Uncertainty-Aware Reconciliation of Conflicting Sources on the Probability Simplex via Choquet Aggregation over Fuzzy Measures

We study the reconciliation of several biased, partially-overlapping estimators of a latent distribution on the probability simplex (the set of non-negative credit shares summing to one) when no ground truth is available to adjudicate their disagreement—the situation faced when conversion credit is reported by independent commercial attribution sources. We cast this as non-additive information fusion and develop a four-layer fuzzy framework: a reliability-weighted fuzzy representation, an interaction-corrected conflict measure, a Choquet integral with respect to an elicited fuzzy measure (capacity) followed by an L1-closure onto the simplex (a per-cell renormalization returning a valid distribution), and a Mamdani layer producing a conformally calibrated uncertainty band. Our theoretical contributions are (i) a simplex-consistency result—channel-wise Choquet aggregation with L1-closure always returns a valid distribution and reduces to the weighted mean under an additive capacity; (ii) variational and axiomatic characterizations of the operator; (iii) an exact Shapley–disagreement decomposition that quantifies how non-additivity reweights redundant sources; and (iv) a Lipschitz stability bound that guarantees robustness to noisy inputs. The capacity is elicited from observable signals alone, so the method requires no labels. On a firewalled, ten-seed benchmark across eight regimes the framework attains the lowest MAE in five of eight conditions and the lowest KL in six, improving on Dempster–Shafer, correlation-clustering, and reliability-weighted baselines by 1.6–2.3% (MAE) and 3.1–4.4% (KL)—significant in four of its five targeted redundancy- and bias-dominated regimes—with the conformal step attaining nominal coverage. This advantage stems from the elicited capacity rather than the Choquet operator (a simpler ordinal integral matches it on point error); Choquet is retained for its cardinal, calibratable output. An illustrative two-source real-data study exposes a 13.7% cost-per-install distortion in the single-source view, with the (uncalibrated) band widest where the sources disagree most.