Rough set based processing of inconsistent information in decision analysis

Inconsistent information is one of main difficulties in the explanation and recommendation tasks of decision analysis. We distinguish two kinds of such information inconsistencies: the first is related to indiscernibility of objects described by attributes defined in nominal or ordinal scales, and the other follows from violation of the dominance principle among attributes defined on preference ordered ordinal or cardinal scales, i.e. among criteria. In this paper we discuss how these two kinds of inconsistencies are handled by a new approach based on the rough sets theory. Combination of this theory with inductive learning techniques leads to generation of decision rules from rough approximations of decision classes. Particular attention is paid to numerical attribute scales and preference-ordered scales of criteria, and their influence on the syntax of induced decision rules.