Decision Making by a Multiple-Rule Classifier: The Role of Rule Qualities

Decision Making by a Multiple-Rule Classifier: The Role of Rule Qualities

Ivan Bruha (McMaster University, Canada)
DOI: 10.4018/978-1-59904-843-7.ch020
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Abstract

A rule-inducing learning algorithm yields a set of decision rules that depict knowledge discovered from a (usually large) dataset; therefore, this topic is often known as knowledge discovery from databases (KDD). Any classifier (or, expect system) then can utilize this decision set to derive a decision about given problems, observations, or diagnostics. The decision set (induced by a learning algorithm) may be either of the form of an ordered or unordered set of rules. The latter seems to be more understandable by humans and directly applicable in most expert systems, or generally, any decision- supporting one. However, classification utilizing the unordered-mode decision set may be accompanied by some conflict situations, particularly when several rules belonging to different classes match (are satisfied by, “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 (An & Cercone, 2001; Bergadano et al., 1988; Bruha, 1997; Kononenko, 1992; Mingers, 1989; Tkadlec & Bruha, 2003). This article first briefly introduces the underlying principles for defining rules qualities, including statistical tools such as contingency tables and then surveys empirical and statistical formulas of the rule quality and compares their characteristics. Afterwards, it presents an application of a machine learning algorithm utilizing various formulas of the rule qualities in medical area.

Key Terms in this Chapter

Decision-Set Quality: Decision-set quality is a numerical factor that characterizes a measure of belief in a given decision set; it is a conglomerate of the qualities of all its elements (decision rules).

Completeness: Completeness of a decision rule characterizes its power, that is, a rule with high completeness factor should cover the maximum of objects belonging to the rule’s class.

Ordered or Unordered Set of Decision Rules: There are two modes of decision sets: either the order of its decision rules is substantial (ordered mode), or not (unordered mode). In the first mode, the system inspects the decision set from the beginning and stops at the first rule that is satisfied for a given object; in the latter, all rules must be inspected and decision is carried out according to a combination scheme.

Decision Rule: Decision rule is an element (piece) of knowledge, usually in the form of “if-then statement”: if then . If its Condition is satisfied (i.e., matches a fact in the corresponding database of a given problem), then its Action (e.g., classification or decision making) is performed.

Decision Set: Decision set is a set (list) of decision rules; a common knowledge representation tool (utilized, e.g., in most expert systems).

Consistency: Consistency of a decision rule exhibits its reliability, that is, a rule with high consistency should cover the minimum of the objects that do not belong to the class of the given rule.

Contingency Table: A contingency table is a statistical tool, usually in the form of a matrix that exhibits the relation between two random variables; in case of decision rules, it portrays the relation between rule characteristics and the corresponding class.

Rule Quality: Rule quality is a numerical factor that characterizes a measure of belief in the given decision rule, its power, predictability, reliability, and likelihood.

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