On FBZ-Algebras

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Submitted: March 23, 2026
Published: Apr 4, 2026
DOI: 10.29328/journal.jairi.1001015
Keywords:
FBZ-algebra, s-FBZ-algebra, L-algebra, Quotient FBZ-algebras, MSC(2020): 06F35, 03G25, 08A30

Main Article Content

Deng Fang-an
School of Mathematics and Statistics, YiLi Normal University, 835000 YiLi, China
Zhou Xin
School of Mathematics and Statistics, YiLi Normal University, 835000 YiLi, China
Zhang Liang
School of Mathematics and Statistics, YiLi Normal University, 835000 YiLi, China
Yi Lanlan
School of Mathematics and Statistics, YiLi Normal University, 835000 YiLi, China
Li Qiaoxia
School of Mathematics and Statistics, YiLi Normal University, 835000 YiLi, China

Abstract

This paper introduces the concept of FBZ-algebra as a generalization of fuzzy implication algebra and investigates its fundamental properties. We establish a sufficient condition for an FBZ-algebra to become a fuzzy implication algebra. Furthermore, we examine s-FBZ-algebras, filters, and upper sets, and explore the relationships between FBZ-algebras and other logical algebras, including GE-algebras, BE-algebras, KU-algebras, UP-algebras, GK-algebras, L-algebras, and BCK-algebras. Finally, the structure of quotient FBZ-algebras is constructed and analyzed.

Article Details

Fang-an, D., Xin, Z., Liang, Z., Lanlan, Y., & Qiaoxia, L. (2026). On FBZ-Algebras. Journal of Artificial Intelligence Research and Innovation, 021–035. https://doi.org/10.29328/journal.jairi.1001015
Research Articles

Copyright (c) 2026 Fang-an D, et al.

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