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Climate change threatens human survival and development. Cities, as the main gathering places for human production and life, serve as the focal points for the implementation of the policies related to energy efficiency, energy transition, and environmental protection. This study constructs an index system for the evaluation of carbon-neutral cities from the perspectives of carbon sources and carbon sinks. The system includes thirteen indicators under six dimensions. It combines objective and subjective data (i.e., statistical data and expert evaluations) by integrating two approaches: the fuzzy analytic hierarchy process (fuzzy AHP) and vise kriterijumska optimizacija i kompromisno resenje with hesitant fuzzy sets (HFS-VIKOR). We verify the efficacy of the proposed approach through a case study of thirteen low-carbon pilot cities in China. The results indicate that among these cities, Shenzhen performs the best, followed by Guangzhou and Hangzhou, while Kunming, Baoding, and Tianjin show poor performance in terms of carbon neutrality. Kunming and Baoding exhibit shortcomings mainly in carbon sources, while Tianjin faces deficiencies in both carbon sources and carbon sinks. Sensitivity analysis and comparative analysis show the availability and effectiveness of the proposed method. The proposed radar chart further highlights the improvement directions for each city to achieve carbon neutrality. [ABSTRACT FROM AUTHOR]