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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.

Classification rules should be open for public inspection to ensure fairness.These rules can be originally induced from some dataset. If induced classification rules are supported only by a small number of objects in the dataset, publication can lead to identification of objects supporting the rule, given their speciality. Eventually, it is possible to retrieve information about the identified objects. This identifiability is not desirable in terms of data privacy.In this paper, to avoid such privacy breaches, we propose rule clustering for achievingk-anonymity of all induced rules, i.e., the induced rules are supported by at leastkobjects in the dataset. The proposed approach merges similar rules to satisfyk-anonymity while aiming to maintain the classification accuracy. Two numerical experiments were executed to verify both the accuracy of the classifier with the rules obtained by the proposed method and the ratio of decision classes revealed from leaked information about objects. The experimental results show the usefulness of the proposed method.

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