Two novel methods for BBA approximation based on focal element redundancy

Abstract

The theory of belief functions is a very appealing theory for uncertainty modeling and reasoning which has been widely used in information fusion. However, when the cardinality of the frame of discernment and the number of the focal elements are large the fusion of belief functions requires in general a high computational complexity. To circumvent this difficulty, many methods were proposed to implement more efficiently the combination rules and to approximate basic belief assignments (BBA's) into simplest ones to reduce the number of focal elements involved in the fusion process. In this paper, we present a novel principle for approximating a BBA by withdrawing more redundant focal elements of the original BBA. Two methods based on this principle are presented (using batch and recursive implementations). Numerical examples, simulations and related analyses are provided to illustrate and evaluate the performances of this new BBA approximation method.