An efficient uncertainty integrated aggregation scheme for water quality detection and longitudinal carbon offset estimation in the Yamuna River

River water quality deterioration caused by industrialization and urbanization not only threatens public health but also weakens ecosystem services such as carbon assimilation. Conventional water quality indices and deterministic assessment models inadequately represent the heterogeneous and uncertain nature of hydrochemical and microbial monitoring data, particularly in complex river systems like the Yamuna. This study aims to develop an uncertainty-aware framework for (i) reliable detection of water quality degradation hotspots and (ii) quantitative estimation of longitudinal carbon offset capacity along the Yamuna River by explicitly modeling measurement indeterminacy and nonlinear pollution effects. An ellipsoidal single-valued neutrosophic modeling structure is introduced to represent directional and anisotropic uncertainty in physicochemical and microbial parameters. Two trigonometric aggregation operators—ellipsoidal single-valued neutrosophic trigonometric weighted averaging (E-SvNVTWA) and weighted geometric (E-SvNVTWG)—are formulated to capture overall ecological condition and extreme pollution sensitivity, respectively. Neutrosophic efficiency indices derived from 25 CPCB monitoring stations are further linked to a normalized carbon offset estimation model to evaluate ecosystem service potential. The dual-operator framework reveals a pronounced upstream–downstream gradient in ecological condition. Upstream stations (e.g., Dehradun, Hanumanchatti) exhibit high neutrosophic efficiency (> 0.9) and higher relative ecological processing efficiency, while downstream industrial stretches (e.g., Hasanpur, Mohena Palwal) show sharp efficiency decline and near-zero TWG values, indicating ecological functional stress. The TWG operator demonstrates enhanced sensitivity to severe organic and microbial pollution, effectively identifying critical degradation hotspots. The proposed ellipsoidal neutrosophic dual-aggregation model provides a structured uncertainty-aware decision-support framework that integrates uncertainty modeling, nonlinear pollution response, and ecosystem service evaluation. By linking water quality diagnostics with carbon offset potential, the framework advances climate-relevant river basin assessment and supports sustainability-oriented management of heavily stressed river systems.