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PurposeThe purpose of this work is to construct a grey entropy comprehensive evaluation model to measure the regional green innovation vitality (GIV) of 31 provinces in China.Design/methodology/approachThe traditional grey relational proximity and grey relational similarity degree are integrated into the novel comprehensive grey evaluation framework. The evaluation system of regional green innovation vitality is constructed from three dimensions: economic development vitality, innovative transformation power and environmental protection efficacy. The weights of each indicator are obtained by the entropy weight method. The GIV of 31 provinces in China is measured based on provincial panel data from 2016 to 2020. The ward clustering and K-nearest-neighbor (KNN) algorithms are utilized to explore the regional green innovation discrepancies and promotion paths.FindingsThe novel grey evaluation method exhibits stronger ability to capture intrinsic patterns compared with two separate traditional grey relational models. Green innovation vitality shows obvious regional discrepancies. The Matthew effect of China's regional GIV is obvious, showing a basic trend of strong in the eastern but weak in the western areas. The comprehensive innovation vitality of economically developed provinces exhibits steady increasing trend year by year, while the innovation vitality of less developed regions shows an overall steady state of no fluctuation.Practical implicationsThe grey entropy comprehensive relational model in this study is applied for the measurement and evaluation of regional GIV, which improves the one-sidedness of traditional grey relational analysis on the proximity or similarity among sequences. In addition, a three-dimensional evaluation system of regional GIV is constructed, which provides the practical guidance for the research of regional development strategic planning as well as promotion paths.Originality/valueA comprehensive grey entropy relational model based on traditional grey incidence analysis (GIA) in terms of proximity and similarity is proposed. The three-dimensional evaluation system of China's regional GIV is constructed, which provides a new research perspective for regional innovation evaluation and expands the application scope of grey system theory.

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