Estimation of fuzzy memberships from histograms
The values of membership of a fuzzy set are either obtained subjectively or as the values of a function for patterns. Desirable characteristics of the membership function are: The chosen form should reflect the real fuzziness. The number of parameters in the membership function should be small. The parameters should be infered from the elements of the training set. It should be computationally manageable in the estimation and decision making operations involved. Based on relationships between probability and possibility functions the authors recommend the histograms of the experimental data for estimation of the membership function in each class. A rational function approximation to the histogram is proposed and the estimated parameters of the approximation are normalized to derive the fuzzy membership function. The parameters representing the rational function are used for classifying the pattern samples based on max-min decision rule. The method is illustrated with the well-known Iris data and an example for vowel recognition.
scientific article; zbMATH DE number 3903995
scientific article