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Tests of Statistical Hypotheses with Respect to a Fuzzy Set

Author

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  • P. Pandian
  • D. Kalpanapriya

Abstract

Tests of statistical hypotheses with crisp data using small samples are extended to with membership function of the fuzzy sets. The t-test statistic and the F-test statistic with respect to fuzzy sets are defined using the membership grades of the fuzzy sets. The rules for taking decision about the hypotheses are provided. In the proposed tests, the optimistic and pessimistic approach, h-level set, alpha-cut and fuzzy interval are not used. Numerical examples are provided for understanding the proposed testing procedures. The proposed tests of hypotheses may be useful to decision makers who are handling real life problems involving linguistic variables / fuzzy sets for taking suitable decisions in an acceptable manner.

Suggested Citation

  • P. Pandian & D. Kalpanapriya, 2013. "Tests of Statistical Hypotheses with Respect to a Fuzzy Set," Modern Applied Science, Canadian Center of Science and Education, vol. 8(1), pages 1-25, February.
    • Handle: RePEc:ibn:masjnl:v:8:y:2013:i:1:p:25
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    References listed on IDEAS

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    1. Viertl, Reinhard, 2006. "Univariate statistical analysis with fuzzy data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 133-147, November.
    2. Casals, M. R. & Gil, M. A. & Gil, P., 1986. "The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information," European Journal of Operational Research, Elsevier, vol. 27(3), pages 371-382, December.
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    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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