IDEAS home Printed from https://ideas.repec.org/a/ibn/masjnl/v8y2013i1p25.html
   My bibliography  Save this article

Tests of Statistical Hypotheses with Respect to a Fuzzy Set

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://ccsenet.org/journal/index.php/mas/article/download/31651/19050
    Download Restriction: no
    File URL: https://ccsenet.org/journal/index.php/mas/article/view/31651
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Muhammad Aslam, 2022. "Neutrosophic F-Test for Two Counts of Data from the Poisson Distribution with Application in Climatology," Stats, MDPI, vol. 5(3), pages 1-11, August.
    2. Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
    3. Gil, Maria Angeles & Lopez-Diaz, Miguel & Lopez-Garcia, Hortensia, 1998. "The fuzzy hyperbolic inequality index associated with fuzzy random variables," European Journal of Operational Research, Elsevier, vol. 110(2), pages 377-391, October.
    4. Mohsen Arefi & Reinhard Viertl & S. Taheri, 2012. "Fuzzy density estimation," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(1), pages 5-22, January.
    5. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    6. Pierpaolo D’Urso & María Ángeles Gil, 2017. "Fuzzy data analysis and classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 645-657, December.
    7. Kimberly F. Sellers & Nozer D. Singpurwalla, 2008. "Many‐valued Logic in Multistate and Vague Stochastic Systems," International Statistical Review, International Statistical Institute, vol. 76(2), pages 247-267, August.
    8. Wu, Hsien-Chung, 2003. "The fuzzy estimators of fuzzy parameters based on fuzzy random variables," European Journal of Operational Research, Elsevier, vol. 146(1), pages 101-114, April.
    9. Maria Gil, 1988. "On the loss of information due to fuzziness in experimental observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 40(4), pages 627-639, December.
    10. Ana Colubi & Renato Coppi & Pierpaolo D’urso & Maria angeles Gil, 2007. "Statistics with fuzzy random variables," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 277-303.

    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ibn:masjnl:v:8:y:2013:i:1:p:25. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.