Naive possibilistic classifiers for imprecise or uncertain numerical data

In real-world problems, input data may be pervaded with uncertainty. In this paper, we investigate the behavior of naive possibilistic classifiers, as a counterpart to naive Bayesian ones, for dealing with classification tasks in presence of uncertainty. For this purpose, we extend possibilistic classifiers, which have been recently adapted to numerical data, in order to cope with uncertainty in data representation. Here the possibility distributions that are used are supposed to encode the family of Gaussian probabilistic distributions that are compatible with the considered data set. We consider two types of uncertainty: i) the uncertainty associated with the class in the training set, which is modeled by a possibility distribution over class labels, and ii) the imprecision pervading attribute values in the testing set represented under the form of intervals for continuous data. Moreover, the approach takes into account the uncertainty about the estimation of the Gaussian distribution parameters due to the limited amount of data available. We first adapt the possibilistic classification model, previously proposed for the certain case, in order to accommodate the uncertainty about class labels. Then, we propose an algorithm based on the extension principle to deal with imprecise attribute values. The experiments reported show the interest of possibilistic classifiers for handling uncertainty in data. In particular, the probability-to-possibility transform-based classifier shows a robust behavior when dealing with imperfect data.