Fuzzy histograms and fuzzy chi-squared tests for independence

Histograms and chi-squared tests for independence are well defined for discrete data. In order to apply these methods to continuous data, some kind of discretization is necessary. A standard way of discretizing data is to use equally spaced (crisp) intervals. In this paper, this crisp discretization is modified to a fuzzy discretization. With this fuzzy discretization, definitions of fuzzy histograms and fuzzy chi-squared tests for independence are achieved. Six experiments indicate that these fuzzy data analysis methods outperform their crisp relatives in terms of smoothness, robustness against outliers, sensitivity for the position of data clusters, and sensitivity for the number of discretization bins.