关于BL-代数的模糊滤子与模糊理想(英文)  

On Fuzzy Filters and Fuzzy Ideals of BL-algebras

作　　者：张小红[1] Jun Young Bae Doh Myung Im 

机构地区：[1]宁波大学数学系,浙江宁波315211 [2]Department of Mathematics Education,Gyeongsang National University

出　　处：《模糊系统与数学》2006年第3期8-20,共13页Fuzzy Systems and Mathematics

基　　金：ZhejiangProvincialNaturalScienceFoundationofChinaunderGrant(Y605389);NingboYouthScienceFund(2005A620032)

摘　　要：在BL-代数中引入模糊超滤子和模糊固执滤子的概念,证明了如下条件对于BL-代数的非常数模糊滤子f来说是等价的:(1)f是布尔的和素的,(2)f是蕴涵的和素的,(3)f是超的,(4)f是固执的。应用模糊正蕴涵滤子给出G-代数的若干特征性质。提出BL-代数模糊理想的概念,给出一些重要例子,并通过例子说明在BL-代数中模糊理想一般不能由模糊滤子导出。同时,从模糊理想出发构造了商BL-代数,并建立了相应的同态基本定理。最后,研究了BL-代数的几类模糊理想及其相互关系,给出模糊布尔理想、模糊素理想、模糊超理想的特征性质。The notions of fuzzy ultra filters and fuzzy obstinate filters in BL-algebras are introduced and the following are proved to be equivalent for non-constant fuzzy filter f in BL-algebra L： （1）f is Boolean and prime, （2）f is implicative and prime, （3）f is ultra, （4）f is obstinate. By fuzzy positive implicative filter, some characterizations of G-algebra are established. The notion of fuzzy ideal is introduced and some important examples are given, by these examples the fact that fuzzy ideal can not be derived from fuzzy filter in BL-algebras is showed. Moreover, a quotient BL-algebra via a fuzzy ideal is constructed, and the Fuzzy Homomorphism Fundamental Theorem is given. Finally, some classes of fuzzy ideals are defined and the relations of them are investigated. Some characterizations of fuzzy Boolean ideals, fuzzy prime ideals and fuzzy ultra ideals are established.

关 键 词：BL-代数 模糊超滤子 模糊固执滤子 G-代数 模糊理想 商BL-代数 

分 类 号：O159[理学—数学]