Credible rules in incomplete decision system based on descriptors

This paper proposes a new approach to knowledge acquisition in the incomplete decision system with preference-ordered domains of attributes. In such incomplete system, the concepts of up arrow and down arrow descriptors are proposed. Two types of certain rules, up arrow and down arrow credible rules are then generated by using the up arrow and down arrow descriptors. With introduction of the relative reducts of up arrow and down arrow descriptors into the incomplete decision system, up arrow and down arrow optimal credible rules are further proposed. The judgment theorems and discernibility functions associated with the relative reducts of up arrow and down arrow descriptors are also obtained, from which we can derive up arrow and down arrow optimal credible rules from the incomplete decision system. Some numerical examples are employed to substantiate the conceptual arguments. (C) 2008 Elsevier B.V. All rights reserved.