Fuzzifying Bi-Ideals of Semigroups and Implication Operators

In this paper the notion of (α,β)-fuzzy bi-ideal of a semigroup is introduced and related properties are investigated. Also, the definition of implication operator in the Lukasiewicz system of continuous-valued logic for fuzzy bi-ideals is considered. In particular, the relationship between fuzzy bi-ideals with thresholds and implication-based fuzzy bi-ideals is analyzed.