计算机工程与应用 ›› 2016, Vol. 52 ›› Issue (10): 39-43.

• 理论与研发 • 上一篇    下一篇

正则FI代数的MP滤子与同构基本定理

寇海燕,吴洪博   

  1. 陕西师范大学 数学与信息科学学院,西安 710062
  • 出版日期:2016-05-15 发布日期:2016-05-16

MP-filters and fundamental isomorphism theorem of regular FI-algebras

KOU Haiyan, WU Hongbo   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China
  • Online:2016-05-15 Published:2016-05-16

摘要: 正则FI-代数是仅基于蕴涵算子在一般集合上建立的逻辑代数,它是[BR0]-代数和BL-代数的基础逻辑代数。基于经典代数的思想和方法,讨论了正则FI-代数的MP滤子与同构基本定理。引入正则FI-代数中MP滤子的概念,并讨论了其基本性质,给出了正则FI-代数中包含任意子集的最小MP滤子的构造方法;讨论了正则FI-代数的MP滤子和同余关系之间的内在联系;给出了正则FI-代数的同构基本定理。

关键词: 逻辑代数, 正则模糊蕴涵(FI)-代数, 分离规则(MP)滤子, 同余关系, 模糊蕴涵(FI)-同态, 同构基本定理

Abstract: The regular FI-algebras are built up on general sets by the implication operation uniquely. Both [BR0]-algebras and BL-algebras are examples of regular FI-algebras. This paper, by using the related ideas and methods in classical algebra, studies the MP-filters and isomorphism theorem of regular FI-algebras. Firstly, a concept of MP-filters is introduced and their basic properties are discussed. It gives the concrete structure of an MP-filter generated by a given subset. Secondly, the relations between MP-filters and congruence relations are discussed. Finally, the fundamental isomorphism theorems are established.

Key words: logic algebra, regular Fuzzy , Implication(FI)-algebra, Modus Ponens(MP)-filter, congruence relation, Fuzzy , Implication(FI)-homomorphism, fundamental theorem of isomorphism