Department of Mathematics, School of Sciences, University of Management and Technology, Lahore, Pakistan.
Department of Mathematics, Faculty of Science and Technology, Virtual University of Pakistan, Lahore, Pakistan.
PLoS One. 2024 Oct 24;19(10):e0311580. doi: 10.1371/journal.pone.0311580. eCollection 2024.
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.
双犹豫 Ferate 模糊集（DHFFS）的概念代表了实际应用中的重大进展，它结合了 Ferate 模糊集和双犹豫集。这种新结构使用成员和非成员犹豫，并且更适应于在一个域中得出值。由于它具有在成员和非成员程度上处理多个模糊集的能力，DHFFS 极大地提高了处理多准则决策（MCDM）问题的方法的灵活性。通过应用广义 T-范数（T）和 T-合（T*）运算，推导出改进的并集和交集公式。所提出的工作采用了 Hamacher 运算，例如 Hamacher T-合（HT*）和 Hamacher T-范数（HT），这些运算比传统技术更有效。为 DHFFS 开发了新的聚合算子，如 Hamacher 加权算术、几何、幂算术和幂几何。这些算子在处理 MCDM 问题时最有益。通过一个案例研究，展示了该方法在实际决策中的准确性和有效性。比较和敏感性分析结果表明，这些算子比传统方法更有效。这些结果表明，所提出的方法是有效的，可以应用于大规模决策过程，增强了解决方案的实际意义。
