Reliability-Calibrated Q-Rung Orthopair Neutrosophic Soft Ranking Under Partial Observability: An Auditable Industrial-Process Benchmark

Multi-criteria decision systems often interpret disagreement among criteria as evidence that some criteria are unreliable. This is problematic when the disagreement reflects a genuine operational trade-off. We develop a reliability-and-admissibility-calibrated q-rung orthopair neutrosophic soft ranking procedure (RAC-qRON) that distinguishes recorded evidence quality from the direction of criterion preferences. An explicitly bounded interval for each alternative–criterion observation is mapped to truth, indeterminacy and falsity memberships, with an admissibility proof for every integer rung q ≥ 1. Criterion weights are adjusted according to recorded information coverage rather than cross-criterion correlation, and a fixed-reference ideal-distance calculation produces an auditable rank. The method is evaluated on 21 historical operating records from an ammonia-oxidation plant, using the published Brownlee stack-loss data, four transparently specified criteria and no fictitious expert panel. With q = 3, the leading historical observation is day 21 (closeness 0.6885). Under 10% randomly masked cells, the mean Kendall rank correlation with the respective complete-data ranking is 0.750 for RAC-qRON, versus 0.806 for median-imputed TOPSIS; the model therefore does not exhibit superior missing-data stability. Rung sensitivity also changes the winning observation. The principal contribution is a mathematically admissible, evidence-traceable decision layer and a reproducible diagnosis of its strengths and limitations, rather than an unsupported claim of universal ranking superiority.