Similarity-Based Classification with Dominance-Based Decision Rules

We consider a similarity-based classification problem where a new case (object) is classified based on its similarity to some previously classified cases. In this process of case-based reasoning (CBR), we adopt the Dominance-based Rough Set Approach (DRSA), that is able to handle monotonic relationship "the more similar is object y to object x with respect to the considered features, the closer is y to x in terms of the membership to a given decision class X". At the level of marginal similarity concerning single features, we consider this similarity in ordinal terms only. The marginal similarities are aggregated within induced decision rules describing monotonic relationship between comprehensive similarity of objects and their similarities with respect to single features.