Three-Way Decision: An Interpretation of Rules in Rough Set Theory

A new interpretation of rules in tough set theory is introduced. According to the positive, boundary, and negative regions of a set, one can make a three-way decision: accept, abstain and reject. The three regions enable us to derive three types of decision rules, namely, positive rules for acceptance, boundary rules for indecision or delayed decision, and negative rules for rejection. Within the decision-theoretic rough set model, the associated costs of rules are analyzed.