Support vector regression of membership functions and belief functions – Application for pattern recognition

Caused by many applications during the last few years, many models have been proposed to represent imprecise and uncertain data. These models are essentially based on the theory of fuzzy sets, the theory of possibilities and the theory of belief functions. These two first theories are based on the membership functions and the last one on the belief functions. Hence, it could be interesting to learn these membership and belief functions from data and then we can, for example, deduce the class for a classification task. Therefore, we propose in this paper a regression approach based on the statistical learning theory of Vapnik. The membership and belief functions have the same properties; that we take as constraints in the resolution of our convex problem in the support vector regression.The proposed approach is applied in a pattern recognition context to evaluate its efficiency. Hence, the regression of the membership functions and the regression of the belief functions give two kinds of classifiers: a fuzzy SVM and a belief SVM. From the learning data, the membership and belief functions are generated from two classical approaches given respectively by fuzzy and belief k-nearest neighbors. Therefore, we compare the proposed approach, in terms of classification results, with these two k-nearest neighbors and with support vector machines classifier.