基于模糊等式的Ω-BCK代数

吉林大学学报(理学版) ›› 2026, Vol. 64 ›› Issue (3): 545-0550.

基于模糊等式的Ω-BCK代数

刘芸¹，周鑫^1,2，陈良云³

1. 伊犁师范大学数学与统计学院，新疆伊宁 835000； 2. 伊犁师范大学应用数学研究所，新疆伊宁 835000；
3. 东北师范大学数学与统计学院，长春 130024

收稿日期:2025-08-29 出版日期:2026-05-26 发布日期:2026-05-26
通讯作者: 周鑫 E-mail:zhoux566@nenu.edu.cn

Ω-BCK Algebras Based on Fuzzy Equalities

LIU Yun¹， ZHOU Xin^1,2， CHEN Liangyun³

1. School of Mathematics and Statistics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China;
2. Institute of Applied Mathematics, Yili Normal University, Yining 835000, Xinjiang Uygur Autonomous Region, China;
3. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received:2025-08-29 Online:2026-05-26 Published:2026-05-26

摘要/Abstract

摘要： 在模糊等式的框架下，引入Ω-BCK代数的概念. 首先，将BCK代数中的清晰等式用模糊等式取代，给出Ω-BCK代数的定义；其次，刻画Ω-BCK代数的子结构，并证明Ω-BCK子代数判定的充分必要条件；再次，利用模糊同余关系得到Ω-BCK代数与BCK代数的关系；最后，将BCK代数的偏序关系进行推广，定义Ω-BCK代数的E-偏序关系.

关键词: Ω-BCK代数, 完备格, 模糊等式, 模糊恒等式, 模糊子代数, E-偏序关系

Abstract: We introduced the concept of Ω-BCK algebras in the framework of fuzzy equalities. Firstly, we replaced the crisp equalities in BCK algebras with fuzzy equalities and gave the definition of Ω-BCK algebras. Secondly, we characterized the substructures of Ω-BCK algebras and proved the necessary and sufficient conditions for the determination of Ω-BCK subalgebras. Thirdly, by using fuzzy congruence relations, we obtained the relationship between Ω-BCK algebras and BCK algebras. Finally, we generalized the partial order relation of BCK algebras and defined the E-partial order relation of Ω-BCK algebras.

Key words: Ω-BCK algebra, complete lattice, fuzzy equality, fuzzy identity, fuzzy subalgebra, E-partial order , relation

中图分类号:

O159

刘芸, 周鑫, 陈良云. 基于模糊等式的Ω-BCK代数[J]. 吉林大学学报(理学版), 2026, 64(3): 545-0550.

LIU Yun, ZHOU Xin, CHEN Liangyun. Ω-BCK Algebras Based on Fuzzy Equalities[J]. Journal of Jilin University Science Edition, 2026, 64(3): 545-0550.

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