Where does the indeterminacy come from?

Deriving the I of neutrosophic statistics from its sources

Abstract

In neutrosophic statistics the indeterminate part I of an estimate is usually fixed by hand. We compute I from the records, once the analyst’s choices (confidence level, tolerance band, coding of undecided records) are declared, and split it into typed components with provenance: measurement imprecision, which more data do not remove; sampling, which they do; conflict between sources; and hesitancy. We give the exact split for counts and interval data, a test of certified conflict whose false-conflict rate is guaranteed under stated assumptions, the two readings of a hesitant set, a typed arithmetic that keeps the labels through operations, and a table of actions for each component, together with a step-by-step reporting protocol and a checklist. The inferential tools are classical; what is new is the labelled representation and reporting rule built on them, which we map explicitly to its counterparts in interval statistics, imprecise probability, belief functions and hesitant sets. A decision-oriented example shows what the labels can change: among 298 conversations whose majority safety verdict is undecided, the current estimates suggest different follow-up priorities, additional ratings for 229 and examination of the “unsure” answers for 60, a distinction that a single interval does not make; these priorities have not been validated as interventions. With imprecision alone, a fixed I amounts to an interval representation. A single fused interval hull does not retain the identities of disagreeing sources or distinguish the provenance of its width components; the labelled report makes this information explicit. As a conditional illustration, a paired batch-means test on daily rain forecasts from five weather models flags between-model conflict in Guayaquil in 53 % and 76 % of the 90- and 365-day windows and in no Santiago window; its assumptions cannot be verified here, and its level was supported only in simulated designs matched to a persistence diagnostic estimated from the same data, not at 30 days or under strong persistence. In the DICES safety ratings, absence of certified conflict is inconclusive because power is low.