Fuzzy sets and fuzzy logic: A review of concepts, trends, and applications

In the mid-20th century fuzzy set theory and fuzzy logic developed by Lotfi A. Zadeh, emerged as powerful tools for modeling and reasoning under uncertainty, imprecision, and vagueness—features commonly encountered in real-world systems. This review provides a comprehensive overview of the theoretical foundations, key developments, and modern applications of fuzzy sets and fuzzy logic. It highlights seminal contributions, such as hesitant fuzzy sets, interval-valued intuitionistic fuzzy systems, and type-2 fuzzy logic, which have significantly enhanced the expressive power of classical fuzzy models. Recent advances, including the use of entropy-based decision-making methods, enhanced Karnik-Mendel algorithms for type-2 fuzzy sets, and integration with deep learning frameworks for uncertainty-aware forecasting, are also discussed. By surveying both foundational theories and contemporary innovations, this review underscores the continued relevance and adaptability of fuzzy logic in diverse fields such as decision-making, artificial intelligence, control systems, and data analysis.