Similarity, Boolean Reasoning and Rule Induction

A successful rough set methodology based on discernibility of objects and Boolean reasoning has been developed for computing decision rules. However, the requirement of an equivalent relation seems to be a stringent condition that may limit the application domain of the Pawlak rough set model, especially when the data describing objects is imprecise or when small differences are meaningless in the context of the study. This situation may be modeled by considering similarity relation. In order to induce the minimal decision rules used to support the decision task, a method is proposed based on the combination of similarity relation with Boolean reasoning. The nonsimilarity matrix of a decision table with respect to the lower approximation and boundary is defined to construct the nonsimilarity functions which are Boolean functions. The set of "if ... then ... " decision rules is decoded from prime implicants of the Boolean functions. An example is illustrated to demonstrate the application of this approach.