正则FBR0-代数的弱t-模及其应用

J4 ›› 2015, Vol. 37 ›› Issue (01): 99-103.

正则FBR0-代数的弱t-模及其应用

牛超慧，吴洪博

（陕西师范大学数学与信息科学学院，陕西西安 710062）

收稿日期:2013-04-28 修回日期:2013-09-06 出版日期:2015-01-25 发布日期:2015-01-25
基金资助:
国家自然科学基金资助项目(11171196)

Weak t-norm of regular FBR0-algebras and its application

NIU Chaohui,WU Hongbo

(College of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710062,China)

Received:2013-04-28 Revised:2013-09-06 Online:2015-01-25 Published:2015-01-25

摘要/Abstract

摘要：

吴望名教授建立的FI-代数(模糊蕴涵代数)是重要的基础逻辑代数, 且通过弱化WBR0-代数建立的FBR0-代数与FI-代数有相同的代数结构。对FBR0-代数进行了较细致的研究。首先,证明了正则的FBR0代数与RBR0-代数有相同的代数结构; 其次,讨论了正则FBR0代数中弱t-模的基本性质; 最后,给出了正则FBR0代数的弱t-模表示形式。

关键词: 逻辑代数, 正则FBR0-代数, RBR0-代数, 伴随对, 弱t模

Abstract:

FBR0-algebras (fuzzy BR0-algebras), which are built up by weakening the conditions of WBR0-algebras, have the same algebraic structure with FI-algebras (fuzzy implication algebras) which are important and basic logic algebras proposed by professor Wu Wang-ming. FBR0-algebra is studied in detail. Firstly, it is proved that regular FBR0-algebras have the same algebraic structure with RBR0-algebras. Secondly, the basic properties of weak t-norm of regular FBR0algebras are discussed. Finally, a representation of regular FBR0-algebras is given in the form of weak t-norm.

Key words: logic algebra;regular FBR0-algebras;RBR0-algebras;adjoint pairs;weak t-norm

牛超慧，吴洪博. 正则FBR0-代数的弱t-模及其应用[J]. J4, 2015, 37(01): 99-103.

NIU Chaohui,WU Hongbo. Weak t-norm of regular FBR0-algebras and its application [J]. J4, 2015, 37(01): 99-103.