Fuzzy Generalized Bi-Gamma-Ideals of Type (lambda,theta) In Ordered Gamma-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-Gamma-ideal of an ordered Gamma-semigroup G called a (lambda,theta)- fuzzy generalized bi- Gamma- ideal of G. Fuzzy generalized bi- Gamma- ideals of type (lambda,theta) are the generalization of ordinary fuzzy generalized bi- Gamma-ideals of an ordered Gamma- semigroup G. A new classification of ordered Gamma- semigroups in terms of a (lambda,theta)fuzzy generalized bi- Gamma- ideal is given. Furthermore, we proved that U(mu, t) is a generalized bi- Gamma- ideal if and only if the fuzzy subset mu is a (lambda,theta)- fuzzy generalized bi- Gamma- ideal of G for all t is an element of(lambda,theta]. Similarly, A is a generalized bi- Gamma- ideal if and only if the characteristic function mu A of A is a (lambda,theta)- fuzzy generalized bi- Gamma-ideal of G. Finally, the relationship between ordinary fuzzy generalized bi- Gamma- ideal and (lambda,theta)- fuzzy generalized bi- Gamma- ideal is discussed.