Exploring Fuzzy Algebraic Concepts: From Theory to Applications

Abstract

Uncertainty pervades our understanding of the world, presenting formidable chal- lenges to traditional mathematical frameworks. Fuzzy algebraic concepts offer a specialized approach to address this uncertainty, with roots tracing back to Zadeh’s seminal work in 1965. This paper provides a comprehensive review of the evolution of fuzzy algebra. It covers various aspects of the fuzzification of algebraic structures, such as fuzzy subrings and fuzzy ideals, the characterization of fuzzy zero divisors, and applications of fuzzy polynomials and fuzzy matrices. Through real-life case studies in domains like medical diagnosis and agricultural analysis, the study underscores the versatility and importance of fuzzy algebra in addressing uncertainty. Aimed at researchers and practitioners, this paper serves as a valuable resource for navigating the complexities of uncertainty using fuzzy algebraic concepts.