Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference

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

Part of the Theory and Decision Library book series (TDLB, volume 30)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 1-3
  3. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 5-16
  4. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 17-49
  5. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 51-65
  6. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 67-105
  7. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 107-171
  8. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 173-212
  9. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 213-260
  10. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 261-292
  11. Michel Grabisch, Hung T. Nguyen, Elbert A. Walker
    Pages 293-321
  12. Back Matter
    Pages 323-348

About this book

Introduction

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.

Keywords

Mathematica Pattern Recognition cognition decision making modeling

Authors and affiliations

  • Michel Grabisch
    • 1
  • Hung T. Nguyen
    • 2
  • Elbert A. Walker
    • 2
  1. 1.Thomson-CSF-Central Research LaboratoryOrsayFrance
  2. 2.Department of Mathematical SciencesNew Mexico State UniversityLas CrucesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-8449-4
  • Copyright Information Springer Science+Business Media B.V. 1995
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-4477-8
  • Online ISBN 978-94-015-8449-4
  • About this book
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