On constructing probabilistic fuzzy classifiers from weighted fuzzy clustering

Probabilistic fuzzy classifiers are classifier systems that combine fuzzy set theory with probability theory. These classifiers can deal with two different types of uncertainty simultaneously, namely probabilistic uncertainty and fuzziness. Recently weighted extension of fuzzy clustering has been proposed to design probabilistic fuzzy classifiers for binary classification problems. This method uses a weighting scheme to modify the distances from which the membership values for the fuzzy clusters are determined. The clustering results are influenced by this weighting scheme. In this paper, we investigate the influence of different types of weighting schemes on the classification performance. A target selection model that has been investigated in previous literature is used as a benchmark. It is observed empirically that a weighting scheme that depends linearly on the deviations from a priori average class probability gives the best clustering results.