Possibilistic interpretation of fuzzy statistical tests

  • Olgierd Hryniewicz
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 87)


A new possibilistic method for the interpretation of the results of fuzzy statistical tests has been proposed. The concept of the observed test size (p-value, significance) has been generalised to the case of fuzzy data. Indices of the possibility and necessity of dominance have been used for the comparison of null and alternative hypotheses. An example from statistical quality control is given.


Fuzzy Number Fuzzy Random Variable Fuzzy Data Statistical Quality Control Acceptance Sampling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    Arnold, B.F. (1995). Statistical tests optimally meeting certain fuzzy requirements on the power function and on the sample size, Fuzzy Sets and Systems 75, 365–372.MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bickel, P.J. and Doksum, K.A. (1977). Mathematical Statistics. Basic Ideas and Selected Topics. Holden Day, Inc., San Francisco.zbMATHGoogle Scholar
  3. 3.
    Casals, M.R., Gil, M.A. and Gil, P. (1986). The fuzzy decision problem: an approach to the problem of testing statistical hypotheses with fuzzy information, Europ. Journ. of Oper. Res. 27, 371–382.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Delgado, M., Verdegay, J.L. and Vila, M.A. (1985). Testing fuzzy hypotheses. A Bayesian approach. In Approximate Reasoning in Expert Systems ( M.M. Gupta, A. Kandel, W. Bandler and J.B. Kiszka, Eds.). Elsevier, Amsterdam, 307–316.Google Scholar
  5. 5.
    Dubois, D. and Prade, H. (1983). Ranking fuzzy numbers in the setting of possibility theory, Inform. Sci. 30, 184–244.MathSciNetCrossRefGoogle Scholar
  6. 6.
    Dubois, D. and Prade, H. (1997). Qualitative possibility theory and its applications to reasoning and decision under uncertainty, Belgian Journal of Operations Research, Statistics and Computer Science 37, 5–28.MathSciNetzbMATHGoogle Scholar
  7. 7.
    Grzegorzewski, P. (2000). Testing statistical hypotheses with vague data, Fuzzy Sets and Systems 112, 501–510.MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Grzegorzewski, P. and Hryniewicz, O. (1997). Testing hypotheses in fuzzy environment, Mathware and Soft Computing 4, 203–217.zbMATHGoogle Scholar
  9. 9.
    Hryniewicz, O. (1994). Statistical decisions with imprecise data and requirements. In Systems Analysis and Decision Support in Economics and Technology ( R. Kulikowski, K. Szkatula, J. Kacprzyk, Eds.). Omnitech Press, Warsaw, 135–143.Google Scholar
  10. 10.
    Hryniewicz, O. (2000) Possibilistic interpretation of the results of statistical tests. Proc. 8ht International Conference IPMU, Madrid, vol. I, 215–219.Google Scholar
  11. 11.
    ISO 2859–2 (1985). Sampling procedures for inspection by attributes - Part 2: Sampling plans indexed by limiting quality (LQ) for isolated lot inspection.Google Scholar
  12. 12.
    Kruse, R. (1982). The strong law of large numbers for fuzzy random variables, Inform. Sci. 28, 233–241.MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Kruse, R. and Meyer, K.D. (1987). Statistics with Vague Data. Riedel, Dodrecht.zbMATHCrossRefGoogle Scholar
  14. 14.
    Kwakernaak, H. (1978). Fuzzy random variables, part I: definitions and theorems, Inform. Sci. 15, 1–15MathSciNetzbMATHCrossRefGoogle Scholar
  15. Kwakernaak, H. (1978). Fuzzy random variables, Part II: algorithms and examples for the discrete case, Inform. Sci. 17, 253–278.MathSciNetCrossRefGoogle Scholar
  16. 15.
    Lehmann, E.L. (1986). Testing Statistical Hypotheses, 2nd ed., J. Wiley & Sons, New York.zbMATHGoogle Scholar
  17. 16.
    Saade, J. (1994). Extension of fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems 63, 57–71.MathSciNetzbMATHCrossRefGoogle Scholar
  18. 17.
    Saade, J. and Schwarzlander, H. (1990). Fuzzy hypothesis testing with hybrid data, Fuzzy Sets and Systems 35, 197–212.zbMATHCrossRefGoogle Scholar
  19. 18.
    Son, J.Ch., Song, I. and Kim, H.Y. (1992). A fuzzy decision problem based on the generalized Neyman-Pearson criterion, Fuzzy Sets and Systems 47, 65–75.zbMATHCrossRefGoogle Scholar
  20. 19.
    Watanabe, N. and Imaizumi, T. (1993). A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems 53, 167–178.MathSciNetzbMATHCrossRefGoogle Scholar
  21. 20.
    Zadeh, L.A. (1978). Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems 1, 3–28.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Olgierd Hryniewicz
    • 1
  1. 1.Systems Research InstituteWarsawPoland

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