A Novel Normal Wiggly Fermatean Hesitant Fuzzy VIKOR Approach and Its Application to the Assessment of Development Effects for the Green Finance Reform and Innovation Pilot Zones in China

Evaluating the development effects of the green finance reform and innovation pilot zones (GFRIPZs) is crucial for enhancing green financial services, informing capital allocation decisions, and strengthening risk management, thereby providing valuable policy insights for green economic transformation. To address the lack of systematic quantitative evaluation in the existing literature, this study develops a novel multi-criteria decision-making approach by embedding the normal wiggly Fermatean hesitant fuzzy sets (NWFHFSs) into the VIKOR framework. We first propose the concept of NWFHFSs to capture richer information than conventional Fermatean hesitant fuzzy sets. To enable effective quantification and discrimination of normal wiggly Fermatean hesitant fuzzy elements (NWFHFEs), we construct a score function, an accuracy function, and an associated comparison rule. We then design a distance measure for NWFHFEs to facilitate the integration of information from NWFHFSs with the VIKOR procedure. Moreover, the maximum deviation principle is employed to determine criterion weights in an objective manner. A real-world case study is conducted to assess the development effects of the GFRIPZs, illustrating the feasibility and effectiveness of the proposed framework. The theoretical soundness and practical performance of the method are further examined through detailed sensitivity and comparative analyses. In light of these results, the proposed model is shown to be a reliable decision-support tool for complex decision problems under uncertainty.