On prime fuzzy bi-ideals in ternary semigroups

Abstract

In this research we concentrate on the analyticalstudy and concept of fuzzification on prime bi-ideals in ternarysemigroups and look for some of their related characteristics.Strongly prime and semiprime fuzzy bi-ideals are initiated andtraits are discussed. Besides irreducible and strongly irreduciblefuzzy bi-ideals in ternary semigroups have been researched.Employing the fuzzy bi-ideals of ternary semigroups, paritystatements for a regular ternary semigroup have been collaborated.Furthermore, it has observed that, the set of all strongly primeproper fuzzy bi-ideals in a ternary semigroup form a topology.Conclusively, it has been proved that in case of the totallyordered set of fuzzy bi-ideals of a semigroup $S$, the concept ofirreducible prime and strongly irreducible prime coincides.