An Order-Sensitive Conflict Measure for Random Permutation Sets

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.