Modeling uncertainty from bidimensional histograms by intuitionistic fuzzy sets

Histograms summarize distributions of numerical data into densities per ranges of values and are typically used for fast approximation of selectivities of range predicates. This paper introduces an approach for intuitionistic fuzzy selectivity estimation from histograms when predicates are expressed in fuzzy terms with membership functions on the numeric values, where the degree of indefiniteness corresponds to the level of uncertainty resulting from the accuracy loss due to approximation. In the case of bidimensional histograms, a method for estimating the joint selectivity of conjunctive predicates over the two dimensions is proposed in a way that the joint selectivity can be considered as a measure of correlation. The approach is validated through the use of SQL queries against a synthetically generated dataset and its corresponding bidimensional histogram.