Expressing Relevance Interpretability and Accuracy of Rule-Based Systems

We discuss a problem of synthesis and analysis of rules based on experimental numeric data and study their interpretation capabilities. Two descriptors of the rules being viewed individually and en block are introduced. The relevance of the rules is quantified in terms of the data being covered by the antecedents and conclusions standing in the rule. While this index describes each rule individually, the consistency of the rule deals with the quality of the rule viewed vis-à-vis other rules. It expresses how much the rule “interacts ” with others in the sense that its conclusion is distorted by the conclusion parts coming from other rules. We show how the rules are formed by means of fuzzy clustering and their quality evaluated by means of the above indexes. We also discuss a construction of a granular mapping (that is a mapping between fuzzy clusters in the input and output spaces) and quantify its performance (approximation capabilities at the numeric level). Global characteristics of a set of rules are also discussed and related to the number of information granules formed in the space of antecedents and conclusions.