The development of carbon finance is a significant research area due to ongoing environmental changes and developmental progress. This study addresses the need for innovative evaluation methods in China's rapidly growing carbon market, where existing research often utilizes outdated indicators or generalized data. The research question focuses on identifying the most promising locations for carbon finance investment in China, considering the heterogeneity of provincial environments and the need for a comprehensive evaluation system encompassing environmental and social factors. The importance of this study stems from the lack of a unified consensus on carbon finance evaluation indices and the limitations of previous studies that fail to fully consider the multifaceted dimensions of carbon finance development in China's evolving regulatory and market landscape. A robust and comprehensive assessment framework is crucial for guiding investment decisions and policy formulation within China's burgeoning carbon market.

Several scholars have compared TOPSIS and VIKOR methods independently or in comparative studies. Hezer et al. (2021) used three MCDM methods, including TOPSIS and VIKOR, for COVID-19 security assessment. Sari et al. (2020) applied TOPSIS and VIKOR for environmental suitability analysis. However, these studies used the methods separately, neglecting their potential integration. This paper addresses this gap by combining TOPSIS and VIKOR, incorporating the AISM model (Ni, 2020) previously applied in military training evaluation and further extended by Su et al. (2023) to business and supply chain analysis. The paper also builds on Chen et al. (2020)'s research on measuring regional carbon finance development in China, refining the indicator system to improve regional adaptability and address issues of outdated selection and generalized data usage. It integrates findings from various sources, such as Yang et al. (2023) on low-carbon policies, Abdi et al. (2022) on the impact of social and environmental activities on financial efficiency, Ding et al. (2022) on the PITI index, and Luo et al. (2021) and Ritz (2022) on emissions trading systems. Key studies on carbon bonds (Wei et al., 2022), green credit, stock markets (Sharma et al., 2023), and bank efficiency (Phung et al., 2022) are also incorporated, along with the research of Zhou et al. (2022) and Pan et al. (2022) on low-carbon innovation and tertiary sector development.

The study uses a novel hybrid MCDM method combining TOPSIS and VIKOR. The methodology involves calculating positive and negative ideal solutions (PIS and NIS) using Euclidean distance (equations 1-4). It then incorporates VIKOR's group utility and individual regret calculations (equations 5-9), extending the classical VIKOR method by including distances to both PIS and NIS (equations 6-9). This generates a compromise solution Q (equation 10), enabling ranking based on distance from the NIS. A cluster analysis determines inflection points in K values (0, 1) to identify ranking changes. The AISM model is used to create a relationship matrix (Table 8) from the positive and negative ideal solution distances (Table 5), generating a hierarchical UP and DOWN topology (Table 9) and a general skeleton matrix (Table 10). The entropy weight method (Table 4) determines indicator weights, and a robustness test (Table 11) verifies the method's stability across different decision intervals by changing the decision intervals from the original clustering intervals [0, 0.1866] and [0.8099, 1], shortening the decision intervals [0, 1] to [0.1, 0.9], and rerunning the clustering sensitivity value analysis to assess the stability of the system within different intervals. This builds upon mental accounting theory (Thaler, 2008).

The hybrid TOPSIS-VIKOR method reveals Guangdong and Beijing as the most attractive investment locations for carbon finance in China. The entropy weight analysis indicates that indicators related to financial industry development (D) and R&D intensity (E1) carry the highest weights. The robustness test confirms that the investment ranking remains consistent across various decision intervals, demonstrating the method's stability. The AISM analysis provides a hierarchical ranking, further solidifying the prominence of Guangdong and Beijing, followed by Shenzhen, Shanghai, Hubei, Fujian, Tianjin, and Chongqing. This hierarchical structure, visualized in Figure 4, reveals a robust and stable ranking system. Tables 4, 5, 6, 7, 8, 9, and 10 illustrate the weights, combined positive and negative ideal solutions, compromise values, clustering analysis, relationship matrix, and hierarchy diagram, respectively. Table 11 presents the results of the robustness test.

The findings address the research question by identifying specific regions within China most suitable for carbon finance investment. The dominance of Guangdong and Beijing highlights the importance of well-developed financial sectors and technological innovation in attracting carbon finance investment. The robustness of the findings across different decision intervals enhances confidence in the results. The study's comprehensive methodology and robust results offer valuable insights for investors and policymakers seeking to optimize resource allocation and drive sustainable development within China's carbon market. The use of the hybrid MCDM approach, extending the classical TOPSIS and VIKOR methods, provides a novel and improved evaluation framework for carbon finance development.

This study offers a novel hybrid MCDM method for assessing carbon finance development in China, identifying Guangdong and Beijing as optimal investment locations. The integrated TOPSIS-VIKOR approach, coupled with AISM analysis and robustness testing, provides a robust and comprehensive evaluation framework. Future research could explore the impact of specific policies or events on carbon finance development, further refining the indicator system, or applying this methodology to other countries or regions.

The study relies on existing data sources, potentially limiting the scope of analysis. Future research could incorporate more detailed, granular data to further enhance the accuracy and precision of the analysis. While the robustness test demonstrates stability across specific decision intervals, exploration of alternative weighting methods or sensitivity analyses on other parameters could provide additional insights into the method's resilience.