A Comprehensive Assessment Framework for the Sustainable Ecological Carrying Capacity of Chinese Cities Based on Time-Series Uncertainty and Interval-Valued Fermatean Fuzzy Sets

The assessment of sustainable ecological carrying capacity (SECC) serves as a crucial scientific foundation for supporting high-quality urbanization, advancing ecological civilization, and achieving the strategic goals of the “Dual Carbon” initiative. However, existing assessment methods largely rely on subjective expert scoring, making them difficult to apply at the large-scale urban level; simultaneously, traditional fuzzy assessment frameworks lack effective mechanisms for representing uncertainty when dealing with objective panel data. This paper proposes a temporal-uncertainty-driven interval-valued Fermatean fuzzy set (TU-IVFFS) theoretical framework and integrates it with an improved decision-making trial and evaluation laboratory (DEMATEL), the method based on the removal effects of criteria (MEREC), and the measurement of alternatives and ranking according to compromise solution (MARCOS) approach to construct an integrated urban ecological carrying capacity assessment framework: TU-IVFF-DEMATEL-MEREC-MARCOS. Using panel data from 2021 to 2024 for 690 major Chinese cities (at the county-level-city level and above) as the sample, the analysis found that Beijing, Guangzhou, Shenzhen, Nanjing, and Chongqing ranked in the top five for SECC, while some small cities in the northeast and northwest ranked lower. Sensitivity analysis showed that the city rankings remained stable across the entire range of weight combination coefficients λ ∈ [0, 1], verifying the robustness of the proposed framework. This study provides a methodological breakthrough for the reproducible and generalizable assessment of urban ecological carrying capacity in large-scale samples.