Author: Diwakar Prasad Baranwal
DOI Link: https://doi.org/10.70798/Bijmrd/03120026
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 pseudo-BCK 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: 231-242