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The structure of fuzzy measure families induced by upper and lower probabilities

  • Andrew G. Bronevich
  • Alexander N. Karkishchenko
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 87)

Abstract

This paper contains researches in the fuzzy measure theory. Convex families of measures are considered, among them upper and lower probabilities, superadditive measures, and it is found that these measures can be represented by sums of primitive measures. It gives a possibility us to get important results due to algebraic structure of fuzzy measures on the finite algebra and to generalize the well-known theorems of the probability theory.

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References

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    Sugeno, M. (1972). Fuzzy measure and fuzzy integral, Trans. SICE 8, 95–102.Google Scholar
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    Dempster, A.P. (1967). Upper and lower probabilities induced by multivalued mapping, Ann. Math. Statist. 38, 325–339.MathSciNetzbMATHCrossRefGoogle Scholar
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    Shafer, G. (1976). A mathematical theory of evidence, Princeton University Press, Princeton.zbMATHGoogle Scholar
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    Dubois, D., and Prade, H. (1992). When upper probabilities are possibility measures, Fuzzy Sets and Systems 24, 279–300.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Andrew G. Bronevich
    • 1
  • Alexander N. Karkishchenko
    • 1
  1. 1.Taganrog State University of Radio-EngineeringTaganrogRussia

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