A Survey of Fuzzy and Uncertain Concepts in Applied Mathematics

Real-world systems frequently involve vagueness, partial truth, incomplete information, and various forms of indeterminacy. To address these challenges, numerous generalized set-theoretic frameworks have been developed, including fuzzy sets, intuitionistic fuzzy sets, neutrosophic sets, plithogenic sets, and related extensions. These approaches provide powerful tools for modeling uncertainty in a mathematically rigorous and flexible manner. This book presents a comprehensive and systematic survey of fuzzy and uncertainty-oriented concepts in applied mathematics. It brings together a wide range of theoretical frameworks and applications, spanning discrete structures, algebraic systems, analytical models, and quantitative methods. By organizing these diverse topics within a unified perspective, the work clarifies their underlying mathematical structures, highlights their interrelationships, and compares their expressive capabilities. The book aims to serve both as a reference and as a conceptual guide, offering readers a coherent overview of the landscape of uncertainty modeling. It emphasizes the role of advanced frameworks—particularly neutrosophic and plithogenic systems—in extending classical fuzzy theory and enabling more refined representations of complex, inconsistent, and multi-attribute information in applied mathematics.