© 1988

Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making

  • Janusz Kacprzyk
  • Mario Fedrizzi

Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 310)

Table of contents

  1. Front Matter
    Pages I-IX
  2. Essay on the History of the Development of Many-Valued Logics and Some Related Topics

  3. Introductory Sections

  4. Basic Theoretical Issues

  5. Fuzzy Sets Involving Random Aspects

    1. I. B. Turksen
      Pages 168-183
    2. K. Hirota
      Pages 184-196
  6. Decision — Making — Related Models Involving Fuzziness and Randomness

    1. Ernest Czogała, Peter L. Disney
      Pages 215-226
    2. Augustine O. Esogbue, Mario Fedrizzi, Janusz Kacprzyk
      Pages 266-285

About this book


In the literature of decision analysis it is traditional to rely on the tools provided by probability theory to deal with problems in which uncertainty plays a substantive role. In recent years, however, it has become increasingly clear that uncertainty is a mul­ tifaceted concept in which some of the important facets do not lend themselves to analysis by probability-based methods. One such facet is that of fuzzy imprecision, which is associated with the use of fuzzy predicates exemplified by small, large, fast, near, likely, etc. To be more specific, consider a proposition such as "It is very unlikely that the price of oil will decline sharply in the near future," in which the italicized words play the role of fuzzy predicates. The question is: How can one express the mean­ ing of this proposition through the use of probability-based methods? If this cannot be done effectively in a probabilistic framework, then how can one employ the information provided by the proposition in question to bear on a decision relating to an investment in a company engaged in exploration and marketing of oil? As another example, consider a collection of rules of the form "If X is Ai then Y is B,," j = 1, . . . , n, in which X and Yare real-valued variables and Ai and Bi are fuzzy numbers exemplified by small, large, not very small, close to 5, etc.


Probability theory Random variable decision making fuzzy sets linear optimization optimization simulation

Editors and affiliations

  • Janusz Kacprzyk
    • 1
  • Mario Fedrizzi
    • 2
  1. 1.Systems Research InstitutePolish Academy of SciencesWarsawPoland
  2. 2.Institute of InformaticsUniversity of TrentoTrentoItaly

Bibliographic information

  • Book Title Combining Fuzzy Imprecision with Probabilistic Uncertainty in Decision Making
  • Editors Mario Fedrizzi
  • Series Title Lecture Notes in Economics and Mathematical Systems
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1988
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-50005-6
  • eBook ISBN 978-3-642-46644-1
  • Series ISSN 0075-8442
  • Edition Number 1
  • Number of Pages IX, 399
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Operations Research/Decision Theory
  • Buy this book on publisher's site
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