Neutrosophic Hankel Transforms and Their Application to Cross-Domain Legislative Integration

This paper introduces the Neutrosophic Hankel Transform (NHT) as a novel mathematical framework for modeling systems with radial structure under uncertainty, indeterminacy, and inconsistency. Building upon classical Hankel transforms and neutrosophic logic, we define two complementary realizations: a componentwise transform (NHT–C) that transports uncertainty with the signal, and a kernel-weighted transform (NHT–K) that embeds neutrosophic weights into the integral kernel. We establish linearity, inversion, and Parseval-type relations, and derive operational rules that diagonalize the Bessel radial operator. To demonstrate utility, we formulate a radial diffusion–reaction model for pollutant concentration in a radialized river cross-section and solve it in closed form under neutrosophic initial and boundary information. A legal-compliance belt and sensor-trust heterogeneity are encoded as neutrosophic kernel weights, and an AI-driven calibration loop aligns parameters with multi-source observations under policy constraints. The approach maintains full interpretability via truth/indeterminacy/falsity channels, offering a bridge between advanced mathematical analysis and ecological governance in the Yellow River Basin.