Making the Best of Cases by Approximation, Interpolation and Extrapolation

Abstract

Case-based reasoning usually exploits source cases (consisting of a source problem and its solution) individually, on the basis of the similarity between the target problem and a particular source problem. This corresponds to approximation. Then the solution of the source case has to be adapted to the target. We advocate in this paper that it is also worthwhile to consider source cases by two, or by three. Handling cases by two allows for a form of interpolation, when the target problem is between two similar source problems. When cases come by three, it offers a basis for extrapolation. Namely the solution of the target problem is obtained, when possible, as the fourth term of an analogical proportion linking the three source cases with the target, where the analogical proportion handles both similarity and dissimilarity between cases. Experiments show that interpolation and extrapolation techniques are of interest for reusing cases, either in an independent or in a combined way.