Fuzzy memberships represent graded predicates [2]. When such grades are interpreted as a normalized possibility distribution, they can be represented by consonant belief functions [11]. This semantic assumption is substantive: class probabilities and possibility grades are distinct objects, and simply rescaling a probability vector to maximum one does not preserve its probabilistic interpretation.

The representation must be chosen for the meaning of the input assertions. In the conceptual specification, normalized possibility grades describe singleton plausibilities; in the reported experiments, classifier probability vectors supply numerical inputs. The experiments therefore examine the resulting implemented fusion scores rather than validate a general conversion from linguistic vagueness into belief masses. The Awareness Logic of Ambiguity distinguishes interpretive valuation, contextual alignment, and epistemic restraint [12]; this supplies a semantic reason to record assertion meaning separately from learned source reliability, without replacing the evaluated fusion rule.

Dempster’s multivalued mappings induce lower and upper probabilities [3], and Shafer’s theory provides belief assignments on a frame of discernment [4]. The transferable belief model distinguishes credal representation from pignistic decision making [9]. We use that distinction to state mass-level discounting separately from the final read-out; it does not establish probability calibration.

Dempster's rule combines independent evidence by multiplying the masses of intersecting focal sets and renormalizing by one minus the conflict coefficient. The rule is commutative, associative, and justified when its assumptions hold, which explains its canonical status [3], [4]. Its normalization step, however, redistributes conflict proportionally among the remaining focal sets, and Zadeh showed that slight overlap between two highly conflicting but reliable sources can be inflated into certainty [6]. This pathology motivated a family of alternative rules that differ in where the conflict mass is deposited [7], [11].

Yager and Dubois–Prade rules differ in how they reallocate conflict [7], [11]. Murphy’s repeated-combination construction first averages masses [8]. Denoeux’s cautious combination concerns nondistinct bodies of evidence [13] and is a different operator. Averaging can moderate outlier evidence, but repeated Dempster self-combination still sharpens the pooled mass and can magnify systematic errors.

Contextual discounting models reliability that varies with the state of the world [10]. The present source-wise weights are a simpler scalar choice. Our comparison examines their effect within one implemented fusion pipeline; it does not establish that weighted pre-averaging is universally preferable to other conflict-management rules.

Truth-discovery research studies conflicting claims from sources of unknown quality [5], [14]. Agreement-based estimators connect inferred source quality to inferred truth, but copying and other dependencies can distort agreement [15]. These ideas motivate the conceptual unsupervised component. The reported experiments use supervised validation accuracy instead and do not evaluate this fixed-point estimator. A provenance record should retain the inputs, transformations, weighting parameters, and decision rule needed to explain a fused output. This design treats the estimated weights and their versions as part of the record. Recording them supports inspection; it does not make those weights identifiable as true source accuracies.

The Open Provenance Model supplies a vocabulary for artifacts, processes, and agents [16], while reproducible computational research requires inspectable inputs and executable procedures [17]. The present architecture adopts these as design requirements. The experimental description reports a rerun check and limited logs, rather than a complete independently audited replay system.

Across the reviewed streams, four requirements emerge for trustworthy fusion of conflicting assertions. The representation layer must express graded assertions without pretending to more precision than the sources possess, and the weighting layer must estimate reliability without ground truth while degrading gracefully when its assumptions fail. The combination layer must resist conflict pathologies while remaining interpretable. The systems layer must emit decisions that are versioned, deterministic, and auditable by third parties.

The framework connects representation, weighting, combination, and provenance as an engineering specification. The contribution is their explicit separation and a supervised proof-of-concept comparison, rather than a verified claim that no prior framework meets these requirements.

Three questions organize the analysis. RQ1 concerns the mathematical and semantic conditions for a consonant mapping. RQ2 concerns how source-quality weights influence fusion under heterogeneous corruption. RQ3 concerns what inputs and records are needed to reproduce a decision. The reported experiments address a supervised realization of RQ2 and provide only partial evidence on RQ3.

The empirical comparison examines whether reliability-weighted fusion loses less accuracy than raw Dempster combination as one source is corrupted, and whether learned weights improve on uniform weights. It also reports a deterministic rerun check. The unsupervised fixed-point estimator, its convergence, and a complete provenance replay were not evaluated, so the campaign does not validate a universal unsupervised reliability guarantee or necessary-and-sufficient audit conditions.

For each entity e, let Θ_e be a finite, exhaustive frame of mutually exclusive candidates. Sources s ∈ S supply profiles on that same frame. In the conceptual specification these are possibility grades; α_s ∈ [0, 1] is a reliability-discounting coefficient, β_s is a normalized averaging weight, m_s a mass assignment, and G a provenance ledger. The supervised experimental realization is specified separately in Section 5.

Order a nonnegative profile as μ_(1) ≥ … ≥ μ_(K) and normalize its positive maximum to one. Let B_(k) contain the k highest-ranked candidates, with a deterministic tie order. Interpreting the normalized grades as singleton plausibilities gives the consonant assignment [11].

m_s(B_(k)) = mu_(k) − mu_(k + 1), k = 1, . . . , K, with mu_(K + 1) = 0, B_(K) = Theta_e.

Eq. (1) telescopes to total mass one; tied adjacent grades generate zero masses, so the representation is unaffected by their ordering after zero-mass focal sets are removed. Reliability discounting uses α_s ∈ [0, 1], moving the undiscounted complement to Θ_e [4], [10]. Eq. (3) defines pairwise conflict.

m_s^{alpha_s}(A) = alpha_s ∗ m_s(A) for A ! = Theta_e; m_s^{alpha_s}(Theta_e) = 1 − alpha_s + alpha_s ∗ m_s(Theta_e).

K_{ij} = sum_{A intersect B = empty set} m_{s_i}^{alpha_i}(A) ∗ m_{s_j}^{alpha_j}(B). (3)

m̄ = Σ_s β_s m_s^{α_s}, β_s = α_s / Σ_j α_j when Σ_j α_j > 0; m_fuse = m̄ ⊕ ⋯ ⊕ m̄ (n factors). If Σ_j α_j = 0, set m_fuse(Θ_e) = 1.

In Eq. (4), ⊕ denotes normalized Dempster combination, defined only when its conflict is less than one. Repeating the average is a Murphy-style sharpening operation [8], not independent acquisition of new evidence and not cautious combination. If a normalization is undefined, the specification returns the vacuous mass on Θ_e and records that fallback. For normalized masses with m_fuse(∅) = 0, the pignistic transformation distributes each focal mass over its elements [9].

BetP(theta_k) = sum_{A contains theta_k} m_fuse(A) / |A|. (5)

The conceptual task is to choose a reliability-estimation procedure and fusion rule for aligned profiles while recording sufficient inputs and transformations for replay. Without labels or an identifiable generative model, Discounting reduces committed mass before combination, but high disagreement does not guarantee convergence toward maximal ignorance. For two fully reliable point masses on different singleton candidates, the equal average has mass 0.5 on each singleton and zero on the full frame; its two-fold normalized self-combination retains those masses. Thus it yields a non-vacuous tie rather than full ignorance. Source order is immaterial to the specified fixed-weight average, but it can matter if weights are adapted sequentially. The supervised experiment adds a different high-conflict fallback described in Section 5.

A proposed provenance record contains input hashes, reliability estimates and traces, conflict values, the rule identifier, code and environment versions, random seeds, and the output [16], [17]. Replay also requires the original input bytes, ordering conventions, and numerical environment. Fixed ordering and seeds help reproducibility but do not alone guarantee bitwise identity across platforms. The reported experiment claims two identical result files; a complete independent audit of G is not supplied.

Pairwise concordance over M overlapping entities costs O(n²MK), and constructing each ranked consonant profile costs O(K log K). Each source has at most K nonzero focal sets. Averaging sources with different candidate orders and taking repeated intersections can destroy consonance and produce many more focal sets, up to an exponential dependence on frame size in general. Complexity therefore depends on the actual focal-set representation and pruning policy. Aligned frames, informative source diversity, and complete retained records are assumptions; coherent collusion or unlogged input errors need not be detectable from internal logs.

Algorithm 1. Conceptual fusion specification with optional agreement weighting.

Input: aligned profiles μ_{s,e}, finite frame Θ_e, supplied coefficients α_s ∈ [0,1], deterministic tie order 1: for each entity e do 2: validate nonnegative finite profiles and their common possibility interpretation 3: if any profile has maximum zero, record rejection and continue with the next entity; otherwise normalize profiles to maximum one 4: build each consonant mass m_s using Eq. (1) 5: record the estimator, data split and version associated with every supplied α_s 6: if Σ_s α_s = 0, set m_fuse(Θ_e) = 1 and go to step 12 7: discount each mass using Eq. (2) 8: set β_s = α_s / Σ_j α_j 9: set m = Σ_s β_s m_s^{α_s} 10: combine m with itself n times by normalized Dempster combination 11: if a normalization is undefined, replace the output by the vacuous mass and record the fallback 12: compute BetP using Eq. (5) 13: select its maximum using the declared deterministic tie order 14: record inputs, coefficients, conflicts, rule, versions and output in G 15: end entity loop 16: return decisions and records Output: conceptual fused estimates and their provenance records

The reported experiment uses breast cancer (569 instances, 30 features, 2 classes), optical digits (1,797 instances, 64 features, 10 classes), and wine (178 instances, 13 features, 3 classes) from scikit-learn [18], [19]. Features are standardized with inner-training statistics and partitioned into contiguous blocks of widths 10/10/10, 22/21/21, and 5/4/4. Sources 1–3 use logistic regression (C = 1), seven-nearest-neighbor classification, and Gaussian naive Bayes. These are constructed classifier sources on a shared dataset, not independently acquired sensors or human assertions.

Corruption is injected at source 2 only, at four levels c in {0, 10, 20, 30}%, combining two fault modes. Feature dropout sets a c-fraction of source-2 entries to zero after standardization - that is, replaces them with the feature mean - and is applied to the inner-training, validation, and test partitions alike, emulating a sensor whose readings drop out persistently rather than only during model fitting. Label noise flips a c-fraction of source-2's training-fold labels to a different class, so the corrupted source's own model is also fitted on mislabelled data; the labels seen by the other sources, by the validation split, and by the test evaluation remain clean. The source reports seeded generators for the splits and corruption draws.

Each of ten seeds uses a stratified 75/25 train/test split and an 80/20 inner-training/validation split of the training portion. The reported Essential Work of Fracture (EWF)-Fuse realization learns static weights proportional to acc_s² from clean validation labels; it is supervised. It then adapts effective strengths through consensus-referenced exponential averaging (rate 0.3) over ten test batches and uses reliability-weighted averaging when instance-level raw pairwise conflict exceeds τ = 0.5. The description also reports evidence strength 1−H(p)/log K for source probability vectors, direct discounted Dempster combination, and pignistic read-out. It does not supply the exact focal-mass allocation or establish equivalence to the consonant mapping and repeated-average combination of Eqs. (1) and (4). The empirical results therefore concern this described implementation rather than validate the conceptual algorithm. Averaging and voting are conventional comparators [20]; stacking fits a logistic meta-learner (C = 1) to concatenated validation probabilities [21]. Expected Calibration Error (ECE) uses ten equal-width bins and is reported alongside Negative Log-Likelihood (NLL) [22].

The source reports a 27-second campaign on three datasets, four corruption levels, ten seeds, five methods, and six ablation variants under Python 3.12 with NumPy, SciPy, scikit-learn, statsmodels, and Matplotlib. It also reports two byte-identical result files with SHA-256 prefix 07a96ea9c2a0. The executable files and complete hashes are not established by the supplied DOCX. These statements remain reported reproducibility observations rather than an independently rerun result or complete provenance audit.

Table 1 reports pooled accuracy means and standard deviations over three datasets and ten seeds. EWF-Fuse exceeds probability averaging, voting, and raw Dempster–Shafer combination at all four displayed corruption levels; it is itself learned from labels. At 30%, its mean accuracy is 90.2 ± 8.5%, versus 77.6 ± 25.4%, 84.7 ± 15.1%, and 82.9 ± 12.0% for those comparators. Stacking reaches 93.3 ± 4.9%. The displayed clean-to-30% changes are approximately 4.1 percentage points for EWF-Fuse, 8.5 for raw Dempster–Shafer, 7.5 for averaging, and 2.3 for stacking. These differences use rounded table means and may differ from unrounded run-level contrasts. Pooled standard deviations reflect dataset heterogeneity as well as repeated-split variability; they are not confidence intervals.

The source reports a 93.2–96.4% breast-cancer range across the grid and a 97.6% tie between EWF-Fuse and stacking on wine at 30% corruption. On digits, raw Dempster–Shafer accuracy changes from 66.7% to 42.6%, while EWF-Fuse changes from 90.4% to 78.8% and stacking from 93.7% to 87.4%. These observations are consistent with sensitivity of the tested combination and classifiers to corruption. They do not isolate conflict normalization as the sole cause, because evidence construction, source accuracy, and confidence change together.

Table 2 compares the full supervised realization with its ablations. Uniform weights reduce aggregate accuracy at 30% corruption from 90.2% to 78.0%, with digits accuracy changing from 78.8% to 43.2%. This supports the usefulness of validation-based weights within this implementation; it does not test the unsupervised estimator or prove the corrupt source is always identified. Weight exponents 1 and 3 yield aggregate accuracies 87.8% and 89.7%, respectively, against 90.2% for exponent 2.

Removing consensus adaptation changes displayed aggregate accuracy from 91.4% to 91.2% at 20% corruption and from 90.2% to 90.0% at 30%, a 0.2-point difference in both cases. Removing the conflict fallback leaves the displayed accuracy unchanged. These small ablation differences do not establish an unmeasured benefit on longer streams. The representative logged run shows the source-2 effective strength decreasing from about 0.32 to 0.19 over ten batches.

Fig. 2 shows a reported digits run at 30% corruption, seed 0. Per-batch mean raw conflict is approximately 0.30–0.37, while the fraction of instances using the fallback is approximately 0.07–0.20. A batch mean below τ = 0.5 can coexist with individual instances above τ; the branch must therefore be interpreted at the instance level. The source reports decreasing mean conflict as corruption increases because flatter outputs reduce entropy-based strength. The effective source coefficients in panel b) do not sum to one and should be read as discounted strengths, separately from normalized averaging weights β. Declining agreement with a consensus is not itself proof of corrupted-source identification.

At 20% corruption, voting has the lowest displayed ECE (0.090), and stacking has the lowest ECE among the continuous soft combiners (0.127) and the lowest NLL (0.29). EWF-Fuse has the highest ECE (0.319) and NLL 0.63. Raw Dempster–Shafer has the highest NLL (2.02), but its ECE (0.196) is below EWF-Fuse’s. Discounting can flatten decision probabilities, yet unsigned ECE does not establish systematic underconfidence; reliability diagrams or signed calibration summaries would be needed. Any recalibration must use a separate training or validation partition.

The source applies Friedman and paired Wilcoxon tests to 30 dataset-by-seed blocks per condition, with Holm adjustment across four EWF-Fuse comparisons [23], [24]. At 30% corruption it reports Friedman χ²(4) = 54.4, p = 4.2×10⁻¹¹ and the contrasts in Table 4. These are reported exploratory statistics: repeated random splits overlap within only three datasets, so the 30 blocks are not 30 independent datasets. The p-values do not by themselves validate broad population significance. Dataset-level or hierarchical, dependence-aware analysis and raw paired outcomes are needed. The reported NLL comparison at 20% gives W = 0, p = 1.9×10⁻⁹, subject to the same dependence limitation.

The reported campaign shows smaller pooled accuracy loss under the tested corruption protocol and a substantial advantage of supervised weights over uniform weights. The evidence does not evaluate agreement-based unsupervised convergence or its error guarantees. The stated byte-identical reruns address deterministic output in one environment only, and do not establish complete replay or negligible provenance overhead. Stacking has the highest pooled accuracy at every corruption level and leads EWF-Fuse by the reported paired contrast of 3.1 points at 30% corruption (Holm-adjusted p = 0.0016, with the dependence limitation above). Both methods have access to labelled validation information. A meta-learner can use class-specific patterns that scalar reliability weights cannot, but this mechanism is an interpretation rather than an isolated causal finding. The wine tie does not establish that small validation sets generally favor EWF-Fuse. Reliability-only deployment and label-free operation remain separate untested questions.

The corruption protocol modifies only source 2 through coupled dropout and training-label noise. Multi-source, adversarial, and drifting corruption are untested. Reliability is learned from validation labels rather than the conceptual agreement estimator. Test-batch adaptation also changes the inference protocol; confirmation that each batch is scored before updates and that no test labels enter any update is needed to assess causal online use. The calibration deficit limits probability-sensitive deployment without further validation.

The reported outcomes are proof-of-concept observations on three tabular benchmarks. Independent execution, dataset-level inference, and evaluation on genuinely heterogeneous acquisition sources are needed before stronger application claims can be made.

The conceptual consonant mapping assumes possibility semantics and does not capture arbitrary non-consonant evidence. Agreement cannot identify coherent collusion without additional assumptions or anchors [15]. Repeated combination may enlarge the focal-set space and sharpen dependent evidence. The supervised campaign does not validate the unsupervised estimator, complete provenance architecture, or actual sensor/database/human fusion. Its repeated splits overlap and its pooled metrics mix three datasets. Code, raw outcomes, exact mass allocation, adaptation order, and independent replay remain material evidence requirements.

Alternative probability, belief-function, and possibility models should be compared under the same input semantics and validation access. The present campaign demonstrates the value of supervised reliability weighting within one implementation while stacking remains stronger in pooled accuracy. It does not establish an advantage when validation labels are unavailable. Provenance requirements can be applied to any of these calculi, and their implementation should be tested independently of the fusion-score comparison.