(∈,∈∨q_λ,μ)（Intuitionistic） Fuzzy Regular Subsemigroups

In this paper, the definitions of (∈,∈∨q)-intuitionistic fuzzy completely regular subsem-igroups,(∈,∈∨q(μ,λ))-fuzzy completely regular subsemigroups, generalized intuitionistic fuzzy subsets,(∈,∈∨q(λ,μ))-intuitionistic fuzzy completely regular subsemigroups are given. And some of their equivalent conditions and related properties are discussed. Besides, some new properties of (∈,∈∨q(λ,μ))-fuzzy regular subsemigroup and generalized fuzzy regular subsemigroup are obtained. At the same time, some results of homomorphic image and homomorphic preimage are shown. In thie way, we can more clearly know the nature of (∈,∈∨q(λ,μ))-fuzzy regular subsemigroup. This paper is organized as follows:In Chapter three, based on the concept of cut sets on intuitionistic fuzzy sets and the neighborhood relations between a fuzzy point xt and an intuitionistic fuzzy set A, the definition of (∈,∈∨q)-intuitionistic fuzzy completely regular subsemigroups are given by the3-valued Lukasiewicz implication. And some of its equivalent conditions and properties are obtained.In Chapter four, the definition and equivalent condition of (∈,∈∨q(μ,λ))-fuzzy complet-ely regular subsemigroups is given. Intuitionistic fuzzy subset is extended to the generalized intuitionistic fuzzy subsets and its basic operation properties and the generalized intuitionistic fuzzy subsets extension principle are discussed. The definition of (∈,∈∨q(λ,μ)-intuitionistic fuzzy completely regular subsemigroups is given by the3-valued Lukasiewicz implication. And some of their equivalent conditions and properties are obtained. The main results generalize and develop the corresponding results for the ordinary fuzzy algebra.In Chapter five, based on the theory of fuzzy points some new properties of (∈,∈∨q(λ,μ))-fuzzy regular subsemigroup and generalized fuzzy regular subsemigroup are shown. Besides, some results of homomorphic image and homomorphic preimage are obtained.