Survey of Fuzzy and Uncertain Logical Operators

This book presents a comprehensive and systematic survey of fuzzy and uncertain logical operators developed to model reasoning under imprecision, incompleteness, and partial reliability. Building upon foundational frameworks such as fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, vague sets, and hesitant fuzzy sets, the work focuses on the extension of classical logical connectives into uncertainty-aware environments. It provides a structured overview of a wide range of operators, including basic set-theoretic operations, conjunctive–disjunctive families (t-norms, t-conorms, uninorms), relational and inferential operators, aggregation mechanisms, and integral-based models such as Choquet and Sugeno integrals. The book organizes these operators within a unified uncertain-set framework, clarifying their mathematical properties, interrelationships, and functional roles in reasoning processes. By developing a coherent taxonomy and highlighting connections across different uncertainty paradigms, it establishes a solid theoretical foundation for future research. The survey also emphasizes applications in approximate reasoning, decision-making systems, control theory, and artificial intelligence, making it a valuable reference for both theoretical investigation and practical implementation of uncertainty-based logic.