Fuzzy generalized bi–Γ–ideals of type (λ, θ) in ordered Γ–semigroups

• Main Authors: Muhammad Khan, Faiz, Sarmin, Nor Haniza, Khan, Asghar
• Format: Article
• Language: English
• Published: Penerbit UTM 2013
• Subjects: Q Science (General)
• Online Access: http://eprints.utm.my/id/eprint/50193/1/NorHanizaSarmin2013_FuzzygeneralizedBi.pdf; http://eprints.utm.my/id/eprint/50193/; https://dx.doi.org/10.11113/jt.v62.1881

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 ofG. 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 μA 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