Permutation Jensen-Shannon divergence for Random Permutation Set

Random Permutation Set (RPS) considers the permutation of elements for a certain set, which is an efficient tool for dealing with uncertainty with ordered information. An important feature of RPS theory is that in the fusion rule of RPS sources, the fusion order has a great impact on fusion results. However, how to determine the fusion order has not yet been discussed. To address this problem, this paper first proposes Permutation Jensen-Shannon (PJS) divergence for measuring the distance between two RPSs. Based on PJS divergence, a new Reliability Assessment algorithm, named RAPJS, is then presented for determining the fusion order of RPSs. The proposed PJS divergence satisfies the properties of non-degeneracy, boundary, and symmetry, and has desirable compatibility with Belief Jensen-Shannon divergence and Jensen-Shannon divergence under certain conditions. The presented RAPJS makes use of the divergence information to calculate the reliability degree of RPS sources, the RPS with a higher reliability is fused first. Experiment results in threat assessment reveal that the presented RAPJS algorithm can determine the fusion order reasonably and effectively. The assessment results using the proposed RAPJS algorithm has the highest target recognition rate compared to other results under different fusion orders.