(∈,∈∨q_((λ,μ)))-模糊子半群和(∈,∈∨q_((λ,μ)))-模糊完全正则子半群

(∈,∈∨q_((λ,μ)))-Fuzzy Subsemigroup and(∈,∈∨q_((λ,μ)))-Fuzzy Completely Regular Subsemigroups

文中给出了(∈,∈∨q(λ,μ))-模糊子半群,(∈,∈∨q(λ,μ))-模糊完全正则子半群和广义模糊完全正则子半群的概念及它们之间的等价刻画。当λ=0,μ=0.5时,(∈,∈∨q(0,0.5))-模糊子半群和(∈,∈∨q(0,0.5))-模糊完全正则子半群即为(∈,∈∨q)-模糊子半群和(∈,∈∨q)-模糊完全正则子半群;当λ=0,μ=1时,(∈,∈∨q(0,1))-模糊子半群和(∈,∈∨q(0,1))-模糊完全正则子半群即为Rosenfe ld意义下的模糊子半群和模糊完全正则子半群,这将通常的模糊代数与(∈,∈∨q)-模糊代数进行了统一和推广。

The paper introduces the definition of （ ∈, ∈∨ q（λ,μ） ）-fuzzY subsemigroup, （ ∈, ∈ ∨ q（λ,μ））-fuzzy completely regular subsemigroups and generalized completely regular subsemigroups and discusses the equivalence conditions between them. When λ = 0,μ = 0.5 ,we can get （ ∈, ∈∨ q）-fuzzy subsemigroup and （ ∈, ∈ V q）-fuzzy completely regular subsemigroups; When λ = 1 ,μ = 0, we can get the usual results. We unify and generalize （∈, ∈ ∨ q）-fuzzy algebra and Rosenfeldg algebra to （ ∈, ∈ ∨ q（λ,μ） ）-fuzzy algebra.