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山东大学学报(理学版) ›› 2016, Vol. 51 ›› Issue (2): 119-126.doi: 10.6040/j.issn.1671-9352.0.2015.156

• • 上一篇    

格蕴涵代数的不分明化滤子

彭家寅   

  1. 内江师范学院数学与信息科学学院, 四川 内江 641100
  • 收稿日期:2015-04-14 出版日期:2016-02-16 发布日期:2016-03-11
  • 作者简介:彭家寅(1962— ),男,博士,教授,研究方向为模糊数学与人工智能. E-mail:pengjiayin62226@163.com
  • 基金资助:
    教育部与四川省“数学与应用数学专业综合改革”资助项目(ZG0464,01249);国家自然科学基金资助项目(11071178)

PENG Jia-yin   

  1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641100, Sichuan, China
  • Received:2015-04-14 Online:2016-02-16 Published:2016-03-11

摘要: 利用一元模糊谓词逻辑和连续格值逻辑语义方法来发展格蕴涵代数的不分明化滤子。引入格蕴涵代数的不分明化滤子的概念,讨论其相关性质,研究了在格蕴涵同态映射下格蕴涵代数的不分明化滤子的象与原象之间的关系。

关键词: 格蕴涵代数, 连续格值逻辑, 格蕴涵同态, 一元模糊谓词, 不分明滤子

Abstract: The aim of this paper is to extend fuzzifying filter of lattice implication algebras by introducing a unary fuzzy predicate and by adopting the semantic method of continuous lattice valued logic. The concept of fuzzifying filters in lattice implication algebras is defined, and their related properties are discussed. How to deal with the lattice implication homomorphic images and inverse images of fuzzifying filters are studied.

Key words: continuous lattice valued logic, unary fuzzy predicate, fuzzifying filter, lattice implication homomorphism, lattice implication algebra

中图分类号: 

  • O159
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