A new dominance-based rough set model based on interval knowledge granules

The dominance-based rough set approach (DRSA) takes dominating sets or dominated sets as basic knowledge granules to define lower and upper approximations in an ordered decision information system. The DRSA can cope with inconsistency and draw “at least” decision rules (or “at most” decision rules). By these rules, an object can be assigned to classes not worse (or not better) than a specific decision class, however, it can not be assigned to decision classes not worse than a specific decision class and not better than another specific decision class at the same time, and particularly, it can not be assigned to one decision class. So, DRSA can not be conveniently used in classification problem for ordered information systems. To solve this problem, we employ “interval”, an intersection of the dominating set of one object and the dominated set of another object, as a basic knowledge granule, and use intervals to define the lower and upper approximations. By this new model, the “at least and at most” decision rules, which can assign objects to the decision classes not worse than a specific decision class and not better than another specific decision class, can be induced.