Luyuan Chen

Distance measures in random permutation set (RPS) theory are crucial for characterizing inconsistency among permutation-based information distributions. However, existing RPS discrepancy measures do not explicitly distinguish ordering conflicts according to their positional importance under propensity semantics. To address this issue, this paper proposes a new RPS distance, termed MEOWA-KTC, by combining maximum-entropy-based ordered weighted averaging (MEOWA) weights with Kendall’s tau coefficient (KTC). Specifically, MEOWA-KTC constructs a top-weighted similarity between permutation events by using KTC to evaluate the ordinal consistency of corresponding sub-permutations and MEOWA weights controlled by an adjustable orness parameter to emphasize discrepancies at leading positions. Additionally, a spectral correction is applied to ensure that the proposed distance satisfies the metric axioms. Numerical examples and ablation results demonstrate the positional sensitivity of the proposed distance and the respective contributions of MEOWA weighting and KTC. Based on this distance, a fusion model is further developed to derive source support degrees and fusion weights from pairwise RPS distances. In the threat-assessment application, the proposed method produces stable decisions and generally larger decision margins than the benchmark methods. Monte Carlo experiments further demonstrate its robustness to mass-distribution and permutation-order noise.

Constructing basic probability assignments (BPAs) objectively and adaptively remains an important issue in Dempster–Shafer theory. To reduce the uncertainty caused by rigid nested focal element structures, this paper proposes ODE-BPA, a BPA generation method based on OTSU and Deng entropy. In ODE-BPA, hypothesis support values are normalized and sorted into an ordered sequence. OTSU is then used to construct two non-overlapping focal elements, while Deng entropy regulates the confidence degree for mass allocation. Experiments are conducted on twenty-five benchmark datasets, including mapping-structure comparison, ablation analysis, comparisons with existing BPA generation methods and classical machine learning classifiers, as well as the robustness evaluation under noisy and conflicting evidence. Rigorous statistical analysis demonstrates that ODE-BPA achieves competitive accuracy and ranking among existing BPA generation methods; exhibits performance comparable to that of SVM, naive Bayes, and decision tree under standard settings; and alleviates the influence of local noise and conflicting evidence in certain cases.

As an ordered extension of evidence theory, Random permutation set (RPS) theory has received increasing attention due to its advantage in dealing with order-structured uncertain information. However, a significant research gap remains in the current literature concerning the construction of RPS. Building on the interpretation of RPS as a layer-2 belief structure, this paper proposes a data-driven hierarchical method for generating RPS, called DDHRPS. Specifically, DDHRPS first generates BPA from statistical features of data on the layer-1 belief structure, and then refines them with propensity information derived from distance analysis between samples to single classes, ultimately forming RPS on the layer-2 belief structure. Moreover, a DDHRPS-based classification algorithm (DDHRPSCA) is presented. Experimental comparisons involving two kinds of classifiers, namely, two uncertainty-based classifiers and seven machine learning classifiers validate the effectiveness and superiority of DDHRPSCA in handling uncertain information in classification tasks.