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.