Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference

This decade has witnessed increasing interest in fuzzy technology both from academia and industry. It is often said that fuzzy theory is easy and simple so that engineers can progress quickly to real applications. However, the lack of knowledge of design methodologies and the theoretical results of fuzzy theory have often caused problems for design engineers. The aim of this book is to provide a rigorous background for uncertainty calculi, with an emphasis on fuzziness. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference is primarily about the type of knowledge expressed in a natural language, that is, in linguistic terms. The approach to modeling such knowledge is based upon the mathematical theory of uncertainty related to the fuzzy measures and integrals and their applications. The book consists of two parts: Chapters 2--6 comprise the theory, and applications are offered in Chapters 7--10. In the theory section the exposition is mathematical in nature and gives a complete background on uncertainty measures and integrals, especially in a fuzzy setting. Applications concern recent ones of fuzzy measures and integrals to problems such as pattern recognition, decision making and subjective multicriteria evaluations.