计算机科学与探索 ›› 2014, Vol. 8 ›› Issue (3): 376-384.DOI: 10.3778/j.issn.1673-9418.1310036

• 人工智能与模式识别 • 上一篇    

格蕴涵代数的(∈,∈∨q(λ,μ))-模糊滤子

傅小波1,2,3，战学秋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:2014-03-01 发布日期:2014-03-05

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

FU Xiaobo 1,2,3, ZHAN Xueqiu1, 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:2014-03-01 Published:2014-03-05

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摘要： 给出了点态化(∈,∈∨q(λ,μ))-模糊滤子和广义模糊滤子的概念，讨论了两者之间的等价关系；得到了(∈,∈∨q(λ,μ))-模糊滤子的若干等价刻画，并研究了其相关性质；讨论了(∈,∈∨q(λ,μ))-模糊滤子的同态像与同态原像的基本性质；最后研究了(∈,∈∨q(λ,μ))-模糊滤子的直积。

关键词: 格蕴涵代数, (&isin, &isin, &or, q(&lambda, &mu, ))-模糊滤子, 广义模糊滤子, 直积

Abstract: Firstly, this paper introduces the concepts of the pointwise (∈,∈∨q(λ,μ))-fuzzy filter and generalized fuzzy filter, and discusses the relationship between them. Secondly, this paper obtains some equivalent descriptions of the (∈,∈∨q(λ,μ))-fuzzy filter, and studies the related properties. Thirdly, this paper discusses some basic properties of homomorphic image and homomorphic preimage of the (∈,∈∨q(λ,μ))-fuzzy filter. Finally, this paper studies the direct product of the (∈,∈∨q(λ,μ))-fuzzy filter.

Key words: lattice implication algebra, [(∈,∈∨q(λ,μ))-]fuzzy filter, generalized fuzzy filter, direct product

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