Some Study Of L-fuzzy Theory On Γ-semigroups

Firstly,the related properties of L-fuzzy equivalence relations and L-fuzzy congruences on Γ-semigroups are studied,and the equivalent characterizations of L-fuzzy equivalence relations and L-fuzzy congruences on Γ-semigroups are given.Secondly,a L-fuzzy congruence on Γ-semigroup is defined,and its properties are studied.Furthermore,the characterization of the minimum L-fuzzy congruence containing a L-fuzzy relation,u on a Γ-semigroup is obtained.Finally,the concepts of L-anti fuzzy subsemigroups and L-anti fuzzy Γ-subsemigroups are introduced,and the related properties are studied.It is given that a necessary and sufficient condition for the L-fuzzy subset of a Γ-semigroup to be a L-anti fuzzy Γ-subsemigroup or L-anti fuzzy bi-Γ-ideal.