×

zbMATH — the first resource for mathematics

Goodman-Kruskal measure of association for fuzzy-categorized variables. (English) Zbl 1213.93199
Summary: 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.

MSC:
93E12 Identification in stochastic control theory
62A86 Fuzzy analysis in statistics
93C42 Fuzzy control/observation systems
PDF BibTeX XML Cite
Full Text: Link EuDML
References:
[1] Agresti, A.: Categorical Data Analysis. Second Edition. J. Wiley, New York 2002. · Zbl 1018.62002
[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.
[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.
[4] Dubois, D., Prade, H.: Ranking of fuzzy numbers in the setting of possibility theory. Inform. Sci. 30 (1983), 183-224. · Zbl 0569.94031
[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.: Comparison of fasting and 2-hour glucose and HbA1c levels for diagnosing diabetes: diagnostic critera and performance revisited. Diabetes Care 20 (1997), 785-791.
[6] Gibbons, J. D.: Nonparametric Measures of Association. Sage Publication, Newbury Park 1993.
[7] Goodman, L. A., Kruskal, W. H.: Measures of association for cross classifications. J. Amer. Statist. Assoc. 49 (1954), 732-764. · Zbl 0056.12801
[8] Goodman, L. A., Kruskal, W. H.: Measures of Association for Cross Classifications. Springer, New York 1979. · Zbl 0426.62034
[9] Grzegorzewski, P.: Statistical inference about the median from vague data. Control Cybernet. 27 (1998), 447-464. · Zbl 0945.62038
[10] Grzegorzewski, P.: Distribution-free tests for vague data. Soft Methodology and Random Information Systems (M. Lopez-Diaz et al., Springer, Heidelberg 2004, pp. 495-502. · Zbl 1064.62052
[11] Grzegorzewski, P.: Two-sample median test for vague data. Proc. \(4\)th Conf. European Society for Fuzzy Logic and Technology-Eusflat, Barcelona 2005, pp. 621-626.
[12] Grzegorzewski, P.: K-sample median test for vague data. Internat. J. Intelligent Systems 24 (2009), 529-539. · Zbl 1160.62039
[13] Holena, M.: Fuzzy hypotheses testing in a framework of fuzzy logic. Fuzzy Sets and Systems 145 (2004), 229-252. · Zbl 1050.68137
[14] Hryniewicz, O. : Selection of variables for systems analysis, application of a fuzzy statistical test for independence. Proc. IPMU, Perugia 3 (2004), 2197-2204.
[15] Hryniewicz, O.: Goodman-Kruskal \(\gamma \) measure of dependence for fuzzy ordered categorical data. Comput. Statist. Data Anal. 51 (2006), 323-334. · Zbl 1157.62424
[16] Hryniewicz, O.: Possibilistic decisions and fuzzy statistical tests. Fuzzy Sets and Systems 157 (2006), 2665-2673. · Zbl 1099.62008
[17] Kahranam, C., Bozdag, C. F., Ruan, D.: Fuzzy sets approaches to statistical parametric and non-parametric tests. Internat. J. Intelligent Systems 19 (2004), 1069-1078. · Zbl 1074.62029
[18] Kruse, R., Meyer, K. D. : Statistics with Vague Data. Reidel Publishing, New York 1987. · Zbl 0663.62010
[19] Lee, K. H.: First Course on Fuzzy Theory and Applications. Springer, Heidelberg 2005. · Zbl 1063.94129
[20] MareŇ°, M.: Fuzzy data in statistics. Kybernetika 43 (2007), 491-502. · Zbl 1134.62001
[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. · Zbl 1326.62166
[22] Tabaei, B. P., Herman, W. H.: A multivariate logistic regression equation to screen for diabetes. Diabetes Care 25 (2002), 1999-2003.
[23] Venkataraman, P.: Applied Optimization with MATLAB Programming. J. Wiley, New York 2002.
[24] Wang, X., Kerre, E.: Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets and Systems 118 (2001), 387-405. · Zbl 0971.03055
[25] Yoan, Y.: Criteria for evaluating fuzzy ranking methods. Fuzzy Sets and Systems 43 (1991), 139-157. · Zbl 0747.90003
[26] Viertl, R.: Statistical Methods for Non-Precise Data. CRC Press, Boca Raton 1996. · Zbl 0853.62004
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.