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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 76))

Abstract

The paper is devoted to nonclassical approaches to hypotheses testing. We consider testing statistical hypotheses in fuzzy environment, i.e. tests with vague data, tests for fuzzy hypotheses and tests for fuzzy hypotheses with vague data. We also present a possibilistic interpretation of statistical tests.

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References

  • Arnold B. F. (1996), An approach to fuzzy hypothesis testing, Metrika 44, 119–126.

    Article  Google Scholar 

  • Arnold B. F. (1998), Testing fuzzy hypotheses with crisp data, Fuzzy Sets and Systems 94, 323–333.

    Google Scholar 

  • Dubois D., Prade H. (1980), Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.

    Google Scholar 

  • Dubois, D., Prade H. (1983), Ranking fuzzy numbers in the setting of possibility theory, Information Sciences 30, 184–244.

    Article  Google Scholar 

  • Dubois, D., 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.

    Google Scholar 

  • Grzegorzewski P. (1998), Fuzzy tests — defuzzification and randomization,Fuzzy Sets and Systems (to appear).

    Google Scholar 

  • Grzegorzewski, P. (2000a), Testing statistical hypotheses with vague data, Fuzzy Sets and Systems 112, 501–510.

    Article  Google Scholar 

  • Grzegorzewski, P. (2000b), Testing fuzzy hypotheses with vague data (submitted).

    Google Scholar 

  • Grzegorzewski, P.,Hryniewicz O. (1997), Testing hypotheses in fuzzy environment,Mathware and Soft Computing 4 203–217.

    Google Scholar 

  • Hryniewicz, O. (1994), Statistical decisions with imprecise data and requirements, In: R. Kulikowski, K. Szkatula, J. Kacprzyk (Eds.), Systems Analysis and Decision Support in Economics and Technology, Omnitech Press, Warsaw, 135–143.

    Google Scholar 

  • Hryniewicz, O. (2000a), Possibilistic interpretation of the results of statistical tests, Proc. of the Eight International Conference IPMU, Madrid

    Google Scholar 

  • Hryniewicz, O. (2000b), Possibilistic interpretation of fuzzy statistical tests (submitted for publication).

    Google Scholar 

  • Kruse R. (1982), The strong law of large numbers for fuzzy random variables,Inform. Sci. 28 233–241.

    Article  Google Scholar 

  • Kruse R., Meyer K. D. (1987), Statistics with Vague Data,D. Riedel Publishing Company.

    Google Scholar 

  • Kwakernaak H. (1978), Fuzzy random variables, Part I: Definitions and theorems,Inform. Sci. 15 1–15.

    Article  Google Scholar 

  • Kwakernaak H. (1978), Fuzzy random variables, Part II: Algorithms and examples for the discrete case,Inform. Sci. 17 253–278.

    Article  Google Scholar 

  • Lehmann E. L. (1986), Testing Statistical Hypotheses, Wiley, New York, 2nd ed.

    Google Scholar 

  • Puri M. L., Ralescu D. A. (1986), Fuzzy random variables, J. Math. Anal. Appl. 114, 409–422.

    Article  Google Scholar 

  • Taheri S.M., Behboodian J (1999), Neyman—Pearson lemma for fuzzy hypotheses testing, Metrika 49, 3–17.

    Article  Google Scholar 

  • Watanabe N., Imaizumi T (1993), A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems 53, 167–178.

    Article  Google Scholar 

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© 2001 Physica-Verlag Heidelberg

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Grzegorzewski, P., Hryniewicz, O. (2001). Soft Methods in Hypotheses Testing. In: Ruan, D., Kacprzyk, J., Fedrizzi, M. (eds) Soft Computing for Risk Evaluation and Management. Studies in Fuzziness and Soft Computing, vol 76. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-1814-7_4

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  • DOI: https://doi.org/10.1007/978-3-7908-1814-7_4

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-662-00348-0

  • Online ISBN: 978-3-7908-1814-7

  • eBook Packages: Springer Book Archive

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