Author: Diwakar Prasad Baranwal
DOI Link: https://doi.org/10.70798/PP/020400021
Abstract: Fuzzy algebra has emerged as a powerful extension of classical algebraic systems by incorporating graded membership and uncertainty. This review paper presents a comprehensive overview of the development of fuzzy algebra, focusing on fuzzy groups, fuzzy rings, and fuzzy algebraic logic structures such as BCK, BCI, and pseudoBCK algebras. The paper highlights key definitions, known results, and major theoretical advances reported in the literature, along with recent trends toward intrinsic, membership-based formulations. Special emphasis is given to quotient constructions, homomorphism theorems, and fuzzy filters in implication-based algebras. The review also discusses open problems and future research directions, positioning fuzzy algebra as a mature and unified mathematical framework for reasoning under uncertainty.
Keywords: Fuzzy Algebra, Fuzzy Groups, Fuzzy Rings, Fuzzy Ideals, Fuzzy Filters, Pseudo-Bck Algebras, Algebraic Logic.
Page No: 142-154