Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables

S. M. Taheri; Gholamreza Hesamian

Kybernetika (2011)

  • Volume: 47, Issue: 1, page 110-122
  • ISSN: 0023-5954

Abstract

top
The Goodman-Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy p -value. The applicability of the proposed approach is explained using a numerical example.

How to cite

top

Taheri, S. M., and Hesamian, Gholamreza. "Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables." Kybernetika 47.1 (2011): 110-122. <http://eudml.org/doc/196869>.

@article{Taheri2011,
abstract = {The Goodman-Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy $p$-value. The applicability of the proposed approach is explained using a numerical example.},
author = {Taheri, S. M., Hesamian, Gholamreza},
journal = {Kybernetika},
keywords = {fuzzy frequency; fuzzy category; fuzzy Goodman–Kruskal statistic; fuzzy $p$-value; fuzzy significance level; NSD index; fuzzy frequency; fuzzy category; fuzzy Goodman-Kruskal statistics; fuzzy -value; fuzzy significance level; NSD index},
language = {eng},
number = {1},
pages = {110-122},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables},
url = {http://eudml.org/doc/196869},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Taheri, S. M.
AU - Hesamian, Gholamreza
TI - Goodman-Kruskal Measure of Association for Fuzzy-Categorized Variables
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 1
SP - 110
EP - 122
AB - The Goodman-Kruskal measure, which is a well-known measure of dependence for contingency tables, is generalized to the case when the variables of interest are categorized by linguistic terms rather than crisp sets. In addition, to test the hypothesis of independence in such contingency tables, a novel method of decision making is developed based on a concept of fuzzy $p$-value. The applicability of the proposed approach is explained using a numerical example.
LA - eng
KW - fuzzy frequency; fuzzy category; fuzzy Goodman–Kruskal statistic; fuzzy $p$-value; fuzzy significance level; NSD index; fuzzy frequency; fuzzy category; fuzzy Goodman-Kruskal statistics; fuzzy -value; fuzzy significance level; NSD index
UR - http://eudml.org/doc/196869
ER -

References

top
  1. Agresti, A., Categorical Data Analysis, Second Edition. J. Wiley, New York 2002. (2002) Zbl1018.62002MR1914507
  2. Brown, M. B., Benedetti, J. K., Sampling behavior of tests for correlation in two-way contingency tables, J. Amer. Statist. Assoc. 72 (1977), 309–315. (1977) 
  3. Denoeux, T., Masson, M. H., Herbert, P. H., Non-parametric rank-based statistics and significance tests for fuzzy data, Fuzzy Sets and Systems 153 (2005), 1–28. (2005) MR2202121
  4. Dubois, D., Prade, H., 10.1016/0020-0255(83)90025-7, Inform. Sci. 30 (1983), 183–224. (1983) MR0730910DOI10.1016/0020-0255(83)90025-7
  5. Engelgau, M. M., Thompson, T. J., Herman, W. H., Boyle, J. P., Aubert, R. E., Kenny, S. J., Badran, A., Sous, E. S., Ali, M. A., 10.2337/diacare.20.5.785, Diabetes Care 20 (1997), 785–791. (1997) DOI10.2337/diacare.20.5.785
  6. Gibbons, J. D., Nonparametric Measures of Association, Sage Publication, Newbury Park 1993. (1993) 
  7. Goodman, L. A., Kruskal, W. H., Measures of association for cross classifications, J. Amer. Statist. Assoc. 49 (1954), 732–764. (1954) Zbl0056.12801
  8. Goodman, L. A., Kruskal, W. H., Measures of Association for Cross Classifications, Springer, New York 1979. (1979) Zbl0426.62034MR0553108
  9. Grzegorzewski, P., Statistical inference about the median from vague data, Control Cybernet. 27 (1998), 447–464. (1998) Zbl0945.62038MR1663896
  10. Grzegorzewski, P., Distribution-free tests for vague data, In: Soft Methodology and Random Information Systems (M. Lopez-Diaz et al., eds.), Springer, Heidelberg 2004, pp. 495–502. (2004) Zbl1064.62052MR2118134
  11. Grzegorzewski, P., Two-sample median test for vague data, In: Proc. th Conf. European Society for Fuzzy Logic and Technology-Eusflat, Barcelona 2005, pp. 621–626. (2005) 
  12. Grzegorzewski, P., 10.1002/int.20345, Internat. J. Intelligent Systems 24 (2009), 529–539. (2009) Zbl1160.62039DOI10.1002/int.20345
  13. Holena, M., 10.1016/S0165-0114(03)00208-2, Fuzzy Sets and Systems 145 (2004), 229–252. (2004) MR2073999DOI10.1016/S0165-0114(03)00208-2
  14. Hryniewicz, O. , Selection of variables for systems analysis, application of a fuzzy statistical test for independence, Proc. IPMU, Perugia 3 (2004), 2197–2204. (2004) 
  15. Hryniewicz, O., 10.1016/j.csda.2006.04.014, Comput. Statist. Data Anal. 51 (2006), 323–334. (2006) Zbl1157.62424MR2297603DOI10.1016/j.csda.2006.04.014
  16. Hryniewicz, O., Possibilistic decisions and fuzzy statistical tests, Fuzzy Sets and Systems 157 (2006), 2665–2673. (2006) Zbl1099.62008MR2328390
  17. Kahranam, C., Bozdag, C. F., Ruan, D., 10.1002/int.20037, Internat. J. Intelligent Systems 19 (2004), 1069–1078. (2004) DOI10.1002/int.20037
  18. Kruse, R., Meyer, K. D. , Statistics with Vague Data, Reidel Publishing, New York 1987. (1987) Zbl0663.62010MR0913303
  19. Lee, K. H., First Course on Fuzzy Theory and Applications, Springer, Heidelberg 2005. (2005) Zbl1063.94129
  20. Mareš, M., Fuzzy data in statistics, Kybernetika 43 (2007), 491–502. (2007) Zbl1134.62001MR2377927
  21. Pourahmad, S., Ayatollahi, S. M. T., Taheri, S. M., Fuzzy logistic regression, a new possibilistic model and its application in clinical diagnosis, Iranian J. Fuzzy Systems, to appear. 
  22. Tabaei, B. P., Herman, W. H., A multivariate logistic regression equation to screen for diabetes, Diabetes Care 25 (2002), 1999–2003. (2002) 
  23. Venkataraman, P., Applied Optimization with MATLAB Programming, J. Wiley, New York 2002. (2002) 
  24. Wang, X., Kerre, E., Reasonable properties for the ordering of fuzzy quantities (II), Fuzzy Sets and Systems 118 (2001), 387–405. (2001) Zbl0971.03055MR1809387
  25. Yoan, Y., 10.1016/0165-0114(91)90073-Y, Fuzzy Sets and Systems 43 (1991), 139–157. (1991) MR1127998DOI10.1016/0165-0114(91)90073-Y
  26. Viertl, R., Statistical Methods for Non-Precise Data, CRC Press, Boca Raton 1996. (1996) MR1382865

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.