Fuzzy Set Theory and Its Applications in Decision-Making Problems

Abstract

Fuzzy set theory is an important mathematical approach used to deal with uncertainty, vagueness, and imprecise information in complex systems. Unlike classical set theory, where elements either belong or do not belong to a set, fuzzy set theory allows elements to have varying degrees of membership. it particularly useful for modeling real-world situations where information is not always precise or clearly defined. Developed to address limitations in traditional mathematical models, fuzzy set theory has become widely applied in areas that require flexible decision-making methods. the role of fuzzy set theory in solving decision-making problems, especially in situations involving uncertainty and incomplete information. By using fuzzy logic and membership functions, decision-makers can evaluate multiple criteria and assign different levels of importance to various factors. This approach allows more realistic analysis of complex problems compared to traditional binary decision methods.