Imprecise Regression and Regression on Fuzzy Data - A Preliminary Discussion

Abstract:  Abstract The paper provides a discussion of the possibilistic regression method originally proposed by H. Tanaka. This method has the advantage of allowing the learning of an imprecise model, in the form of an interval-valued function. It may lead to an imprecise model even in presence of precise data, which is satisfactory from a learning point of view. Indeed, finding a precise model that perfectly represents the concept to be learned is illusory, due to the existence of the bias caused by the choice of a modeling representation space, the limited amount of data, and the possibility of missing relevant data. However, what is obtained with possibilistic regression is more an imprecise model than a genuine fuzzy one. The paper illustrates and emphasizes this point on environmental data and suggest two different approaches for learning genuine fuzzy regression models from precise data.