Measuring public sense-of-gain with urban renewal from the low-carbon perspective: a case study of Fuzhou, China

China’s rapid urbanization has intensified energy consumption and carbon emissions, underscoring the urgency of low-carbon urban renewal strategies. The impacts of urban renewal on the community deserve to be evaluated to inform the mode and direction of implementation. However, the knowledge base lacks a comprehensive framework for evaluating the public sense of gain (SOG). This study aims to develop and measure indicators of public SOG in low-carbon urban renewal. A questionnaire survey was conducted among residents from different occupations, and an empirical study was carried out in Fuzhou. Both traditional fuzzy and cloud model-based fuzzy comprehensive evaluation methods were applied. The results showed that the economic dimension exerted the strongest influence, with an expected value of 4.04 in the cloud model. In addition, structural equation modeling (SEM) was used to perform a first-order confirmatory factor analysis (CFA), which validated the internal structure of the SOG evaluation system. All standardized loadings exceeded 0.6, and composite reliability (CR) values exceeded 0.8, verifying the model’s good fit. The proposed evaluation framework helps fill a methodological gap and provides a rational tool to measure public SOG in low-carbon urban renewal. The findings could support more inclusive and sustainable urban redevelopment practices and offer practical guidance for policy and implementation.