Order-2 Probabilistic Information Fusion on Random Permutation Set

In this paper, a multi-object recognition scenario is considered to extend the random finite set into random permutation set. Probabilistic information on random permutation set can be viewed as an distribution determined by three random variables. We use another emerging uncertainty representation, order-2 information granule, to realize the probabilistic information fusion on random permutation sets. First, the probabilistic information on random permutation sets is viewed as an order-2 probability distribution. Second, corresponding information fusion approach is proposed. Finally, the proposed approach is applied to random permutation sets, resolving the decision-making issue under the multi-object recognition scenario. This paper pioneers the connection of order-2 information processing logic to a multi-object recognition task and develops order-2 probability distribution and its combination rules. Compared to the traditional probabilistic information fusion approaches, the proposed approach takes into account not only the propositions’ beliefs provided by the sources, but the structural dependency among propositions as well.