On mining rules that involve inequalities from decision table

We introduce the notion of generating decision rules that involve inequalities. While a conventional decision rule expresses the trivial equality relations between attributes and values from the same or different objects, inequality rules express the non-equivalent relationships between attributes and values. The problem of mining inequality rules is formulated as a process of mining equality rules from a compensatory decision table. In order to mine high-order inequality rules, one can transform the original decision table to a high-order compensatory decision table, in which each new entity is a pair of objects. Any standard data-mining algorithm can then be used. We theoretically analyze the complexity of proposed models based on their meta-level representation in cognitive informatics. Mining inequalities in decision table makes a complementary feature of a rule induction system, which may result in generating a small number of short rules for domains where attributes have large number of values, and when majority of them are correlated with the same decision class.