Heuristic Methods to Identify Fuzzy Measures Applied to Choquet Integral Classification of Breast Cancer Data

Abstract

When the search space for optimisation or classification problems gets large heuristics and soft computing are often used to find the needed parameters. The Choquet integral methods needs one parameter for each subset of the condition attributes because these sets form a lattice on which the fuzzy measure needed for integration is defined. In this paper the frequency of how many data from each class pass through each set in the lattice provides information that is then used to construct the fuzzy measure. Several heuristics based on this idea are tested upon the well-known Wisconsin breast cancer data set. The heuristics prove to be as successful, or more so, than a range of other methods quoted in the literature when 10-fold cross validation is performed.In order for the Choquet to separate classes after integration a boundary value has to be calculated.Remarkably, it is found that switching the way to view success from number of records correctly classified to the distance of the wrongly classified record from the boundary leads to a hill climbing approach that can reclassify the data with a 100% success rate.