On Different Ways of Handling Inconsistencies in Ordinal Classification with Monotonicity Constraints

Ordinal classification problem with monotonicity constraints involves a monotonic relationship between the description of an object and the class to which it is assigned. An example of such a relationship is: “the higher the quality of service and the lower the price, the higher the customer satisfaction level (class)”. Violation of the monotonic relationship is considered as an inconsistency. Rough set approaches to induction of the monotonic relationships in form of decision rules handle these inconsistencies at the stage of data pre-processing. As a result, the data sufficiently consistent for rule induction are identified. In this paper, we compare two ways of handling inconsistencies. The first one consists in distinguishing objects that are not less consistent than a specified threshold from those which are less consistent. The second one involves iterative removal of the most inconsistent objects until the data set is consistent. We present results of a computational experiment, in which rule classifiers are induced from data pre-processed in the two considered ways.