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Goodman-Kruskal \(\gamma\) measure of dependence for fuzzy ordered categorical data. (English) Zbl 1157.62424
Summary: The generalisation of the Goodman-Kruskal \(\gamma \) statistic that is used for the measurement of the strength of dependence (association) between two categorical variables with ordered categories is presented. The case when some data are not precise, and observations are described by possibility distributions over a set of categories of one variable is considered. For such data the fuzzy version of \(\gamma \) statistic has been defined.

MSC:
62H20 Measures of association (correlation, canonical correlation, etc.)
62H99 Multivariate analysis
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[1] Dubois, D.; Prade, H., Ranking fuzzy numbers in the setting of possibility theory, Inform. sci., 30, 184-244, (1983)
[2] Goodman, L.A.; Kruskal, W.H., Measures of association for cross classifications, J. amer. statist. assoc., 49, 732-764, (1954) · Zbl 0056.12801
[3] Goodman, L.A.; Kruskal, W.H., Measures of association for cross classifications, III: approximate sampling theory, J. amer. statist. assoc., 58, 310-364, (1963)
[4] Goodman, L.A.; Kruskal, W.H., Measures of association for cross classifications, IV: simplification of asymptotic variances, J. amer. statist. assoc., 67, 414-421, (1972) · Zbl 0243.62038
[5] Grzegorzewski, P., Testing statistical hypotheses with vague data, Fuzzy sets and systems, 112, 501-510, (2000) · Zbl 0948.62010
[6] Hryniewicz, O., 2004a. Selection of variables for systems analysis—application of a fuzzy statistical test for independence. Proceedings of IPMU’2004, Perugia, vol. 3, pp. 2197-2204.
[7] Hryniewicz, O. 2004b. Goodman-Kruskal gamma measure of dependence for fuzzy ordered categorical data. Research Report of the Systems Research Institute, RB/10/2004. Available from the author’s web page: \(\langle\)www.ibspan.waw.pl/\(\sim\)hryniewi⟩.
[8] Kruse, R.; Meyer, K.D., Statistics with vague data, (1987), Riedel Dodrecht · Zbl 0663.62010
[9] Loughin, T.M.; Scherer, P.N., Testing for association in contingency tables with multiple column responses, Biometrics, 54, 630-637, (1998) · Zbl 1058.62534
[10] Zadeh, L.A., Fuzzy sets as a basis for a theory of possibility, Fuzzy sets and systems, 1, 3-28, (1978) · Zbl 0377.04002
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