With respect to multiple attribute group decision making problems in which the attribute weights and the expert weights take the form of real numbers and the attribute values take the form of interval-valued uncertain linguistic variable. In this paper, we introduce the idea of variable precision into the incomplete interval-valued fuzzy information system and propose the theory of variable precision rough sets over incomplete interval-valued fuzzy information systems. Then, we give the properties of rough approximation operators and study the knowledge discovery and attribute reduction in the incomplete interval-valued fuzzy information system under the condition that a certain degree of misclassification rate is allowed to exist. Furthermore, a decision rule and decision model are given. Finally, an illustrative example is given and compared with the existing methods, the practicability and effectiveness of this method are further verified.
Attribute Reduction Algorithm Based on Structure Discernibility Matrix in Composite Information Systems