Rough sets and ordinal classification

Abstract

The classical theory of Rough Sets describes objects by discrete attributes, and does not take into account the ordering of the attributes values. This paper proposes a modification of the Rough Set approach applicable to monotone datasets. We introduce respectively the concepts of monotone discernibility matrix and monotone (object) reduct. Furthermore, we use the theory of monotone discrete functions developed earlier by the first author to represent and to compute decision rules. In particular we use monotone extensions, decision lists and dualization to compute classification rules that cover the whole input space. The theory is applied to the bankruptcy problem.