Sequential optimization of γ-decision rules

Abstract

The paper is devoted to the study of an extension of dynamic programming approach which allows sequential optimization of approximate decision rules relative to length, coverage and number of misclassifications. Presented algorithm constructs a directed acyclic graph Δγ(T) which nodes are subtables of the decision table T. Based on the graph Δγ(T) we can describe all irredundant γ-decision rules with minimum length, after that among these rules describe all rules with maximum coverage, and among such rules describe all rules with minimum number of misclassifications. We can also change the set of cost functions and order of optimization. Sequential optimization can be considered as tool that help to construct simpler rules for understanding and interpreting by experts.