Skip to main content
SpringerLink
Log in

Testing Fuzzy Hypotheses: A New p-value-based Approach

  • Chapter
  • First Online:
Fuzzy Statistical Decision-Making

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 343))

  • 1486 Accesses

Abstract

In this paper, on the basis of Zadeh’s probability measure of fuzzy events, the p-value concept is generalized for testing fuzzy hypotheses. We prove that the introduced p-value has uniform distribution over (0, 1) when the null fuzzy hypothesis is true. Then, based on such a p-value, a procedure is illustrated to test various types of fuzzy hypotheses. Several applied examples are given to show the performance of the method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. ‎Arefi, M., Taheri, S.M.: Testing fuzzy hypotheses using fuzzy data based on fuzzy test statistic. J. Uncertain Syst. 5, 45–61 (2011)

    Google Scholar 

  2. Arefi, M., Taheri, S.M.: A new approach for testing fuzzy hypotheses based on fuzzy data. Int. J. Comput. Intell. Syst. 6, 318–327 (2013)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  4. Arnold, B.F.: Testing fuzzy hypothesis with crisp data. Fuzzy Sets Syst. 94, 323–333 (1998)

    Article  MATH  Google Scholar 

  5. Arnold, B.F., Gerke, O.: Testing fuzzy hypotheses in linear regression models. Metrika 57, 81–95 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  6. Casals, M.R., Gil, M.A., Gil, P.: On the use of Zadeh’s probabilistic definition for testing statistical hypotheses from fuzzy information. Fuzzy Sets Syst. 20, 175–190 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  7. Casals, M.R., Gil, M.A., Gil, P.: The fuzzy decision problem: an approach to the problem of testing statistical hypotheses with fuzzy information. Eur. J. Oper. Res. 27, 371–382 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  8. Denœux‎, T., ‎Masson, M.H., Hébert‎, P.A.: Nonparametric rank-based statistics and significance tests for fuzzy data. Fuzzy Sets and Systems 153, 1–28 (2005)

    Google Scholar 

  9. Filzmoser, P., Viertl, R.: Testing hypotheses with fuzzy data: the fuzzy p-value. Metrika 59, 21–29 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  10. González-Rodríguez, G., Colubi, A., Gil, M.A.: A fuzzy representation of random variables: an operational tool in exploratory analysis and hypothesis testing. Comput. Stat. Data Anal. 51, 163–176 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  11. González-Rodríguez, G., Colubi, A., Gil, M.A.: Fuzzy data treated as functional data: a one-way ANOVA test approach. Comput. Stat. Data Anal. 56, 943–955 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. González-Rodríguez, G., Montenegro, M., Colubi, A., Gil, M.A.: Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data. Fuzzy Sets Syst. 157, 2608–2613 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Grzegorzewski, P., Hryniewicz, O.: Testing hypotheses in fuzzy environment. Math. Soft Comput. 4, 203–217 (1997)

    MATH  Google Scholar 

  14. Holeňa, M.: Fuzzy hypotheses testing in the framework of fuzzy logic. Fuzzy Sets Syst. 145, 229–252 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  15. Knight, K.: Mathematical Statistics. Chapman and Hall, Boca Raton (2000)

    MATH  Google Scholar 

  16. Lehmann, E.L., Romano, J.P.: Testing Statistical Hypotheses, 3rd edn. Springer, New York (2005)

    Google Scholar 

  17. Montenegro, M., Colubi, A., Casals, M.R., Gil, M.A.: Asymptotic and bootstrap techniques for testing the expected value of a fuzzy random variable. Metrika 59, 31–49 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Neyman, J., Pearson, E.S.: The theory of statistical hypotheses in relation to probabilities a priori. Proc. Camb. Phil. Soc. 29, 492–510 (1933)

    Article  MATH  Google Scholar 

  19. Pais, I., Benton, J.J.: The Handbook of Trace Elements. St. Lucie Press, Boca Raton, Florida (1997)

    Google Scholar 

  20. Parchami, A., Taheri, S.M., Mashinchi, M.: Fuzzy p-value in testing fuzzy hypotheses with crisp data. Stat. Pap. 51, 209–226 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  21. Parchami, A., Ivani, R., Mashinchi, M.: An application of testing fuzzy hypotheses: a soil study on bioavailability of Cd. Scientia Iranica 18, 470–478 (2011)

    Article  Google Scholar 

  22. Parchami, A., Taheri, S.M., Mashinchi, M.: Testing fuzzy hypotheses based on vague observations: a p-value approach. Stat. Pap. 53, 469–484 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  23. Rohatgi, V.K., Ehsanes Saleh, A.K.: An Introduction to Probability and Statistics, 2nd edn. Wiley, New York (2001)

    Google Scholar 

  24. Taheri, S.M., Behboodian, J.: Neyman-Pearson Lemma for fuzzy hypotheses testing. Metrika 49, 3–17 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  25. Taheri, S.M., Behboodian, J.: A Bayesian approach to fuzzy hypotheses testing. Fuzzy Sets Syst. 123, 39–48 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  26. Tanaka, H., Okuda, T., Asai, K.: Fuzzy information and decision in a statistical model. In: Gupta, M.M., et al. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 303–320. North-Holland, Amsterdam (1979)

    Google Scholar 

  27. Torabi, H., Behboodian, J.: Sequential probability ratio test for fuzzy hypotheses testing with vague data. Austrian J. Stat. 34, 25–38 (2005)

    Google Scholar 

  28. Torabi, H., Behboodian, J.: Likelihood ratio tests for fuzzy hypotheses testing. Stat. Pap. 48, 509–522 (2007)

    Article  MATH  Google Scholar 

  29. Viertl, R.: Statistical Methods for Fuzzy Data. Wiley, New York (2011)

    Book  MATH  Google Scholar 

  30. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Statistics‎, Faculty of Mathematics and Computer‎, Shahid Bahonar University of Kerman, Kerman, Iran

    Abbas Parchami & Mashaallah Mashinchi

  2. Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    S. Mohmoud Taheri

  3. Department of Statistics, ‎Faculty of Mathematical Science, Ferdowsi University of Mashhad, Mashhad, Iran

    Bahram Sadeghpour Gildeh

Authors
  1. Abbas Parchami
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Mohmoud Taheri
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bahram Sadeghpour Gildeh
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mashaallah Mashinchi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abbas Parchami .

Editor information

Editors and Affiliations

  1. Management Faculty, Industrial Engineering Department, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. Management Facult, Industrial Engineering Department, Istanbul Technical University, Istanbul, Turkey

    Özgür Kabak

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Parchami, A., Taheri, S.M., Sadeghpour Gildeh, B., Mashinchi, M. (2016). Testing Fuzzy Hypotheses: A New p-value-based Approach. In: Kahraman, C., Kabak, Ö. (eds) Fuzzy Statistical Decision-Making. Studies in Fuzziness and Soft Computing, vol 343. Springer, Cham. https://doi.org/10.1007/978-3-319-39014-7_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-39014-7_10

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39012-3

  • Online ISBN: 978-3-319-39014-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation