MTL代数的反模糊LI理想  

Anti-fuzzy LI-ideals in MTL Algebras

作　　者：刘春辉[1] LIU Chun-hui(Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, China)

机构地区：[1]赤峰学院数学与统计学院

出　　处：《数学的实践与认识》2018年第9期245-252,共8页Mathematics in Practice and Theory

基　　金：内蒙古自治区高等学校科学研究项目(NJSY14238)

摘　　要：将模糊集与LI理想概念相结合，在MTL代数中引入反模糊LI理想和反模糊素（布尔／关联／超／固执）LI理想的概念并考察它们的特征性质和相互关系．证明了对MTL代数的非常值反模糊LI理想4而言，下列四条陈述是等价的：1）A既是反模糊布尔LI理想又是反模糊素LI理想；2）A既是反模糊关联LI理想又是反模糊素LI理想；3）A是反模糊超LI理想；4）A是反模糊固执LI理想．Combining fuzzy sets and LI-ideals, the concepts of anti-fuzzy LI-ideals and anti- fuzzy Boolean（implicative/prime/ultra/obstinate） LI-ideals in MTL-algebras are introduced and their properties and relations are investigated. It is proved that the following four states are equivalent for a non-constant anti-fuzzy LI-ideal A in a MTL-algebra： （1） A is both a anti-fuzzy Boolean and a anti-fuzzy prime LI-ideal; （2） A is both a anti-fuzzy implicative and a anti-fuzzy prime LI-ideal; （3） A is a anti-fuzzy ultra LI-ideal; （4） A is a anti-fuzzy obstinate LI-ideal.

关 键 词：模糊逻辑 MTL代数 反模糊(布尔/关联/素/超/固执)LI理想 

分 类 号：O159[理学—数学]