Combining Permutation Mass Functions based on distance and entropy of Random Permutation Set

A novel set type, termed Random Permutation Set (RPS), has recently been introduced to account for permutations of sets. Serving as an extension of evidence theory, the concern about whether it might yield counterintuitive outcomes when confronted with high conflict akin to evidence theory arises as a pertinent issue in practical engineering applications. In this paper, we initially explore the outcomes of direct fusion amidst varying levels of extreme conflict. Following this, we innovatively proposed a fusion method based on RPS distance and entropy metrics. This method utilizes the distances between RPS for weighting and determines the final RPS subset used for weighting through the entropy of the RPS. Through the presentation of several examples and specific experiments, we demonstrate its efficacy in handling extreme conflict scenarios and enhancing the quality of fusion outcomes.