非交换剩余格上模糊PMTL滤子的特征及其性质  

The Characterizations and Properties of Fuzzy PMTL-filters in Non-commutative Residuated Lattices

作　　者：左卫兵 张一旎 ZUO Weibing;ZHANG Yini(School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou 450046, China)

机构地区：[1]华北水利水电大学数学与统计学院,河南郑州450046

出　　处：《郑州大学学报（理学版）》2022年第1期81-87,共7页Journal of Zhengzhou University:Natural Science Edition

基　　金：河南省自然科学基金项目(152300410112);国家自然科学基金项目(12071133)。

摘　　要：滤子理论在多值逻辑及其相关代数的研究中起到了非常重要的作用。为进一步研究非交换剩余格上的滤子理论,基于非交换剩余格上模糊滤子的定义,在非交换剩余格上引入模糊PMTL滤子的概念,给出了这类模糊滤子的一系列刻画,并进一步提出非交换剩余格上模糊同余和模糊商代数的定义,证明了由模糊PMTL滤子生成的模糊商代数是伪MTL代数。The filter theory plays an important role in studying multiple-valued logic and the related algebras.In order to further study the filter theory of non-commutative residuated lattices,based on the definition of fuzzy filters in non-commutative residuated lattices,the concept of fuzzy PMTL-filters in non-commutative residuated lattices was introduced.Several characterizations of fuzzy PMTL-filters were derived.Moreover,the notions of fuzzy congruences and fuzzy quotient algebras in non-commutative residuated lattices were introduced,and it was proved that the fuzzy quotient algebras introduced by fuzzy PMTL-filters were pseudo-MTL algebras.

关 键 词：非交换剩余格 模糊PMTL滤子 模糊同余 

分 类 号：O159[理学—数学] O141.1[理学—基础数学]