Dempster-Shafer Theory

Anti-UAV systems increasingly fuse multiple sensors, yet their detection heads provide no per-modality reliability signal. This study evaluates whether evidential deep learning (EDL) heads, Dempster-Shafer (DS) evidence fusion, and uncertainty-driven temporal sensor gating improve anti-UAV detection through a controlled ablation on three benchmarks: thermal tracking (AntiUAV600), RGB-audio-RF classification (TRIDENT), and RGB-IR tracking (MM-UAV). The EDL training objective improves accuracy over retrained sigmoid baselines (+5.9 percentage points in accuracy and a tripled tracker-on-absent rate in E1; +4.8 percentage points in classification accuracy in E2, surviving a clip-clustered bootstrap, p = 0.011) and ranks classification errors substantially better (entropy UAUC approximately 0.94 vs. 0.51). The remaining components do not support their respective hypotheses. DS fusion does not outperform simple probability averaging. Dirichlet vacuity adds no ranking power beyond predictive entropy and inverts at the detection level, where extreme background imbalance causes it to encode class membership rather than error likelihood, a failure also observed for entropy and sigmoid confidence. Temporal gating preserves accuracy only when nearly inactive and yields no realised latency saving on shared-backbone hardware. The benefit of evidential learning therefore arises primarily from its training objective rather than its uncertainty estimate; a crop-level control further localises the detection-level breakdown to anchor-level evaluation rather than the learned representation.

Multi-source evidence fusion under Dempster-Shafer theory faces two persistent challenges: existing conflict measures assess inter-evidence inconsistency and intra-evidence uncertainty independently, yielding incomplete evaluations, and current fusion methods evaluate evidence sources exclusively through instantaneous comparisns without exploiting their long-term reliability across diverse decision contexts. This paper proposes a unified evidence reasoning framework that addresses both limitations. Specifically, a chaos-conflict measurement is introduced to jointly quantify cross-evidence conflict and intra-evidence non-specificity, with five formally proven properties ensuring consistent assessment. A historical experience driven weighting scheme partitions the decision space via spectral clustering and applies regret theory to compute context-specific reliability profiles from past fusion outcomes. These mechanisms feed into a hybrid combination rule that adaptively balances uncertainty preservation against weighted consensus, controlled by the global conflict level, followed by a belief-interval decision strategy that enables robust classification without discarding epistemic uncertainty. Experiments on 16 real-world benchmark datasets demonstrate that the proposed framework achieves an average F1 score of 85.78 and a mean AUC of 93.30, outperforming eight DST-based baselines and three gradient boosting methods. Ablation analysis confirms the contribution of each component we proposed. The framework offers an effective approach for adaptive evidence fusion in multi-source decision making.

Reducing the number of focal elements of a mass function is classically driven by an intrinsic distance, such as Jaccard or Jousselme, that keeps the approximation close to the original as a body of evidence. We consider instead the case where the mass function feeds a linear combinatorial optimisation problem with evidential costs. What should then be preserved is not the closeness of the two mass functions, but the quality of the decision they induce. We introduce a decision-aware approximation that targets the regret of the decision: one decides with the cheaper approximation and is evaluated under the true mass function. On a minimal shortest path, the distance-optimal approximation flips the decision while a decision-aware merge preserves it, and this occurs on a non-negligible fraction of random instances. We prove a one-point bound that localises the regret at the true optimum, turn it into an exact dynamic program for the scalar case, and extend it to an online version that prunes focal elements before the final cost is known. In experiments the decision-aware compressor flips the decision less often than representation-aware compression, for both the linear criterion and a non-linear proxy read-out.

Multimodal fusion architectures typically assume all modalities are available at inference, yet sensor failures, acquisition variability, and cost constraints routinely produce incomplete observations. Existing work treats modality absence as a prediction-accuracy problem, leaving a more basic question unanswered: whether a model's confidence estimates remain calibrated when an entire input stream is removed. We argue that missing-modality robustness and calibrated uncertainty are a single coupled property, and introduce Modality-Conditioned Conformal Fusion (MCCF), an architecture that addresses both at once. MCCF combines a multimodal bottleneck fusion backbone trained with modality dropout, per-modality evidential heads producing modality-decomposed Dirichlet distributions, and a Dempster-Shafer combination rule that fuses the per-modality evidence into a joint predictive distribution; an absent modality contributes vacuous evidence that is structurally ignored, so the fused uncertainty automatically reflects the reduced information without test-time imputation. A Mondrian conformal calibration module keyed on the modality-presence mask then provides finite-sample group-conditional coverage for every non-empty modality subset. MCCF is, to our knowledge, the first method with formal coverage guarantees under arbitrary modality availability through architectural integration rather than post-hoc recalibration, and the evidential decomposition yields per-modality vacuity scores that localise uncertainty to the absent modality responsible. Across a synthetic problem and three real multimodal benchmarks, MCCF holds its target coverage on every modality-presence subset, substantially narrows the coverage gap between full and partial modalities relative to a marginal split-conformal baseline, and imposes no measurable accuracy cost relative to temperature-scaled and evidential baselines.

Recent multimodal survival prediction models have demonstrated strong predictive performance by leveraging complementary information across modalities. However, such models generally assume data completeness and exhibit limited robustness toward missing modalities, which are frequently encountered in real-world clinical settings. We propose the Evidential Missing Modality Survival Fusion (EMMS) model for multimodal survival prediction under missing modalities. EMMS offers a straightforward, computationally effective approach to survival analysis without requiring a generative phase for missing data. By employing Dempster-Shafer theory and Gaussian Random Fuzzy Numbers for multimodal decision fusion, it considers both aleatoric and epistemic uncertainty alongside modality reliability for fusion. Moreover, the model treats missing modalities as vacuous evidence, preventing interference with available inputs and naturally reflecting increased uncertainty and calibrated predictions. Extensive experiments on four cancer datasets demonstrate state-of-the-art performance while providing calibrated and interpretable uncertainty estimates under incomplete multimodal observations, without introducing additional computational overhead.

Audit risk assessment increasingly benefits from combining heterogeneous evidence sources, yet existing approaches typically produce point predictions without quantifying how well different evidence streams agree. We propose UMAR (Uncertainty-Aware Multi-Agent Risk Assessment), a framework that employs three specialized agents: an MD&A Text Agent, a Financial Ratio Agent, and a CAM Agent, each producing independent risk scores with calibrated uncertainty estimates. An Uncertainty Aggregator based on Dempster-Shafer evidence theory fuses these scores while explicitly measuring inter-agent conflict. We evaluate UMAR on a U.S. dataset of 3,200 firm-year observations from SEC 10-K filings (2019-2023), with financial restatement as the target label. Experimental results show that UMAR achieves an AUROC of 0.782 and a PR-AUC of 0.341, outperforming logistic regression, XGBoost, FinBERT, and single-agent and dual-agent LLM baselines. UMAR attains the lowest expected calibration error (ECE = 0.052) among all methods and identifies evidence-conflict patterns that correlate with actual restatement risk, offering auditors potentially actionable and interpretable risk signals.

Biomedical question answering often requires decisions from retrieved literature whose relevance, quality, and support for candidate answers are uneven. Most retrieval-augmented large language model (LLM) methods feed this literature to the model as flat text, leaving evidence reliability and remaining uncertainty largely implicit. We propose BELIEF, a structured evidence modeling and uncertainty-aware fusion framework for closed-set biomedical question answering. Rather than treating retrieved documents as undifferentiated context, BELIEF converts them into evidence objects that record clinical attributes, source quality, question relevance, support strength, and the associated candidate hypothesis. These evidence objects provide a shared basis for two complementary reasoning paths. The symbolic path constructs reliability-weighted basic probability assignments based on Dempster--Shafer (D-S) theory over a finite answer space and performs uncertainty-aware symbolic evidence fusion to estimate belief and residual uncertainty. The neural path uses the same structured evidence for LLM-based semantic inference, while a reliability-aware arbitration module reconciles the symbolic and neural outputs according to belief strength, uncertainty, evidence reliability, and semantic consistency. Experiments on PubMedQA, MedQA, and MedMCQA with five general-purpose LLM backbones show that BELIEF obtains the best result in 25 of 30 backbone--dataset--metric settings. Comparisons with biomedical-domain models indicate that BELIEF is competitive on MedQA and MedMCQA, while specialized biomedical pretraining remains advantageous on PubMedQA. Ablation, complementarity, uncertainty-stratified, and cost analyses further show that BELIEF improves retrieved-evidence utilization by making evidence structure, path disagreement, and decision uncertainty explicit.

Dempster's rule is a fundamental tool for combining belief functions from distinct and reliable sources. However, its intersection-based semantics imposes strong structural restrictions, which limits its flexibility in handling complex source states and diverse information fusion scenarios. To overcome this limitation, we propose a reversible transformation, derived from the isopignistic principle, between belief functions and a possibilistic structure defined on the power set. In this transformation, the relationships among subsets are explicitly characterized by a belief evolution network, which provides a more flexible representation of evidential information beyond the conventional mass function structure. On this basis, we further introduce the triangular norm family to develop a general and adaptive evidential information fusion framework. Unlike fusion methods rooted in Dempster semantics, the proposed framework supports more flexible combination behaviors and exhibits advantages in non-distinct source fusion, conflict management, parametric combination design, and heterogeneous information fusion.

Belief functions are a powerful and popular framework for the mathematical characterisation of uncertainty, in particular in situations in which lack of data renders learning a probability distribution for the problem impractical. The first step in a reasoning chain based on belief functions is inference: how to learn a belief measure from the available data. In this survey we focus, in particular, on making inference from statistical data, and review the most significant contributions in the area.