MTL代数的直觉模糊理想  

Intuitionistic fuzzy ideals in MTL-algebras

作　　者：刘春辉 LIU Chunhui(Education Science College,Chifeng University,Chifeng 024000,China)

机构地区：[1]赤峰学院教育科学学院,内蒙古赤峰024000

出　　处：《安徽大学学报（自然科学版）》2023年第6期7-17,共11页Journal of Anhui University(Natural Science Edition)

基　　金：内蒙古自治区高等学校科学研究项目(NJZY21138,NJZY22146);内蒙古自治区残疾人联合会研究项目(2023KTYJ19);赤峰学院2022年教育教学研究项目(JYJXZ202204);内蒙古自治区社会科学基金项目(2022DY31)。

摘　　要：将直觉模糊集与理想概念相结合,在MTL代数中引入直觉模糊理想和直觉模糊素(Boolean/关联/超/固执)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代数的非常值直觉模糊理想A而言,如下各条件是等价的:(ⅰ)A是直觉模糊Boolean理想和直觉模糊素理想;(ⅱ)A是直觉模糊关联理想和直觉模糊素理想;(ⅲ)A是直觉模糊超理想;(ⅳ)A是直觉模糊固执理想.Combining intuitionistic fuzzy sets and ideals,the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy prime(Boolean/implicative/ultra/obstinate)ideals in MTLalgebras are introduced and their properties and relations are investigated.It is proved that the following conditions are equivalent for a non-constant intuitionistic fuzzy ideal A in a MTL-algebra:(i)A is both an intuitionistic fuzzy Boolean and an intuitionistic fuzzy prime ideal;(i)A is both an intuitionistic fuzzy implicative and an intuitionistic fuzzy prime ideal;(ii)A is an intuitionistic fuzzy ultra ideal;(iv)A is an intuitionistic fuzzy obstinate ideal.

关 键 词：模糊逻辑 MTL代数 直觉模糊素理想 直觉模糊Boolean理想 直觉模糊超理想 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]