Role of Robustness Measure in Rule Induction

Abstract

Rough set approaches provide useful tools to induce minimal decision rules from given data. Acquired minimal rules are typically used to build a classifier. However, minimal rules are sometimes used for design knowledge. Specifically, if a new object is designed to satisfy the condition of a minimal rule, it can be classified into a class suggested by the rule. Although we are interested in the goodness of the set of obtained minimal decision rules for the purpose of building a classifier, we are more interested in the goodness of an individual minimal decision rule for design knowledge. In this study, we propose robustness measures as a new type of evaluation index for decision rules. The measure evaluates the extent to which interestingness is preserved after the some conditions are removed. Four numerical experiments are conducted to examine the usefulness of robusetness measures. Decision rules selected by robustness scores are compared with those selected by recall, which is the well-known measure to select good rules. Our results reveal that a different aspect of the goodness of a rule is evaluated by the robustness measure and thus, the robustness measure acts as an independent and complementary index of recall.