Some New Characterization of Ordered Semigroups In Terms Of (Λ; Θ)-Fuzzy Bi-Ideals
Abstract
In this paper, we demonstrate a new concept of fuzzy bi-ideals called a (λ;θ)-fuzzy bi-ideals of
an ordered semigroup. Fuzzy ideals of type (λ;θ) are the generalization of fuzzy bi-ideals and an
(€;€ vq)-fuzzy bi-ideals of an ordered semigroup. We show that U(μ; t)(≠ Ø) is a bi-ideal if and
only if the fuzzy subset is a (λ;θ)-fuzzy i-ideal of S for all t 2 (λ;θ]. Similarly, A is a bi-ideal if
and only if the characteristic function A of A is a (λ;θ)-fuzzy bi-ideal of S. With the help of
some examples, we show that (λ; θ)-fuzzy bi-ideals (λ; θ)-fuzzy subsemigroups) are neither
fuzzy bi-ideals (fuzzy subsemigroups) nor (€;€ vq)-fuzzy bi-ideals (€;€ vq)-fuzzy
subsemigroups) of an ordered semigroup S. Finally, the characterization of completely ordered
semigroups in terms of (λ;θ)-fuzzy bi-ideals is given.