Regression analysis based on fuzzy evidence theory

We propose an approach to functional regression analysis based on fuzzy evidence theory. This method uses a training set for computing a fuzzy belief structure that quantifies different sorts of uncertainties, such as nonspecificity, discord in the output data, or low density around the input data. The method can use a very large class of output data, such as real, interval or fuzzy numbers, or, more generally, what we called fuzzy belief structure numbers. We show that our approach can be regarded as a kind of a fuzzy system and we present the analogies with the fuzzy model proposed by Yager and Filev (1995), which can take output discord into account. The proposed model can provide predictions, in a variety of forms depending on the accuracy of the available information, such as: a crisp output, a fuzzy output, a probability distribution and some information criteria (nonspecificity, strife, ignorance degree).