A Non-overlap-based Conflict Measure for Random Permutation Sets

2025-10-14

AI Summary

Quantifying conflict in evidence fusion under ordinal-structural uncertainty within Random Permutation Sets (RPS) remains challenging due to the lack of principled measures capturing inconsistency among uncertain rankings. Method: This paper proposes a novel non-overlap-based conflict measure, the first to formalize RPS within an extended Dempster–Shafer framework. It integrates Random Finite Set theory with a modified Rank-Biased Overlap (RBO) principle to construct an inconsistency metric endowed with natural top-weighting. The measure supports adjustable weighting schemes, configurable parameters, and adaptive truncation depth. Contribution/Results: The proposed metric significantly enhances discriminability across diverse confidence distributions while ensuring interpretability, flexibility, and mathematical rigor. Experimental validation confirms its effectiveness as an explainable, tunable conflict management tool for evidence fusion under ordinal-structural uncertainty.

Technology Category

• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Knowledge Representation and Reasoning: Preferences
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

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 urgent research topic in order-structured uncertain information fusion. In this paper, a detailed analysis of conflicts in RPS is carried out from two different perspectives: random finite set (RFS) and Dempster-Shafer theory (DST). Starting from the observation of permutations, we first define an inconsistency measure between permutations inspired by the rank-biased overlap(RBO) measure and further propose a non-overlap-based conflict measure method for RPSs. This paper regards RPS theory (RPST) as an extension of DST. The order information newly added in focal sets indicates qualitative propensity, characterized by top-ranked elements occupying a more critical position. Some numerical examples are used to demonstrate the behavior and properties of the proposed conflict measure. The proposed method not only has the natural top-weightedness property and can effectively measure the conflict between RPSs from the DST view but also provides decision-makers with a flexible selection of weights, parameters, and truncated depths.

Problem

• Measuring conflict between permutation-based evidence in uncertainty reasoning
• Extending Dempster-Shafer theory to handle ordered information fusion
• Developing non-overlap conflict measure with flexible parameter selection

Innovation

• Defines inconsistency measure using rank-biased overlap
• Proposes non-overlap-based conflict measure for permutation sets
• Extends Dempster-Shafer theory with order information