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Sequential Test of Fuzzy Hypotheses

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DOI: 10.4236/ojs.2011.12010    4,197 Downloads   7,855 Views   Citations

ABSTRACT

In testing statistical hypotheses, as in other statistical problems, we may be confronted with fuzzy concepts. This paper deals with the problem of testing hypotheses, when the hypotheses are fuzzy and the data are crisp. We first give new definitions for notion of mass (density) probability function with fuzzy parameter, probability of type I and type II errors and then state and prove the sequential probability ratio test, on the basis of these new errors, for testing fuzzy hypotheses. Numerical examples are also provided to illustrate the approach.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

M. Akbari, "Sequential Test of Fuzzy Hypotheses," Open Journal of Statistics, Vol. 1 No. 2, 2011, pp. 87-92. doi: 10.4236/ojs.2011.12010.

References

[1] M. Delgado, J. L. Verdegay and M. A. Vila, “Testing Fuzzy-Hypotheses: A Bayesian Approach,” In: M. M. Gupta, Ed., Approximate Reasoning in Expert Systems, Elsevier Science Ltd, 1995, pp. 307-316.
[2] B. F. Arnold, “An Approach to Fuzzy Hypothesis Testing,” Metrika, Vol. 44, No. 1, 1996, pp.119-126. doi:10.1007/BF02614060
[3] B. F. Arnold, “Testing Fuzzy Hypothesis with Crisp Data,” Fuzzy Sets and Systems, Vol. 94, No. 3, 1998, pp. 323-333. doi:10.1016/S0165-0114(96)00258-8
[4] M. Holena, “Fuzzy Hypotheses for GUHA Implications,” Fuzzy Sets and Systems, Vol. 98, No. 1, 1998, pp. 101-125. doi:10.1016/S0165-0114(96)00369-7
[5] M. Holena, “Fuzzy Hypotheses Testing in the Framework of Fuzzy Logic,” Fuzzy Sets and Systems, Vol. 145, No. 2, 2004, pp. 229-252. doi:10.1016/S0165-0114(03)00208-2
[6] S. M. Taheri and J. Behboodian, “Neyman-Pearson Lemma for Fuzzy Hypotheses Testing,” Metrika, Vol. 49, No. 1, 1999, pp. 3-17. doi:10.1007/s001840050021
[7] H. Torabi, J. Behboodian and S. M. Taheri, “Neyman- Pearson Lemma for Fuzzy Hypotheses Testing withVague Data,” Metrika, Vol. 64, No. 3, 2006, pp. 289-304. doi:10.1007/s00184-006-0049-8
[8] P. Filzmoser and R. Viertl, “Testing Hypotheses with Fuzzy Data: The Fuzzy p-value,” Metrika, Vol. 59, No. 1, 2004, pp. 21-29. doi:10.1007/s001840300269
[9] R. Viertl, “Univariate Statistical Analysis with Fuzzy Data,” Computational Statistics and Data Analysis, Vol. 51, No. 1, 2006, pp. 133-147. doi:10.1016/j.csda.2006.04.002
[10] J. J. Buckley, “Fuzzy Probabilities: New Approach and Applications,” Springer-Verlag, Berlin, 2005.
[11] J. J. Buckley, “Fuzzy Probability and Statistics,” Springer -Verlag, Berlin, 2006.
[12] E. A. Thompson and C. J. Geyer, “Fuzzy p-values in Latent Variable Problems,” Biometrika, Vol. 94, No. 1, 2007, pp. 49-60. doi:10.1093/biomet/asm001
[13] S. M. Taheri and M. Arefi, “Testing Fuzzy Hypotheses Based on Fuzzy Statistics,” Soft Computing, Vol. 13, No. 6, 2009, pp. 617-625. doi:10.1007/s00500-008-0339-3
[14] A Parchami, S. M. Taheri and M. Mashinchi, “Fuzzy p-value in Testing Fuzzy Hypotheses with Crisp Data,” Statistical Papers, Vol. 51, No. 1, 2010, pp. 209-226. doi:10.1007/s00362-008-0133-4
[15] P. Billingsley, “Probability and Measure,” 2nd Edition, John and Wiley, New York, 1995.
[16] G. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic-Theory and Applications,” Prentice-Hall, Upper Saddle River, 1995.
[17] M. G. Akbari and A. Rezaei, “Bootstrap Testing Fuzzy Hypotheses and Observations on Fuzzy Statistic,” Expert Systems with Applications, Vol. 37, No. 8, 2010, pp. 5782- 5787. doi:10.1016/j.eswa.2010.02.030
[18] M. G. Akbari and A. Rezaei, “Discrete and Continuous Random Variables with Fuzzy Parameter,” Far East Journal of Theoretical Statistics, Online, 2009.
[19] G. Casella and R. L. Berger, “Statistical Inference,” 2nd Edition, Duxbury Press, Belmont, 2002.
[20] E. L. Lehmann, “Testing Statitical Hypotheses,” Chapman and Hall, London, 1994.
[21] Maple 6, Waterloo Maple Inc. Waterloo, Canada.

  
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