Fuzzy Generalized Bi-Г-Ideals of Type (λ, θ) In Ordered Г-Semigroups

Subscribing to the Zadeh’s idea on fuzzy sets, many researchers strive to identify the key attributes of these sets for new finding in mathematics. In this perspective, we introduce a new concept of fuzzy generalized bi-Γ-ideal of an ordered Γ-semigroup G called a (λ, θ)-fuzzy generalized bi-Γ-ideal of G. Fuzzy generalized bi-Γ-ideals of type (λ, θ) are the generalization of ordinary fuzzy generalized bi-Γ- ideals of an ordered Γ-semigroup G. A new classification of ordered Γ-semigroups in terms of a (λ, θ)- fuzzy generalized bi-Γ-ideal is given. Furthermore, we proved that U(μ, t) is a generalized bi-Γ-ideal if and only if the fuzzy subset μ is a (λ, θ)-fuzzy generalized bi-Γ-ideal of G for all t∈(λ, θ) . Similarly, A is a generalized bi-Γ-ideal if and only if the characteristic function μ_A of A is a (λ, θ)-fuzzy generalized bi-Γ- ideal of G. Finally, the relationship between ordinary fuzzy generalized bi-Γ-ideal and (λ, θ)-fuzzy generalized bi-Γ-ideal is discussed.