The Distance of Random Permutation Set

Abstract

The Random Permutation Set (RPS) is a newly proposed type of set. An RPS takes the permutation of a certain set into consideration and can be regarded as a generalization of evidence theory. Since distance is an important metric, an immediate question which arises is how to calculate the distance between RPSs. To address this problem, the distance between RPSs is first presented in this paper. Based on a geometrical interpretation of RPS, the distance between RPSs is measured by considering the similarity between their permutation sets, both in the number and order of elements. Numerical examples demonstrate the behavior of the proposed RPS distance. Thereafter, based on the proposed RPS distance, a Data-Driven Reliability Determination (DDRD) algorithm is put forth and applied in threat assessment. The experimental results show that the proposed DDRD algorithm can effectively identify the fusion order of RPSs. The corresponding fusion result is in agreement with theoretical predictions and has the highest accuracy of identification.