Generalized Fuzzy Regular Subsemigroups And Generalized Fuzzy Ideals

This article gave the notions of generalized fuzzy(weakly) regular subsemigroup, (∈,∈∨q_λ,μ)-fuzzy (weakly)regular subsemigroup, generalized fuzzy ideals and generaliz- ed fuzzy semiprime in semigroups. And we studied the properties and equivalent characteri- zation of them. Besides that the relations between generalized fuzzy ideals and regular semigroup and completely regular semigroup were studied too.In the weakened conditions we generalized the other scholars' results,and studied them by reducti to absurdity, algebra and mathematical analysis.In chapter 2,first in the section of 2.1,we gave the preparation of this chapter.Next in the section of 2.2, (∈,∈∨q_λ,μ)-fuzzy regular subsemigroup was defined,and the properties were studied.Moreover we gained generalized fuzzy regular subsemigroup and (∈,∈∨q_λ,μ)-fuzzy regular subsemigroup are equivalent.Finally in the section of 2.3 (∈,∈∨q_λ,μ)-fuzzy weakly regular subsemigroup was given and studied.we also got that generalized fuzzy weakly regular subsemigroup and (∈,∈∨q_λ,μ)-fuzzy weakly regular subsemigroup are equivalent.In chapter 3, the concept of generalized ideals were defined in the section of 3.1.Then in the section of 3.2 the equivalent characterization and properties of generalized fuzzy ideals were given,and the relations of generalized fuzzy ideals were studied.In chapter 4,we depicted the regualr semigroup by generalized fuzzy ideals(quasi- ideals,interior ideals,two-side ideals,bi-ideals,generalized bi-ideals).In chapter 5,we gave the concept and the properties of generalized fuzzy semiprime in semigroups. we used generalized fuzzy semiprime and generalized fuzzy ideals in semigroups to describe completely regular semigroup.