Credible rules in incomplete decision system based on descriptors

Abstract

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 ↑ and ↓ descriptors are proposed. Two types of certain rules, ↑ and ↓ “credible rules” are then generated by using the ↑ and ↓ descriptors. With introduction of the relative reducts of ↑ and ↓ descriptors into the incomplete decision system, ↑ and ↓ “optimal credible rules” are further proposed. The judgment theorems and discernibility functions associated with the relative reducts of ↑ and ↓ descriptors are also obtained, from which we can derive ↑ and ↓ “optimal credible rules” from the incomplete decision system. Some numerical examples are employed to substantiate the conceptual arguments.