

The central objective of this paper is to introduce $(\alpha,\beta)$-bipolar fuzzy ideals (left, lateral and right) and bi-ideals in ternary semirings by applying the definitions of belongingness $(\epsilon)$ 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 $(\epsilon,\epsilon\vee q)$-bipolar fuzzy (left, lateral and right) ideals and $(\epsilon,\epsilon\vee q)$-bipolar fuzzy bi-ideals are characterized. This paper generalizes some ideals to bipolar fuzzy ideals in semirings. All results are typical.