Advertisement

Informative value of the possibilistic extension principle

  • Andrzej Piegat
Conference paper

Abstract

The present fuzzy arithmetic is based on possibilistic extension-principle of Zadeh. Fuzzy arithmetic is necessary to accomplish calculation in Computing with Words [6]. However, arithmetic operations carried out with the standard, possibilistic extension-principle often yield results which have small or no practical value. Sometimes the results are paradoxical ones. An example of such case is presented in the paper and also a new cardinality extension-principle in a version that enables regard for all additional constraints resulting from the context of the problem to be solved. The principle can be used only to fuzzy sets of numbers of probabilistic character which often occur in practical problems.

Key words

fuzzy arithmetic extension-principle constrained extension-principle Computing with Words 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bronstein I.N., Siemiendiajew K.A., 1996, Handbook of Mathematics, (in Polish), Wydawnictwo Naukowe PWN, WarszawaGoogle Scholar
  2. [2]
    Driankov D., Hellendorn M., Reinfrank M., 1993, An introduction to fuzzy control, Springer-Verlag, BerlinGoogle Scholar
  3. [3]
    Klirr G.L., 1997, Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems 91, pp.165–175MathSciNetCrossRefGoogle Scholar
  4. [4]
    Piegat A., 2001, Fuzzy modeling and control, A Springer-Verlag Company, Heidelberg-New YorkGoogle Scholar
  5. [5]
    Zadeh L.A., 1978, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, vol.3, No.28Google Scholar
  6. [6]
    Zadeh L.A., 2002, From computing with numbers to computing with words-From manipulation of measurements to manipulation of perceptions. Applied mathematics and computer science, vol.12, No.3, pp.307–324zbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2005

Authors and Affiliations

  • Andrzej Piegat
    • 1
  1. 1.Technical University of SzczecinSzczecinPoland

Personalised recommendations