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Fuzzy probabilities and their applications to statistical inference

  • Probabilistic, Statistical and Informational Methods
  • Conference paper
  • First Online:
Advances in Intelligent Computing — IPMU '94 (IPMU 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 945))

Abstract

We discuss the issue of probability of a fuzzy event. The value of this probability is a fuzzy set rather than a number between zero and one. We compare this concept with the non fuzzy probability of a fuzzy event and we investigate some possible shortcomings of the latter. Explicit formulae for the fuzzy probability are given in both the discrete and continuous cases. In particular, in the discrete uniform case we relate the concepts of fuzzy probability and fuzzy cardinality. Our concept of fuzzy probability is applied to statistical inference and in particular to testing of hypotheses of the form “θ is F”, where F is a fuzzy set. The level of significance and the power function of testing procedures are evaluated as fuzzy probabilities.

On leave from the Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221, U.S.A.

Research supported by the National Science Foundation Grant INT-9303202.

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Author information

Authors and Affiliations

  1. Department of Systems Science, Tokyo Institute of Technology, 4259 Nagatsuta, Midori-ku, 227, Yokohama, Japan

    Dan Ralescu

  2. The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, 106, Tokyo, Japan

    Dan Ralescu

Authors
  1. Dan Ralescu
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Editor information

Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1995 Springer-Verlag Berlin Heidelberg

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Ralescu, D. (1995). Fuzzy probabilities and their applications to statistical inference. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Advances in Intelligent Computing — IPMU '94. IPMU 1994. Lecture Notes in Computer Science, vol 945. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0035953

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  • DOI: https://doi.org/10.1007/BFb0035953

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60116-6

  • Online ISBN: 978-3-540-49443-0

  • eBook Packages: Springer Book Archive

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