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Fuzzy Sets Theory and Applications

  • André Jones
  • Arnold Kaufmann
  • Hans-Jürgen Zimmermann

Part of the NATO ASI Series book series (ASIC, volume 177)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Some theoretical aspects

    1. Front Matter
      Pages 1-1
    2. R. Lowen
      Pages 3-38
    3. Anio O. Arigoni
      Pages 61-68
    4. Ulrich Höhle
      Pages 69-76
  3. From theory to applications

    1. Front Matter
      Pages 77-77
    2. H.-J. Zimmermann
      Pages 99-114
    3. R. R. Yager
      Pages 115-131
    4. J. F. Baldwin
      Pages 133-170
  4. Various particular applications

    1. Front Matter
      Pages 231-231
    2. R. Degani, G. Bortolan
      Pages 317-329
    3. Elie Sanchez
      Pages 331-347
    4. A. Jones
      Pages 349-395
  5. Back Matter
    Pages 397-403

About this book

Introduction

Problems in decision making and in other areas such as pattern recogni­ tion, control, structural engineering etc. involve numerous aspects of uncertainty. Additional vagueness is introduced as models become more complex but not necessarily more meaningful by the added details. During the last two decades one has become more and more aware of the fact that not all this uncertainty is of stochastic (random) cha­ racter and that, therefore, it can not be modelled appropriately by probability theory. This becomes the more obvious the more we want to represent formally human knowledge. As far as uncertain data are concerned, we have neither instru­ ments nor reasoning at our disposal as well defined and unquestionable as those used in the probability theory. This almost infallible do­ main is the result of a tremendous work by the whole scientific world. But when measures are dubious, bad or no longer possible and when we really have to make use of the richness of human reasoning in its variety, then the theories dealing with the treatment of uncertainty, some quite new and other ones older, provide the required complement, and fill in the gap left in the field of knowledge representation. Nowadays, various theories are widely used: fuzzy sets, belief function, the convenient associations between probability and fuzzines~ etc ••• We are more and more in need of a wide range of instruments and theories to build models that are more and more adapted to the most complex systems.

Keywords

Mathematica addition equation function logic mathematics probability theory theorem variable

Editors and affiliations

  • André Jones
    • 1
  • Arnold Kaufmann
    • 2
  • Hans-Jürgen Zimmermann
    • 3
  1. 1.Université Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.O.R. and M.S ConsultantGrenobleFrance
  3. 3.Institute of TechnologyAachenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-4682-8
  • Copyright Information Springer Science+Business Media B.V. 1986
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8581-6
  • Online ISBN 978-94-009-4682-8
  • Series Print ISSN 1389-2185
  • Buy this book on publisher's site
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