From: Michel Grabisch Newsgroups: comp.ai.fuzzy Subject: new book Date: 16 Dec 1994 17:27:20 GMT Dear Fuzzy Netters, I am pleased to inform you on the publication of a new book by Kluwer Acad., on uncertainty modeling by fuzzy sets and fuzzy measures. (may be it will be of some help in the probability vs. fuzzy debate!) ******************************************************************************* ANNOUNCEMENT OF A NEW BOOK ******************************************************************************* FUNDAMENTALS OF UNCERTAINTY CALCULI ----------------------------------- with APPLICATIONS to FUZZY INFERENCE ------------------------------------ Michel GRABISCH, Hung T. NGUYEN, Elbert A. WALKER ------------------------------------------------- KLUWER ACADEMIC PUBLISHERS Theory and Decision Library Series B: Mathematical and Statistical Methods ---------------------------------------------- TDLB 30, 1995, ISBN 0-7923-3175-3 346 pages ******************************************************************************* 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 fuzzy measures and integrals and their applications. The book consists of two parts: Chapter 2-6 comprise the theory, and applications are offered in chapter 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. CONTENTS -------- Preface 1. Introduction 2. Modeling Uncertainty 2.1 Randomness and the calculus of probabilities 2.2 Uncertainty in quantum mechanics 2.3 Entropy and information 2.4 Degrees of belief 2.5 Imprecision, vagueness, and fuzziness 2.6 Non-additive set functions in uncertainty 3. Capacities and the Choquet Functional 3.1 Capacities in R^d 3.2 Abstract capacities 3.3 Topological concepts 3.4 Capacities on topological spaces 3.5 Classification of capacities 3.6 Capacities and belief functions 3.6.1 the finite case 3.6.2 the continuous case 3.7 The Choquet functional 3.7.1 an approximation problem 3.7.2 the Choquet functional 3.7.3 properties of the Choquet integral 3.8 Capacities in Bayesian statistics 3.9 A decision making problem 4. Information Measures 4.1 Various aspects of information 4.2 Generalized information measures 4.3 Operations of composition 4.4 Information measures of type Inf 4.5 Connection with capacities 5. Calculus of Fuzzy Concepts 5.1 Mathematical modeling of fuzzy concepts 5.2 Calculus of fuzzy quantities 5.3 Reasoning with fuzzy concepts 5.3.1 t-norms 5.3.2 t-conorms 5.3.3 negations 5.3.4 implication operators 5.3.5 approximate reasoning 5.4 Robustness of fuzzy logic 5.5 Approximation capability of fuzzy systems 5.6 Fuzzy inference 6. Fuzzy measures and integrals 6.1 What are fuzzy measures, and why? 6.2 Fuzzy measures - definitions and examples 6.3 Related issues 6.4 Conditional fuzzy measures 6.5 Choquet integral - meaning and motivation 6.6 The Sugeno integral 6.7 The Choquet integral as a fuzzy integral 6.7.1 notes on comonotonic additivity 6.7.2 comonotonic additivity of functionals 6.8 Further topics 6.8.1 the fuzzy t-conorm integral 6.8.2 some properties of fuzzy integrals 6.8.3 the duality property of fuzzy integrals 6.8.4 on fuzzy measures of fuzzy events 6.8.5 properties of extended fuzzy measures 7. Decision Making 7.1 General framework for decision making 7.2 Non-additive expected utility theory 7.3 Non-additive multiattribute utility theory 7.4 Aggregation in multicriteria decision making 7.4.1 equivalence relations between operators 7.4.2 equivalence classes of operators 7.4.3 equivalence class of the Choquet integral 7.4.4 equivalence class of the Sugeno integral 7.4.5 equivalence class of fuzzy t-conorm integrals 7.5 Fuzzy Analytic Hierarchy Process 8. Subjective Multicriteria Evaluation 8.1 Statement of the problem 8.1.1 marginal evaluation 8.1.2 global evaluation 8.2 Previous approaches 8.3 Fuzzy integral as a new aggregation tool 8.3.1 properties for aggregation 8.3.2 characterization of fuzzy integrals 8.3.3 set relations between fuzzy integrals and other connectives 8.3.4 additivity of fuzzy measures and preferential independence 8.4 Evaluation with fuzzy values 8.5 Practical examples 8.5.1 evaluation of tiles 8.5.2 model of expression grade for face graphs 8.5.3 prediction of wood strength 8.5.4 analysis of public attitude towards the use of nuclear energy 8.5.5 evaluation of printed color images 8.5.6 design of speakers 8.5.7 human reliability analysis 9. Pattern Recognition and Computer Vision 9.1 The use of fuzzy set theory 9.2 Information fusion by fuzzy integrals 9.2.1 consensus in probability theory 9.2.2 consensus in possibility theory 9.2.3 the situation of fuzzy integrals 9.3 Application to pattern recognition 9.3.1 introduction 9.3.2 the approach of Tahani-Keller 9.3.3 the approach of Grabisch-Sugeno 9.3.4 the multiclassifier approach 9.4 Image processing and computer vision 9.4.1 image segmentation 9.4.2 high level vision 10. Identification and Interpretation of Fuzzy Measures 10.1 Interpretation by analysis of the semantics 10.1.1 introduction 10.1.2 early attempts: the necessity coefficients of Ishii and Sugeno 10.1.3 interpretation based on the Shapley value 10.1.4 interaction between criteria 10.2 Identification using learning samples 10.2.1 introduction 10.2.2 monotonicity relations in a fuzzy measure 10.2.3 minimization of the error criterion 10.2.4 heuristic algorithm of Mori and Murofushi 10.2.5 Bayesian-like learning 10.3 Interactive optimization Bibiliography Index