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Rule quality for multiple-rule classifier: Empirical expertise and theoretical methodology

A rule-inducing learning algorithm may yield either an ordered or unordered set of decision rules. The latter seems to be more understandable by humans and directly applicable in most expert systems or decision-supporting ones. However, classification utilizing the unordered-mode decision rules may be accompanied by some conflict situations, particularly when several rules belonging to different classes match ('fire' for) an input to-be-classified (unseen) object. One of the possible solutions to this conflict is to associate each decision rule induced by a learning algorithm with a numerical factor which is commonly called the rule quality. 
 
The paper first surveys empirical and statistical formulas of the rule quality and compares their characteristics. Statistical tools such as contingency tables, measures of association, measures of agreement are introduced as suitable vehicles for depicting a behaviour of a decision rule. The above formulas as well as schemes for their combinations are experimentally tested on several well-known AI databases and compared. The covering learning algorithm CN4, a large extension of CN2, is used as an inductive vehicle. 
 
After that, theoretical methodology for defining rule qualities and schemes for their combination is acquainted. The general definitions of the notions of a Designer, Learner, and Classifier are presented in a formal matter, including parameters that are usually attached to these concepts such as rule consistency, completeness, quality, matching rate, etc. Hence, we provide the minimum-requirement definitions as necessary conditions for the above concepts. Any designer (decision-system builder) of a new multiple-rule system may start with these minimum requirements. 
 
We conclude with a general flow chart for a decision-system builder. He/she can just pursue it and select parameters of a Learner and Classifier, following the minimum characteristics provided.