A scheme for constructing evidence structures in Dempster-Shafer evidence theory for data fusion

This paper addresses the issue of evidence structure construction involved in the Dempster-Shafer evidence theory (DSET) based reasoning for data fusion. An in-depth study is carried out on the properties of the proposed Proportional Difference Evidence Structure Constructing Scheme (PDESCS). Some properties have been mathematically proved for the PDESCS associated DSET. If PDESCS is applied to probabilistic evidence, in terms of posterior probability distributions, the DSET based reasoning with the maximum commonality decision making scheme is equivalent to the Beyesian approach with the maximum a posteriori probability principle (MAP). If PDESCS is applied to fuzzy evidence, in terms of fuzzy sets, the DSET based reasoning is equivalent to applying the maximum fuzzy membership decision making scheme to the intersected fuzzy set by the product T-norm operator. If PDESCS is applied to both probabilistic evidence and fuzzy evidence, the DSET based reasoning is equivalent to applying the maximum fuzzy set probability decision making scheme. To show the effectiveness of the PDESCS associated DSET, experiments are carried out for classifying human brain MR (magnetic resonance) images. It is concluded that the proposed scheme works well, and provides not only a unified framework to accommodate probabilistic evidence and fuzzy evidence, but also an effective reasoning mechanism to deal with different uncertainty, in terms of randomness and fuzziness, as well as precision.