Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Correlation Test by Reduced-Spread of Fuzzy Variance

  • Kang, Man-Ki (Department of Data Information Science, Dong-eui University)
  • Received : 20110800
  • Accepted : 20111100
  • Published : 2012.01.30
Download PDF
⟨ Previous Next ⟩

Abstract

We propose some properties for a fuzzy correlation test by reduced-spread fuzzy variance for sample fuzzy data. First, we define the condition of fuzzy data for repeatedly observed data or that which includes error term data. By using the average of spreads for fuzzy numbers, we reduce the spread of fuzzy variance and define the agreement index for the degree of acceptance and rejection. Given a non-normal random fuzzy sample, we have bivariate normal distribution by apply Box-Cox power fuzzy transformation and test the fuzzy correlation for independence between the variables provided by the agreement index.

Keywords

References

  1. Anderson, T. W. (1971). Multivariate Statistical Analysis, John Willy & Sons.
  2. Colubi, A. (2009). Statistical inference about the means of fuzzy random variables: Applications to the analysis of fuzzy-and real-valued data, Fuzzy Sets and Systems, 160, 344-356. https://doi.org/10.1016/j.fss.2007.12.019
  3. Freeman, J. and Modarres, R. (2001). Properties of the power-normal distribution, Analysis of Trans- formed Environmental Data with Detection Limits, Report for 2001DC3921B.
  4. Gizegorzewski, P. X. (2000). Testing hypotheses with vague data, Fuzzy Sets and Systems, 112, 501-510. https://doi.org/10.1016/S0165-0114(98)00061-X
  5. Goto, M. and Hamasaki, T. (2002). The bivariate power-normal distribution, Research Association of Statistical Science, 34, 29-49.
  6. Kang, M. K., Lee, C. E. and Han, S. I. (2003). Fuzzy hypotheses testing for hybrid numbers by agreement index, Far East Journal of Theoretical Statistics, 10, 1-9.
  7. Kang, M. K. and Seo, H. A. (2009). Fuzzy hypothesis test by Poisson test for most powerful test, Journal of Korean Institute of Intelligent Systems, 19, 809-813. https://doi.org/10.5391/JKIIS.2009.19.6.809
  8. Watanabe, N. and Imaizumi, T. (1993). A fuzzy statistical test of fuzzy hypotheses, Fuzzy Sets and Systems, 53, 167-178. https://doi.org/10.1016/0165-0114(93)90170-M

Cited by

  1. Fuzzy Test of Hypotheses by Rate of Internal Division vol.22, pp.4, 2012, https://doi.org/10.5391/JKIIS.2012.22.4.425
  2. The Wilcoxon Signed-Rank Fuzzy Test on Rate of Internal Division vol.24, pp.6, 2014, https://doi.org/10.5391/JKIIS.2014.24.6.592