An introduction to fuzzy logic and fuzzy sets. (English) Zbl 0985.03002

Buckley, James J.; Eslami, Esfandiar

Advances in Soft Computing. Heidelberg: Physica-Verlag. x, 285 p. (2002).

This book is an undergraduate introduction to the theory of fuzzy sets, giving basic information for beginners. The book is divided into 16 chapters. Its core consists of chapter 3, introducing fuzzy sets, chapter 4, presenting fuzzy numbers, chapters 5 and 6, dealing with fuzzy equations and inequalities, and chapters 7 and 8, discussing fuzzy relations and fuzzy functions.
Some specific topics (fuzzy plane geometry, fuzzy trigonometry, systems of fuzzy linear equations) are treated in the subsequent chapters 9-11. The remaining chapters present alternative and complementary concepts of non-probabilistic uncertainty modeling, namely possibility theory, neural nets, approximate reasoning and genetic algorithms. Finally, the problems of fuzzy optimization are included.
Each chapter ends with a set of relevant problems and exercises. Prerequisites for this book are basic algebra, trigonometry and elementary differential calculus. The book can be recommended as a good textbook for students and beginners in computer science, engineering or economics interested in non-probabilistic uncertainty modeling.

Reviewer: R.Mesiar (Bratislava)

MSC:

03-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematical logic and foundations
03B52	Fuzzy logic; logic of vagueness
03E72	Theory of fuzzy sets, etc.
68T37	Reasoning under uncertainty in the context of artificial intelligence
94D05	Fuzzy sets and logic (in connection with information, communication, or circuits theory)

Keywords:

fuzzy logic; fuzzy inequalities; fuzzy plane geometry; fuzzy sets; fuzzy numbers; fuzzy equations; fuzzy relations; fuzzy functions; fuzzy trigonometry; systems of fuzzy linear equations; uncertainty; possibility theory; neural nets; approximate reasoning; genetic algorithms; fuzzy optimization; textbook