Mathematical Foundations of Fuzzy Sets Introduce yourself to the foundations of fuzzy logic with this easy-to-use guide Many fields studied are defined by imprecise information or high degrees of uncertainty. When this uncertainty derives from randomness, traditional probabilistic statistical methods are adequate to address it; more everyday forms of vagueness and imprecision, however, require the toolkit associated with 'fuzzy sets' and 'fuzzy logic'. Engineering and mathematical fields related to artificial intelligence, operations research and decision theory are now strongly driven by fuzzy set theory. Mathematical Foundations of Fuzzy Sets introduces readers to the theoretical background and practical techniques required to apply fuzzy logic to engineering and mathematical problems. It introduces the mathematical foundations of fuzzy sets as well as the current cutting edge of fuzzy-set operations and arithmetic, offering a rounded introduction to this essential field of applied mathematics. The result can be used either as a textbook or as an invaluable reference for working researchers and professionals. Mathematical Foundations of Fuzzy Sets offers thereader: * Detailed coverage of set operations, fuzzification of crisp operations, and more * Logical structure in which each chapter builds carefully on previous results * Intuitive structure, divided into 'basic' and 'advanced' sections, to facilitate use in one- or two-semester courses Mathematical Foundations of Fuzzy Sets is essential for graduate students and academics in engineering and applied mathematics, particularly those doing work in artificial intelligence, decision theory, operations research, and related fields.