K-means and RS based DEA model and its application in Chinese low-carbon efficiency

This study devises an innovative data envelopment analysis (DEA) model combining K-means and rough sets (RS), applying it to gauge the low-carbon efficiency of Chinese provinces. Regarding index handling, the K-means algorithm along with the contour coefficient method ascertains the optimal cluster number, yielding discrete data. This meets the demands of RS, curtails index redundancy, and fortifies the index system’s unity and reliability. Rough set is then employed for index reduction, extracting crucial kernel attributes to further optimize the system. Through this model, provinces are segmented into four groups based on DEA outcomes. Results indicate Anhui and similar provinces exhibit low-input low-output or high-input low-output; Shanghai and like provinces have low-input high-output with top-notch efficiency; Beijing and related provinces need resource allocation optimization. The study also uncovers spatial autocorrelation in low-carbon efficiency. For instance, Hubei, Chongqing, and Hunan display low–low aggregation, necessitating joint efforts to overcome low-carbon transition hurdles. Yunnan and Guangxi show high-low aggregation, calling for a demonstration-leading and collaborative development role. Heilongjiang presents high–high aggregation, capable of strengthening its advantages to drive neighboring regions. This research furnishes a more precise decision-making foundation for regional low-carbon development and puts forward a raft of measures in light of the findings, which will assist provinces in identifying improvement directions and propel China’s low-carbon development process.