余剩余格的模糊理想和模糊同余关系  

Fuzzy ideals and fuzzy congruences of co-residuated lattices

作　　者：韩新月 姚卫 HAN Xinyue;YAO Wei(School of Mathematics and Statistics,Nanjing University of Information Science and Technology,Nanjing,Jiangsu 210044,China)

机构地区：[1]南京信息工程大学数学与统计学院,江苏南京210044

出　　处：《河北科技大学学报》2025年第2期167-174,共8页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(12231007,12371462)。

摘　　要：为了拓展模糊逻辑代数的相关理论,研究了余剩余格的模糊理想和模糊同余关系及其相互关系。首先,以Heyting代数为赋值域,引入余剩余格的模糊理想和模糊同余关系概念,研究它们之间的相互诱导方式,证明二者之间具有一一对应关系;其次,利用截集和强截集方法,研究模糊理想和模糊同余关系的等价刻画。研究表明,余剩余格的模糊理想与模糊同余关系是相互等价的2个概念,将在结构和分类问题中起到相同的作用。研究结论丰富了模糊逻辑代数的相关理论,可为深入研究其他代数系统提供一定的理论参考。In order to expand the theory of fuzzy logic algebra,the fuzzy ideals and fuzzy congruences of co-residuated lattices and their interrelationships were studied.Firstly,by using Heyting algebra as the valuation domain,the concepts of fuzzy ideals and fuzzy congruences of co-residuated lattices were introduced,and their mutual induction methods were studied to prove a one-to-one correspondence between them.Secondly,the equivalent descriptions of fuzzy ideals and fuzzy congruence relationships were studied using cut set and strong cut set methods.The research shows that fuzzy ideals and the fuzzy congruences are two equivalent concepts and thus will play the same role in structure and classification problems.The research conclusion enriches the relevant theory of fuzzy logic algebraic algebras and can provide certain theoretical reference for further study of other algebraic systems.

关 键 词：模糊数学 余剩余格 模糊理想 模糊同余 截集 

分 类 号：O174.53[理学—数学] TN301.2[理学—基础数学]