ACBC-Adequate Association and Decision Rules Versus Key Generators and Rough Sets Approximations

Abstract

In this paper, we propose an ACBC-evaluation formula, which delivers a flexible way of formulating different kinds of criteria for association and decision rules. We prove that rules with minimal antecedents that fulfill ACBC-evaluation formulae are key generators, which are patterns of a special type. We also show that a number of types of rough set approximations of decision classes can be expressed based on ACBC-evaluation formulae. We prove that decision rules preserving respective approximations of decision classes are rules that satisfy an ACBC-evaluation formula and that antecedents of such optimal decision rules are key generators, too. A number of properties related to particular measures of association rules and key generators are derived.