Dual-hesitant fermatean fuzzy Hamacher aggregation operators and TOPSIS with their application to multi-criteria decision-making.

The concept of the Dual-hesitant fermatean fuzzy set (DHFFS) represents a significant advancement in practical implementation, combining Fermatean fuzzy sets and Dual-hesitant sets. This new structure uses membership and non-membership hesitancy and is more adaptable for arriving at values in a domain. Since it has the capability to treat multiple fuzzy sets over the degrees of membership and non-membership, the DHFFS greatly improves the flexibility of approaches to tackle multiple-criteria decision-making (MCDM) problems. By applying generalized T-norm (T) and T-conorm (T*) operation, improved union and intersection formulas are derived. The proposed work adopts Hamacher operations such as Hamacher T-conorm (HT*) and Hamacher T-norm (HT) that are more efficient than conventional techniques. New aggregation operators such as Hamacher weighted arithmetic, geometric, power arithmetic, and power geometric are developed for DHFFS. These operators are most beneficial when dealing with a MCDM issue. A case study is used to demonstrate the approachs' accuracy and effectiveness in real-world decision-making. The comparative and sensitivity analysis results show that these operators are more effective than traditional methods. These results show that the proposed methods are efficient and can be applied in large-scale decision-making processes, strengthening the solutions' practical implications.