Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference

1. Front Matter

   Pages i-xi

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2. Introduction

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 1-3

3. Modeling Uncertainty

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 5-16

4. Capacities and the Choquet Functional

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 17-49

5. Information Measures

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 51-65

6. Calculus of Fuzzy Concepts

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 67-105

7. Fuzzy Measures and Integrals

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 107-171

8. Decision Making

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 173-212

9. Subjective Multicriteria Evaluation

   • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

   Pages 213-260

10. Pattern Recognition and Computer Vision

    • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

    Pages 261-292

11. Identification and Interpretation of Fuzzy Measures

    • Michel Grabisch, Hung T. Nguyen, Elbert A. Walker

    Pages 293-321

12. Back Matter

    Pages 323-348

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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.

• Mathematica
• Pattern Recognition
• cognition
• decision making
• modeling

`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)

• Thomson-CSF-Central Research Laboratory, Orsay, France

  Michel Grabisch

• Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

  Hung T. Nguyen, Elbert A. Walker

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