Classification in the Presence of Ordered Classes and Weighted Evaluative Attributes

We are interested in an important family of problems in the interface of the Multi-Attribute Decision-Making and Data Mining fields. This is a special case of the general classification problem, in which records describing entities of interest have been expressed in terms of a number of evaluative attributes. These attributes are associated with weights of importance, and both the data and the classes are ordinal. Our goal is to use historical records and the corresponding decisions to best estimate the class values of new data points in a way consistent with prior classification decisions, without knowledge of the weights of the evaluative attributes. We study three variants of this problem. The first is when all decisions are consistent with a single set of attribute weights (called the separable case.) The second is when all decisions are consistent, but involve two sets of attribute weights corresponding to two decision makers, who determine the classification of the data together (called the two-plane separable case.) The third is when there is some inconsistency in the set of weights that must be accounted for (called the non-separable case.) Furthermore, we examine 2-class problems and also multiple class problems. We propose the Ordinal Boundary method, which has a significant advantage over traditional approaches in multi-class problems. Linear programming (optimization) based approaches provide a promising avenue for dealing with these problems effectively. We present computational results that support this argument