河北科技大学学报2025，Vol.46Issue(2)：167-174,8.DOI:10.7535/hbkd.2025yx02006
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
摘要
Abstract
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Key words
fuzzy mathematics/co-residuated lattice/fuzzy ideal/fuzzy congruence/cut set分类
数学引用本文复制引用
韩新月,姚卫..余剩余格的模糊理想和模糊同余关系[J].河北科技大学学报,2025,46(2):167-174,8.基金项目
国家自然科学基金(12231007,12371462) （12231007,12371462）
