Approximating fuzzy measures by hierarchically decomposable ones

Choquet and Sugeno integrals are powerful data fusion operators for numerical data as they generalize some well known aggregation operators as arithmetic means, weighted means, order statistics, OWA operators, medians, and so on. However, real applications of these operators require the definition of the so-called fuzzy measure. Difficulties for defining these measures arise because the number of values to be determined in a fuzzy measure is /sup 2/N, being N the number of values to be aggregated. On the one hand human experts are not usually able to supply the large amount of required values and on the other hand it is difficult to interpret fuzzy measures when learned from examples. To solve this problem, fuzzy measures of reduced complexity have been proposed in the literature. In this work we propose a method to approximate a general fuzzy measure by a Hierarchically Decomposable one (one type of fuzzy measure of reduced complexity). Two applications of the method can be underlined: (i) understanding general fuzzy measures learned from examples; (ii) complete fuzzy measures from noncomplete ones (This is to find all /sup 2/N values from a subset of them and, thus, helping experts on their definition).