基于模糊等式的Ω-BCK代数

Journal of Jilin University Science Edition ›› 2026, Vol. 64 ›› Issue (3): 545-0550.

Previous Articles Next Articles

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

Abstract

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

CLC Number:

O159

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.

[1]	XU Xiaodi, LI Chunhua. Asymptotic Behavior of Derivative Nonlinear Schrodinger Systems with Time-Dependent Potentials in High-Dimensional Space [J]. Journal of Jilin University Science Edition, 2026, 64(3): 475-0482.
[2]	HU Huangshui, CAO Yu, LIU Mingyang, KANG Qi’er. Facial Expression Recognition Based on Local Correlation and Multi-scale Spatial Attention [J]. Journal of Jilin University Science Edition, 2026, 64(1): 104-0112.
[3]	FENG Xinyang, ZHANG Mohua, LI Yinfei. Machine Learning Based Asymmetric Geometric Correction Method for Distorted Images [J]. Journal of Jilin University Science Edition, 2025, 63(5): 1447-1453.
[4]	ZHANG Liyan, LIU Zengli, PENG Yi. Speech Enhancement Method Based on Improved Wavelet Threshold and Optimized VMD Algorithm [J]. Journal of Jilin University Science Edition, 2025, 63(2): 608-0621.
[5]	HE Shan, XIAO Xi, ZHANG Jialing. Simulation of Entity Relationship Extraction Model for Domain Knowledge Graph [J]. Journal of Jilin University Science Edition, 2025, 63(2): 465-0471.
[6]	YANG Hang, ZHANG Xiaocheng, ZHANG Yonggang. Data Analysis and Relation Extraction Model Construction Based on Entity Category Information [J]. Journal of Jilin University Science Edition, 2025, 63(2): 428-0436.
[7]	MENG Lingxin, CAI Hua, FU Qiang, YI Yaxi, LIU Guangwen, ZHANG Chenjie. Multi-hop Knowledge Graph Question Answering Algorithm Based on Relational Memory and Path Information [J]. Journal of Jilin University Science Edition, 2024, 62(6): 1391-1400.
[8]	HUANG Xiaofeng, ZOU Yuhao, YUAN Xiaohui. Subsampling Algorithm for Quantile Regression Based on Optimal Decorrelation Score [J]. Journal of Jilin University Science Edition, 2024, 62(5): 1102-1112.
[9]	ZHANG Qiang, ZENG Junwei, CHEN Rui. Entity-Relation Joint Extraction Model Based on Contrastive Learning and Gradient Penalty [J]. Journal of Jilin University Science Edition, 2024, 62(5): 1155-1162.
[10]	DONG Sa, OUYANG Ruochuan, XU Haixiao, LIU Jie, LIU Dayou, LI Tingting, WANG Xinlu. Introducing Class-Distribution Relational Neighbor Classifier with Activation Spreading [J]. Journal of Jilin University Science Edition, 2024, 62(4): 915-922.
[11]	LI Xin, LIANG Yongling. Multi-source Heterogeneous Data Fusion Model Based on Fuzzy Mathematics [J]. Journal of Jilin University Science Edition, 2024, 62(3): 691-696.
[12]	LIU Xu, YANG Hang, ZHANG Xiaocheng, ZHANG Yonggang. Chinese Relation Extraction Method Based on Relation Filtering and Entity Pair Tagging [J]. Journal of Jilin University Science Edition, 2023, 61(5): 1095-1102.
[13]	JI Bonan, ZHANG Yonggang. Few-Shot Relation Extraction Model Based on Attention Mechanism Induction Network [J]. Journal of Jilin University Science Edition, 2023, 61(4): 845-852.
[14]	DING Guipeng, TAO Gang, PANG Chunqiao, WANG Xiaofeng, DUAN Guiru. Lightweight Siamese Network Target Tracking Algorithm Based on Ananchor Free [J]. Journal of Jilin University Science Edition, 2023, 61(4): 890-898.
[15]	SONG Hanyu, OUYANG Dantong, YE Yuxin. Lightweight Relation Extraction Based on Positive Soft Labels [J]. Journal of Jilin University Science Edition, 2023, 61(2): 317-324.

Ω-BCK Algebras Based on Fuzzy Equalities

PDF (PC)

Like

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0