# An Order-Sensitive Conflict Measure for Random Permutation Sets

arXiv: https://arxiv.org/abs/2510.16001 · HTML: https://mlsanity.com/paper/2510.16001/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 2 of its 50 references that are in the map.
- First posted on arXiv 14 Oct 2025.

## Builds on (most cited first, 2 of 2)

- [The Matter of Chance: Auditing Web Search Results Related to the 2020 U.S. Presidential Primary Elections Across Six Search Engines](https://mlsanity.com/paper/2105.00756/) (2021)
- [Limit of the Maximum Random Permutation Set Entropy](https://mlsanity.com/paper/2403.06206/) (2024)

## Abstract (arXiv)

Random permutation set (RPS) is a new formalism for reasoning with uncertainty involving order information. Measuring the conflict between two pieces of evidence represented by permutation mass functions remains an open issue in order-dependent uncertain information fusion. This paper analyzes conflicts in RPS from two different perspectives: random finite set (RFS) and Dempster-Shafer theory (DST). From the DST perspective, the order information incorporated into focal sets reflects a qualitative propensity where higher-ranked elements are more significant. Motivated by this view and observations on permutations, we define a non-overlap-based inconsistency measure for permutations and develop an order-sensitive conflict measure for RPSs. The proposed method reformulates the conflict in RPSs as a graded, order-dependent notion rather than a simple dichotomy of conflict versus non-conflict. Numerical examples are presented to validate the behavior and properties of the proposed conflict measure. The proposed method not only exhibits an inherent top-weightedness property and effectively quantifies conflict between RPSs within the DST framework, but also provides decision-makers with flexibility in selecting weights, parameters, and truncation depths.