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S. Taheri, G. Hesamian, R. Viertl:
"Contingency tables with fuzzy information";
Communications in Statistics - Theory and Methods, Volume 45 (2016), Issue 20; 5906 - 5917.

This paper extends the classical methods of analysis of a two-way contingency table to the fuzzy environment for two cases: (1) when the available sample of observations is reported as imprecise data, and (2) the case in which we prefer to categorize the variables based on linguistic terms rather than as crisp quantities. For this purpose, the α-cuts approach is used to extend the usual concepts of the test statistic and p-value to the fuzzy test statistic and fuzzy p-value. In addition, some measures of association are extended to the fuzzy version in order to evaluate the dependence in such contingency tables. Some practical examples are provided to explain the applicability of the proposed methods in real-world problems.

Contingency table Fuzzy frequency Fuzzy category Fuzzy chi-square test statistic Fuzzy p-value Fuzzy measure of association Mathematics Subject Classification: 62H17 62H20 62G86

http://dx.doi.org/10.1080/03610926.2014.953688

http://www.tandfonline.com/doi/abs/10.1080/03610926.2014.953688