This paper presents a new approach for constructing regression and classification models for interval-valued data. The risk functional is considered under a set of probability distributions, resulting from the application of a chosen inferential method to the data, such that the bounding distributions of the set depend on the regression and classification parameter. Two extreme (`pessimistic' and `optimistic') strategies of decision making are presented. The method is appicable with a wide variety of inferential methods and risk functionals, in addition to the general theory the specific optimisation problems for several scenarios are formulated and discussed. In particular, the extension of the support vector machine method for the case of interval-valued data is presented.
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