Research on the correlation degree between the manufacturing industry and the digital industry in the Yellow River Basin based on the grey matrix correlation model

Purpose This paper constructs a grey matrix correlation model to thoroughly investigate the integration mechanism between the digital and manufacturing industries and to objectively evaluate their correlation within the Yellow River Basin. Design/methodology/approach First, based on spatial geometry and calculus theory, the surface representation method of behavioral matrices in three-dimensional space is explained, and the calculation method for the volume of the corresponding surface body is provided. Second, inspired by the two-dimensional grey absolute correlation model, a grey matrix correlation model based on the volume of the surface body is established. We analyze the properties of the proposed model, including normalization, proximity, and order preservation under scalar multiplication. Additionally, the MATLAB implementation code for the model is provided to enhance its operability. Finally, the model is applied to empirically analyze the correlation between manufacturing and the digital industry in the Yellow River Basin. Findings The results validate the effectiveness and rationality of the model, and policy recommendations are proposed to optimize resource allocation and enhance the digitalization level of manufacturing in the region. Originality/value This study provides a theoretical basis and methodological support for promoting the high-quality development of manufacturing in the Yellow River Basin, while also offering insights for other regions exploring pathways for the integration of the two industries.