Attribute reduction based on D-S evidence theory in a hybrid information system

Abstract

As an important uncertainty reasoning method, Dempster-Shafer (D-S) evidence theory has been widely applied to expert system, comprehensive evaluation, information fusion and decision analysis. However, it has not been fully valued in uncertainty measurement. A hybrid information system (HIS) means an information system that contains many types of attributes (e.g., categorical attribute, real-valued attribute and attribute with missing values, etc.). It is more difficult to measure an HIS than an ordinary IS. This paper studies the use of evidence theory to measure the uncertainty of an HIS. Firstly, a novel distance between two objects in an HIS considering decision attributes is constructed, and secondly, the tolerance relation based on the constructed distance is established in an HIS. And then, belief and plausibility functions are defined by the tolerance relation. Furthermore, several algorithms for attribute reduction are designed on the basis of the defined belief and plausibility functions. In addition, we come to a series of conclusions on the relation among θ-reduction by using decision attributes, θ-belief reduction and θ-plausibility reduction, which further confirms the effectiveness of the designed attribute reduction algorithms. Finally, the experimental results and statistical test show that the defined belief and plausibility functions work well in measuring the uncertainty of an HIS and the designed reduction algorithm is superior to several state-of-the-art algorithms in classification accuracy. These results will provide a wider perspective on the uncertainty of an HIS.