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How to measure the similarity or distance between the basic probability assignment (BPA) in evidence theory is an open issue. The existing evidence distance function has the shortcoming that the cardinality of each subset is not reasonably considered. To address this issue, a new similarity coefficients matrix is presented to model the cardinality of each subset. Based on the proposed similarity coefficients matrix, a novel distance measure of belief function is presented. Some numerical examples are used to compare the proposed distance with existing evidence distance. The results show the new evidence distance has better performance. The application of the proposed measure in target recognition based on sensor data fusion illustrates the promising aspect of real engineering.

A New Distance Measure of Belief Function in Evidence Theory