计算机科学与探索 ›› 2015, Vol. 9 ›› Issue (2): 227-233.DOI: 10.3778/j.issn.1673-9418.1404012

• 人工智能与模式识别 • 上一篇    下一篇

格蕴涵代数的(∈,∈∨q(λ,μ))-模糊素滤子

傅小波1，廖祖华2,3+   

  1. 1. 无锡职业技术学院 基础部，江苏 无锡 214121
    2. 江南大学 理学院，江苏 无锡 214122
    3. 江南大学 教育部物联网技术应用工程研究中心，江苏 无锡 214122
  • 出版日期:2015-02-01 发布日期:2015-02-03

(∈,∈∨q(λ,μ))-Fuzzy Prime Filter of Lattice Implication Algebra

FU Xiaobo1, LIAO Zuhua2,3+   

  1. 1. Section of Foundation Education, Wuxi Institute of Technology, Wuxi, Jiangsu 214121, China
    2. School of Science, Jiangnan University, Wuxi, Jiangsu 214122, China
    3. Engineering Research Center of Internet of Things Technology Application of Ministry of Education, Jiangnan University, Wuxi, Jiangsu 214122, China
  • Online:2015-02-01 Published:2015-02-03

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摘要： 将(∈,∈∨q(λ,μ))-模糊代数应用于格蕴涵代数，提出了点态化(∈,∈∨q(λ,μ))-模糊素滤子和(λ,μ)-模糊素滤子的概念，并从以下几个方面对(∈,∈∨q(λ,μ))-模糊素滤子进行了详细的研究：讨论了(∈,∈∨q(λ,μ))-模糊素滤子和(λ,μ)-模糊素滤子的等价关系；研究了(∈,∈∨q(λ,μ))-模糊素滤子的相关性质；得到了特定条件下(∈,∈∨q(λ,μ))-模糊素滤子的若干等价刻画，建立了(∈,∈∨q(λ,μ))-模糊素滤子的扩张定理；探讨了(∈,∈∨q(λ,μ))-模糊素滤子的同态像与同态原像。

关键词: 格蕴涵代数；模糊素滤子；(&lambda, ,&mu, )-模糊素滤子；扩张定理

Abstract:  By applying (∈,∈∨q(λ,μ))-fuzzy algebras to lattice implication algebras, this paper introduces the concepts of the pointwise (∈,∈∨q(λ,μ))-fuzzy prime filter and (λ,μ)-fuzzy prime filter, and carries out a detailed investigation on the (∈,∈∨q(λ,μ))-fuzzy prime filter from the following aspects: discussing the equivalence relationship between (∈,∈∨q(λ,μ))-fuzzy prime filter and (λ,μ)-fuzzy prime filter; studying the related properties of (∈,∈∨q(λ,μ))-fuzzy prime filter; with certain conditions, giving some equivalent descriptions of the (∈,∈∨q(λ,μ))-fuzzy prime filter and establishing the extension theorem of (∈,∈∨q(λ,μ))-fuzzy prime filter; investigating the homomorphic image and homomorphic preimage of (∈,∈∨q(λ,μ))-fuzzy prime filter.

Key words: lattice implication algebra; (∈,∈∨q(λ,μ))-fuzzy filter;(λ,μ)-fuzzy filter, extension theorem

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