Case-based reasoning using gradual rules induced from dominance-based rough approximations

Case-based reasoning (CBR) regards the inference of some proper conclusions related to a new situation by the analysis of similar cases from a memory of previous cases. We propose to represent similarity by gradual decision rules induced from rough approximations of fuzzy sets. Indeed, we are adopting the Dominance-based Rough Set Approach (DRSA) that is particularly appropriate in this context for its ability of handling monotonicity relationship of the type "the more similar is object y to object x, the more credible is that y belongs to the same set as x". At the level of marginal similarity concerning single features, we consider only ordinal properties of similarity, and for the aggregation of marginal similarities, we use a set of gradual decision rules based on the general monotonicity property of comprehensive similarity with respect to marginal similarities. We present formal properties of rough approximations used for CBR.