格蕴涵代数(∈,∈∨_(q(λ,μ)))-模糊子代数  

(∈,∈∨_(q(λ,μ)))-fuzzy Subalgebra of Lattice Implication Algebras

作　　者：傅小波[1,2] 廖祖华[1] 郑高平[1] 刘维龙[1] 

机构地区：[1]江南大学理学院,至善学院,江苏无锡214122 [2]无锡职业技术学院基础部,江苏无锡214121

出　　处：《模糊系统与数学》2014年第6期44-52,共9页Fuzzy Systems and Mathematics

基　　金：2012年国家大学生创新创业训练项目(2050205)

摘　　要：本文从以下几个方面对格蕴涵代数的(∈,∈∨q(λ,μ))-模糊子代数进行了详细的研究。首先给出了点态化的(∈,∈∨q(λ,μ))-模糊子代数和广义模糊子代数的概念,讨论了两者之间的等价关系;其次给出了(∈,∈∨q(λ,μ))-模糊子代数的一些等价刻画,并研究了其相关性质;再次讨论了(∈,∈∨q(λ,μ))-模糊子代数的同态像与同态原像的基本性质;最后还研究了(∈,∈∨q(λ,μ))-模糊子代数的直积。In this paper, we carry out a detailed investigation into the （∈,∈Vq（λμ））-fuzzy subalgebra of the lattice implication algebra from the following aspects. Firstly, the concepts of the pointwise （∈,∈Vq（λμ））-fuzzy subalgebra and generalized fuzzy subalgebra are introduced, and the relationship between them is also discussed. Secondly, we present some equivalent descriptions of the （∈,∈Vq（λμ））-fuzzy subalgebra and discusses the related properties; Thirdly, we discuss some basic properties of homomorphic image and homomorphic preimage of the （∈,∈Vq（λμ））-fuzzy subalgebra. Finally, the direct product of the （∈,∈Vq（λμ））-fuzzy subalgebra is studied.

关 键 词：格蕴涵代数 (∈ ∈Vq(λμ))模糊子代数 广义模糊子代数 同态 直积 

分 类 号：O159[理学—数学]