Volume 11 • Issue 1 • PP: 09–16 • 2026
Robust Jensen–Shannon Consensus Geometry for Single-Valued Neutrosophic Information
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© 2026 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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Let x = (T, I,F) ∈ [0,1]3 denote a single-valued neutrosophic assessment and let wT +wI +wF = 1 with wc > 0. This paper introduces the probability-completed embedding Φw(x) = wT T,wT (1−T),wI I,wI(1−I), wFF,wF (1−F) ∈ Δ5. and the pullback distance dw(x,y) = [J(Φw(x),Φw(y))/log2]1/2 , where J is Jensen–Shannon divergence. The construction yields a bounded metric, separates into three weighted Bernoulli Jensen–Shannon terms, is invariant under the neutrosophic complement xc = (F,1−I,T) when wT = wF , and has the local information metric d2w (x,x+δ) = 1 8log2 Σ c∈{T,I,F} wcδ2 c xc(1−xc) +O(∥δ∥3). On this geometry, robust consensus is posed as the bounded M-estimation problem bxτ = argmin x∈(0,1)3 mΣ r=1 ar{1−e−τd2w (x,xr)}. A majorization–minimization iteration reduces each step to three one dimensional weighted Jensen–Shannon barycenters and decreases the objective monotonically. The induced expert weight is proportional to e−τd2w, so strongly conflicting assessments are downweighted without a hard rejection threshold. In a reproducible contamination study with 15 experts, 800 replications at each of five contamination levels, and a fixed τ = 60, the proposed estimator has mean normalized Jensen–Shannon error 0.0149 at 40% oppositional contamination; the coordinate median, ordinary Jensen–Shannon barycenter, and arithmetic mean obtain 0.0380, 0.1448, and 0.1489, respectively. The contribution is therefore a metric and optimization framework for consensus itself, rather than another ranking operator: neutrosophic disagreement is represented on a common information-geometric scale and robust aggregation follows from a bounded variational principle.
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