Structural and Epistemic Symmetry Between the Canonical Biplot and the Gravity Model of Trade: A Neutrosophic Z-Number Proof of Concept

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Abstract
The canonical biplot and the gravity model of trade have developed in isolation, yet both rest on symmetry principles that suggest common analytical ground. This article maps the two literatures (PRISMA 2020; Web of Science and Scopus; 2004–2024; 16 canonical biplot and 2066 gravity model open-access documents) and proposes a symmetry-aware proof of concept for their integration through neutrosophic Z-numbers. Economic mass, geographical distance, and trade policy were represented as neutrosophic Z-numbers elicited against a documented rubric, weighted by an analytic hierarchy process with consistency ratio 0.0079, and aggregated with the weighted arithmetic and weighted geometric operators. The principal components of the biplot are treated as the projection space rather than as a fourth criterion since a methodological artefact and an economic determinant are not commensurable. The arithmetic operator lies marginally closer to the positive ideal (0.1689 against 0.1700), and a Monte Carlo experiment over 400,000 draws preserves that order in every draw, so it is robust but negligible. Against four alternative operators and two reduced frameworks, discarding the reliability layer understates the distance to the ideal by about 9%. The contribution is methodological feasibility; a pre-specified protocol for empirical validation is also provided.

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