We are considering induction of ordinal classification rules, which assign objects to preference-ordered decision classes, within the dominance-based rough set approach. In order to extract such rules, it is necessary to define dominance inconsistencies with respect to a set of condition attributes containing at least one ordinal condition attribute. Furthermore, it is also assumed that we know if there exist increasing or decreasing monotonicity relationships between the values of ordinal condition and decision attributes. Very often, however, this information is unknown a priori. One solution to this issue is to transform the ordinal condition attributes with unknown directions of preference to pairs of attributes with supposed inverse monotonic relationships. Both local and global monotonicity relationships can be represented by decision rules induced from transformed decision tables. However, in some cases, transforming a decision table in this way is overcomplex. In this paper, we propose the inconsistency rates based on dominance and fuzzy preference relations that have the capacity of discovering monotonic relationships directly from data rather than induced decision rules. Moreover, we propose a refined transformation method by introducing an additional monotonicity checking using these inconsistency rates to determine whether an ordinal condition attribute should be cloned or not. Experiments are also provided to evaluate the usefulness of the refined transformation method. 
Induction of ordinal classification rules from decision tables with unknown monotonicity