New basic belief assignment approximations based on optimization

The theory of belief function, also called Dempster-Shafer evidence theory, has been proved to be a very useful representation scheme for expert and other knowledge based systems. However, the computational complexity of evidence combination will become large with the increasing of the frame of discernment's cardinality. To reduce the computational cost of evidence combination, the idea of basic belief assignment (bba) approximation was proposed, which can reduce the complexity of the given bba's. To realize a good bba approximation, the approximated bba should be similar (in some sense) to the original bba. In this paper, we use the distance of evidence together with the difference between the uncertainty degree of approximated bba and that of the original one to construct a comprehensive measure, which can represent the similarity between the approximated bba and the original one. By using such a comprehensive measure as the objective function and by designing some constraints, the bba approximation is converted to an optimization problem. Comparative experiments are provided to show the rationality of the construction of comprehensive similarity measure and that of the constraints designed.