Fuzzy Sets and Fuzzy Logic: Theory and ApplicationsThe primary purpose of this book is to provide the reader with a comprehensive coverage of theoretical foundations of fuzzy set theory and fuzzy logic, as well as a broad overview of the increasingly important applications of these novel areas of mathematics. Although it is written as a text for a course at the graduate or upper division undergraduate level, the book is also suitable for self-study and for industry-oriented courses of continuing education. No previous knowledge of fuzzy set theory and fuzzy logic is required for understanding the material covered in the book. Although knowledge of basic ideas of classical (nonfuzzy) set theory and classical (two-valued) logic is useful, fundamentals of these subject areas are briefly overviewed in the book. In addition, basic ideas of neural networks, genetic algorithms, and rough sets are also explained. This makes the book virtually self-contained. Throughout the book, many examples are used to illustrate concepts, methods, and generic applications as they are introduced. Each chapter is followed by a set of exercises, which are intended to enhance readers' understanding of the material presented in the chapter. Extensive and carefully selected bibliography, together with bibliographical notes at the end of each chapter and a bibliographical subject index, is an invaluable resource for further study of fuzzy theory and applications. |
Contents
THEORY | 1 |
FUZZY SETS VERSUS CRISP SETS | 35 |
OPERATIONS ON FUZZY SETS | 50 |
Copyright | |
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Common terms and phrases
a-cuts algorithm analysis applications appropriate Approximate Reasoning assignment associated Assume Axiom basic calculate called characterized classical concept condition Consider crisp Cybernetics decision defined denote described determine discussed distribution elements employed engineering equation equivalence evidence example exists expert expressed Figure formula fuzzy complement fuzzy control fuzzy logic fuzzy numbers fuzzy relation fuzzy set theory given Hence IEEE Trans illustrate implication increasing inference input Intern intersection involved knowledge linguistic mathematical matrix means measures membership functions membership grade method neural networks obtain operations ordering output parameters particular pattern possibilistic possibility principle probability problem Proof properties proposition referred relevant represented respectively rules satisfies Sciences Sets and Systems shown solution specific standard t-norms Table Theorem truth types uncertainty universal set usually values variable various Yager