A layered framework for neutrosophic statistics: foundational distinctions, empirical validation, and operational implementation
Year: 2026
Type: article
Abstract: Neutrosophic statistics encompasses several mathematically distinct frameworks that are frequently conflated, blurring its relation to interval and classical methods. We organize neutrosophic statistics as three layers: (i) neutrosophic arithmetic ๐ = ๐ + ๐๐ผ with indeterminate components beyond intervals; (ii) neutrosophic set statistics over (๐, ๐ผ, ๐น) triplets as structurally independent dimensions; and (iii) plithogenic statistics with degree of appurtenance. We provide six lines of validation: a formal analysis showing interval projection is a lossy compression of neutrosophic numbers; empirical evidence on 510 expertannotated triplets that (๐, ๐ผ, ๐น) data does not reduce to an interval-derived construction (T-I coupling 3.4ร weaker than the algebraic counter-factual, I-F sign reversal, and 34.9% paraconsistency ๐ + ๐น > 1 which interval-derived data cannot reach); a head-to-head benchmark on ten causal hypotheses where neutrosophic zone classification reaches 90% accuracy against expert ground truth; a UCI benchmark on five datasets with Consensuszone accuracy 0.973โ1.000; an extended evaluation across fourteen UCI datasets and five base classifiers with Friedman ๐2 = 44.55, ๐ < 10โ8; and layer-selection diagnostics. The thirdanswer library provides an open-source implementation. The framework supplies principled tools for multi-criteria decision analysis and uncertainty-aware evaluation.
Authors: Maikel Vazquez, Florentin Smarandache
Institutions: Universidad Bolivariana del Ecuador, University of New Mexico
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W7208760360