Fuzzy Sets and Their Applications

This volume contains a systematic account of a new branch of mathematics, fuzzy sets, which seeks to overcome the problems of applying mathematics to the real world. Fuzzy models have been used for such diverse problems as weather forecasting, predictions of water flow in rivers and flooding, and capital cost estimates in the chemical industry. This monograph provides a detailed exposition of the fuzzy set theory and some of its applications, containing many of the author's original results together with those of other Czech scientists. The first section of the book gives information on fuzzy set theory, fuzzy logic and the model of natural language semantics, which together form an integrated theory based on the unified structure of membership degrees. The second section of the text presents selected applications of fuzzy set theory, such as decision-making, fuzzy systems, algorithms and mathematical programming. The book concludes with various problems, such as determination of the membership function and mathematical foundations of the theory. This book should be of interest to postgraduates and researchers in pure and applied mathematics, and specialists in artificial intelligence, computational linguistics, systems engineering and expert systems.