A distance for belief functions of orderable set

•We proposed a distance for orderable sets.•We discussed the relevant properties of the new distance.•We use the new distance to solve the project budget problem. This paper proposes a distance for measuring conflicts between ordered sets. A similarity coefficient is defined to quantify the distance between focal elements and it can characterize the differences in the distribution of sets in a continuous measurement space, so the distance would still vary with the physical distance even when the focal elements do not overlap. We prove that the proposed method satisfies the properties of distance, and discuss some other properties of the presented approach. An example of engineering budget indicates that the proposed distance can effectively measure the similarity of orderable set. By comparing with the existing methods, we show that the proposed metric is more robust and accurate in characterizing the aggrement of ordered sets.