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.
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)
出处
《郑州大学学报（理学版）》
北大核心
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)。
关键词
非交换剩余格
模糊PMTL滤子
模糊同余
non-commutative residuated lattice
fuzzy PMTL-filter
fuzzy congruence
