R-fuzzy Regular Subsemigroups And Fuzzy K-ideals In Γ-hemi-rings

In this paper, the definitions of R-fuzzy strong regular subsemigroups, generalized fuzzy strong regular subsemigroups,(∈,∈∨q(λ,μ))-fuzzy strong regular subsemigroups, generalized fuzzy k-ideals and (∈,∈∨q(λ,μ))-fuzzy k-ideals in Γ-hemi-rings were given. And some of their related properties and equivalent conditions were discussed. This paper is organized as follows:In Chapter three, the definitions of R-fuzzy strong regular subsemigroups are given, some of its algebraic properties were discussed. Examples show that R-fuzzy strong regular subsemigroups is a different fuzzy algebraic structure from R-fuzzy regular subsemigroups. For discussing nine commonly used implication operators,we got the equivalent forms of R-fuzzy strong regular subsemigroups in nine implication operators, and taking the t=0.5, we got some other results by discussing some of the nine implication operators.In Chapter four, first the definition of generalized fuzzy strong regular subsemigroups is given,second, based on the theory of fuzzy points we gave out the concept of (∈,∈∨q(λ,μ))-fuzzy strong regular subsemigroups,equivalent conditions and properties of generalized fuzzy strong regular subsemigroups and (∈,∈∨q(λ,μ))-fuzzy strong regular subsemigroups,and discussed the relationship between them.Last, some properties of homomorphic image and homomorphic preimage of (∈,∈∨q(λ,μ))-fuzzy strong regular subsemigroups were given.In Chapter five, the definitions of generalized fuzzy k-ideals and (∈,∈∨q(λ,μ))-fuzzy k-ideals in Γ-hemi-rings were given. Relations and other equivalent characterizations between them were discussed,and we also got the properties of homomorphic image and homomorphic preimage of (∈,∈∨q(λ,μ))-fuzzy k-ideals.