The Fermatean fuzzy set (FFS) is a momentous generalization of a intuitionistic fuzzy set and a Pythagorean fuzzy set that can more accurately portray the complex vague information of elements and has stronger expert flexibility during decision analysis. The Combined Compromise Solution (CoCoSo) approach is a powerful decision-making technique to choose the ideal objective by fusing three aggregation strategies. In this paper, an integrated, multi-criteria group-decision-making (MCGDM) approach based on CoCoSo and FFS is used to assess green suppliers. To begin, several innovative operations of Fermatean fuzzy numbers based on Schweizer–Sklar norms are presented, and four aggregation operators utilizing the proposed operations are also developed. Several worthwhile properties of the advanced operations and operators are explored in detail. Next, a new Fermatean fuzzy entropy measure is propounded to determine the combined weight of criteria, in which the subjective and objective weights are computed by an improved best-and-worst method (BWM) and entropy weight approach, respectively. Furthermore, MCGDM based on CoCoSo and BWM-Entropy is brought forward and employed to sort diverse green suppliers. Lastly, the usefulness and effectiveness of the presented methodology is validated by comparison, and the stability of the developed MCGDM approach is shown by sensitivity analysis. The results shows that the introduced method is more stable during ranking of green suppliers, and the comparative results expound that the proposed method has higher universality and credibility than prior Fermatean fuzzy approaches.

Intercity railway is an important system for the development of urban agglomeration, and the site selection of the Line Management Department of Intercity Railway (LMDIR) is a significant task for the railway department when constructing intercity railways. Owing to the complexity and uncertainty during the selection process, we constructed a multiple expert multi-criteria decision making (MEMCDM) method to provide a rational decision support model for a railway management department in the Fermatean cubic fuzzy set context. In this regard, an innovative extension called Fermatean cubic fuzzy sets (FCFSs) that integrates Fermatean fuzzy sets (FFSs) and cubic sets; several basic theories of FCFSs, including the score and accuracy functions; and distance measures are also given. Then, a series of Fermatean cubic fuzzy Hamacher operators are put forward to flexibly fuse Fermatean cubic fuzzy information, and the corresponding valuable characteristics of these operators are also investigated. Thirdly, the Fermatean cubic fuzzy logarithmic percentage-change-driven objective weighting (LOPCOW) approach is recommended based on the score function to recognize the importance of criteria, and the similarity-based method is deployed to identify the expert weight information. Fourthly, a hybrid MEMCDM methodology integrating the proposed Fermatean cubic fuzzy Hamacher operators, the LOPCOW method, whose evaluation is based on distance from average solution (EDAS) method based on regret theory, is designed to ascertain the prioritization of the schemes. Consequently, an empirical test concerning the site selection of LMDIR is shown to validate the feasibility and usefulness of the designed MEMCDM approach. The analysis involving the sensibility test and comparison study with prior methods is displayed to emphasize the effectuality and advantages of the propounded method. The outcomes demonstrate that the hybrid method recommended in this research possesses superior robustness and feasibility to cope with complicated decision issues. The findings of this research show that the presented method can recommend more credible site selection of LMDIR when encountering uncertainties and abundant impact factors.