Approximation of Basic Belief Assignment Based on Focal Element Compatibility

The theory of belief functions is an important tool in the field of information fusion. However, the fusion of Basic Belief Assignments (BBAs) requires high computational cost and long computing time when a large number of focal elements are involved in the fusion rules. This problem becomes a bottleneck of application of Belief Functions (BF) in high-dimensional real problems. To overcome this drawback, many approaches were proposed to approximate BBAs to reduce the computational complexity in the fusion process. In this paper, we present a novel method based on the compatibility of focal elements to approximate a BBA by removing some focal elements of the original BBA. Besides, a new mass assignment strategy based on the distance of focal elements is proposed. Several examples, simulations and related analyses are provided to illustrate the interest and efficiency of the proposed method.