A Review of Fuzzy Subring Algebra: Theories and Case Studies

Abstract

The inherent uncertainty in our understanding of the world presents substantial challenges for standard mathematical approaches. Fuzzy algebraic structures,building on Zadeh’s foundational work in 1965, offer a specialized means to manage this uncertainty. This paper provides a comprehensive review of developments in fuzzy subring algebra, examining key elements such as fuzzy subrings, fuzzy ideals, fuzzy zero divisors, and the application of fuzzy polynomials and matrices. Through practical case studies in areas like medical diagnostics and agriculture, this study demonstrates the flexibility and crucial role of fuzzy algebra in addressing uncertainty. This paper serves as a valuable resource for researchers and practitioners seeking to navigate complex uncertainties using fuzzy algebraic frameworks.