Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference: 30 (Theory and Decision Library B, 30) - Hardcover

Grabisch, Michel; Hung T. Nguyen; Walker, E.A.

Hardcover

ISBN 10: 0792331753 ISBN 13: 9780792331759

Publisher: Springer, 1994

Synopsis

With the vision that machines can be rendered smarter, we have witnessed for more than a decade tremendous engineering efforts to implement intelligent sys­ tems. These attempts involve emulating human reasoning, and researchers have tried to model such reasoning from various points of view. But we know precious little about human reasoning processes, learning mechanisms and the like, and in particular about reasoning with limited, imprecise knowledge. In a sense, intelligent systems are machines which use the most general form of human knowledge together with human reasoning capability to reach decisions. Thus the general problem of reasoning with knowledge is the core of design methodology. The attempt to use human knowledge in its most natural sense, that is, through linguistic descriptions, is novel and controversial. The novelty lies in the recognition of a new type of un­ certainty, namely fuzziness in natural language, and the controversality lies in the mathematical modeling process. As R. Bellman [7] once said, decision making under uncertainty is one of the attributes of human intelligence. When uncertainty is understood as the impossi­ bility to predict occurrences of events, the context is familiar to statisticians. As such, efforts to use probability theory as an essential tool for building intelligent systems have been pursued (Pearl [203], Neapolitan [182)). The methodology seems alright if the uncertain knowledge in a given problem can be modeled as probability measures.

About this title

Review

`It provides the foundations of uncertainty calculus that enables one to complement conventional system theory. ... I can highly recommend the book to those interested in the new developments in this interesting area and who are not afraid of some mathematics.'
International Journal of Electrical Engineering Education, 33:3 (1996)

Synopsis

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 modelling 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.

Edition details

• Publisher: Springer
• Publication date: 1994
• Language: English
• ISBN 10: 0792331753
• ISBN 13: 9780792331759
• Binding: Hardcover
• Number of pages: 362