Variable Probability-possibility Transformation

Our team of research works on diagnosis by pattern recognition using Fuzzy Pattern Matching (FPM) as a classification method, for data coming from industrial and medical sectors. FPM uses a transformation from probability to possibility in order to construct densities of possibilities. These densities are used to assign each new sample to its suitable class which corresponds to a functioning mode. In this paper, a transformation from probability to possibility is proposed. This transformation is named Variable Transformation because its specificity property varies with a parameter. The performances of the Variable Transformation are compared with the ones of some well known ones of the literature using some meaningful criteria. We show that the Variable Transformation has interesting characteristics for the diagnosis by pattern recognition, in particular that it can be the most informative transformation, in the discrete case, and it is the one that best distinguishes the confused elements.