Soft Computing

, Volume 13, Issue 6, pp 617–625 | Cite as

Testing fuzzy hypotheses based on fuzzy test statistic

Original Paper

Abstract

A new approach for testing fuzzy parametric hypotheses based on fuzzy test statistic is introduced. First, we define some models representing the extended versions of the simple, the one-sided and the two-sided crisp hypotheses to the fuzzy ones. Then, we provide a confidence interval for interested parameter, and using α-cuts of the fuzzy null hypothesis, we construct the related fuzzy test statistic. Finally, by introducing a credit level, we can decide to accept or reject the fuzzy hypothesis. The method is applied to test the fuzzy hypotheses for the mean of a normal distribution, the variance of a normal distribution, and the mean of a Poisson distribution.

Keywords

Credit level Fuzzy hypothesis Fuzzy test statistic Testing hypothesis 

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References

  1. Arnold BF (1996) An approach to fuzzy hypothesis testing. Metrika 44: 119–126CrossRefMathSciNetMATHGoogle Scholar
  2. Arnold BF (1998) Testing fuzzy hypothesis with crisp data. Fuzzy Sets Syst 94: 323–333CrossRefMATHGoogle Scholar
  3. Brown LD, Cai T, DusGupta A (2003) Interval estimation in exponential families. Stat Sin 13: 19–49MATHGoogle Scholar
  4. Buckley JJ (2004) Fuzzy statistics: hypothesis testing. Soft Comput 9: 512–518CrossRefGoogle Scholar
  5. Buckley JJ (2005) Fuzzy statistics. Springer, HeidelbergGoogle Scholar
  6. Delagado M, Verdegay JL, Vila MA (1985) Testing fuzzy-hypotheses, a Bayesian approach. In: Gupta MM et al. (ed) Approximate reasoning in expert systems. North-Holland, Amsterdam, pp 307–316Google Scholar
  7. Denoeux T, Masson MH, He′bert PA (2005) Nonparametric rank-based statistics and significance tests for fuzzy data. Fuzzy Sets Syst 153: 1–28CrossRefMathSciNetMATHGoogle Scholar
  8. Desimpelaere C, Marchant T (2007) An empirical test of some measurement-theoretic axioms for fuzzy sets. Fuzzy Sets Syst 158: 1348–1359CrossRefMathSciNetGoogle Scholar
  9. Finney RL, Thomas GB (1994) Calculus, 2nd edn. Addison Wesley, New YorkGoogle Scholar
  10. Hryniewicz O (2006) Possibilitic decisions and fuzzy statistical tests. Fuzzy Sets Syst 157: 2665–2673CrossRefMathSciNetMATHGoogle Scholar
  11. Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic theory and applications. Prentic-Hall, Englewood Cliffs, NJMATHGoogle Scholar
  12. Taheri SM, Behboodian J (1999) Neyman–Pearson Lemma for fuzzy hypothesis testing. Metrika 49: 3–17CrossRefMathSciNetMATHGoogle Scholar
  13. Taheri SM, Behboodian J (2001) A Bayesian approach to fuzzy hypotheses testing. Fuzzy Sets Syst 123: 39–48CrossRefMathSciNetMATHGoogle Scholar
  14. Taheri SM, Behboodian J (2006) On Bayesian approach to fuzzy hypotheses testing with fuzzy data. Ital J Pure Appl Math 19: 139–154MathSciNetMATHGoogle Scholar
  15. Thompson EA, Geyer CJ (2007) Fuzzy p-values in latent variable problems. Biometrika 94: 49–60CrossRefMathSciNetMATHGoogle Scholar
  16. Torabi H, Behboodian J, Taheri SM (2006) Neyman–Pearson lemma for fuzzy hypotheses testing with vague data. Metrika 64: 289–304CrossRefMathSciNetMATHGoogle Scholar
  17. Watanabe N, Imaizumi T (1993) A fuzzy statistical test of fuzzy hypotheses. Fuzzy Sets Syst 53: 167–178CrossRefMathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran
  2. 2.Statistical Research and Training Center (SRTC)TehranIran

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