A general framework for imprecise regression

Many studies on machine learning, and more specifically on regression, focus on the search for a precise model, when precise data are available. Therefore, it is well-known that the model thus found may not exactly describe the target concept, due to the existence of learning bias. In order to overcome the problem of too much illusionary precise models, this paper provides a general framework for imprecise regression from non-fuzzy input and output data. The goal of imprecise regression is to find a model that has the better tradeoff between faithfulness w.r.t. data and (meaningful) precision. We propose an algorithm based on simulated annealing for linear and non-linear imprecise regression with triangular and trapezoidal fuzzy sets. This approach is compared with the different fuzzy regression frameworks, especially with possibilistic regression. Experiments on an environmental database show promising results.