Regular ternary semirings in terms of bipolar fuzzy ideals

The central objective of this paper is to introduce α , β -bipolar fuzzy ideals (left, lateral and right) and bi-ideals in ternary semirings by applying the definitions of belongingness ∈ 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 ∈ , ∈ ∨ q -bipolar fuzzy (left, lateral and right) ideals and ∈ , ∈ ∨ q -bipolar fuzzy bi-ideals are characterized.