Unlike traditional finance, digital inclusive finance is committed to integrating digital technology with the financial industry to bring groups originally excluded from traditional finance back into formal financial services and provide financial services at reasonable prices and matching needs for all social classes. Digital inclusive finance can effectively reduce the financing costs of SMEs, improve the external financing environment of enterprises, and provide more convenient, equal and perfect financial services for enterprises by using technical support such as "big data + artificial intelligence". The development level of digital inclusive finance is a classical multiple attributes group decision making (MAGDM). The Probabilistic hesitant fuzzy sets (PHFSs), which utilize the possible values and its possible membership degrees to depict decision-makers’ behavior in different conditions, has been paid great attention. Though numerous methods have been applied in this environment since PHFSs has been introduced, there are still new fields to be explored. In this paper, we introduce the Cumulative Prospect Theory TODIM (CPT-TODIM) for probabilistic hesitant fuzzy MAGDM(PHF-MAGDM). Meanwhile, the information of entropy is utilized to calculate the weight of attributes, which is used to improve the classical TODIM method. At last, we utilize a numerical case for evaluating the development level of digital inclusive finance to compare the extended CPT-TODIM method with the classical TODIM method.

The competitiveness evaluation of regional financial centers is frequently looked as the multiple attribute group decision-making (MAGDM) problem. Based on the TODIM method and fuzzy number intuitionistic fuzzy sets (FNIFS), this paper proposes a new FNIF-TODIM method to evaluate the competitiveness of regional financial centers. First, some basic theories related to FNIFS are briefly introduced. In addition, the weights of the attributes are obtained objectively using the CRITIC weighting method. Then, the traditional TODIM method is extended to FNIFS to obtain the final order of alternatives. As a result, all alternatives can be ranked and the best one for the competitiveness assessment of regional financial centers can be identified. Finally, an example for competitiveness evaluation of regional financial centers and some decision comparative analysis is listed. The results show that the established algorithmic approach is useful. The main works of this work are: (1) the paper constructs the FNIF-TODIM method for the evaluation of the competitiveness of regional financial centers; (2) the established method is illustrated by a case study for competitiveness evaluation of regional financial centers; and (3) some comparisons prove the rationality and advantages.

Due to the increasingly strengthened role of finance in modern economic development, theoretical research on regional financial competitiveness in the study of regional economic competitiveness becomes very important. For China at this stage, finance is in a period of rapid development, and its role has penetrated into all aspects of social and economic life. Especially after China’s entry into the WTO, the pace of opening up the financial market has been further accelerated, and comprehensive evaluation and analysis of financial competitiveness is of great significance for comprehensively understanding and accurately grasping China’s national conditions, national strength, and international competitiveness, promoting the long-term growth of China’s financial competitiveness, and the sustainable development of the financial industry. The competitiveness evaluation of regional financial centers is looked as the multiple attribute decision-making (MADM) problem. This paper intends to propose a MADM methodology based on CoCoSo (Combined Compromise Solution) method under interval-valued intuitionistic fuzzy sets (IVIFSs) for sustainable competitiveness evaluation of regional financial centers. At the end of this study, we noticed to a comparison between the proposed IVIF-CoCoSo approach with other existing methods to verify the effectiveness of the algorithm.