Evaluation of China's regional innovation capability based on simulated annealing projection pursuit model and nested fuzzy evaluation model

Regional innovation capability is an important indicator of both regional innovative and long‐term development. The purpose of this study is to build an evaluation index system for regional innovation capability in order to identify regional differences and support innovation more effectively. After establishing a reasonable evaluation value for regional innovation capability, a combination of simulated annealing optimized projection pursuit (SA–PP) and N‐layer nested fuzzy comprehensive evaluation models is used to assess China's regional innovation capabilities. The results show that the SA–PP model effectively mitigates the risk of erroneous evaluation results caused by index weight uncertainty, resulting in a more reasonable, robust, and intelligent assessment of regional innovation capability. Furthermore, the nested fuzzy comprehensive evaluation model is capable of easily resolving the evaluation factor set's heterogeneity and multilayer problems. The most significant influences on China's regional innovation capability are knowledge acquisition and enterprise innovation. The comprehensive score of the proposed combinational evaluation model manifests that provinces with strong regional innovation capabilities are mainly concentrated in the southeast coastal regions. The research results allow for precise weight determination and object ranking.