Alballa Tmader, Alamer Ahmed, Nasir Khadija, Yousaf Awais, Abdualziz Alhabeeb Somayah, Abd El-Wahed Khalifa Hamiden
Department of Mathematics, College of Sciences, Princess Nourah Bint Abdulrahman University, P.O. Box 84428, Riyadh, 11671, Saudi Arabia.
Department of Mathematics, Faculty of Science University of Tabuk, Tabuk, 71491, Saudi Arabia.
Heliyon. 2024 Jul 20;10(14):e34570. doi: 10.1016/j.heliyon.2024.e34570. eCollection 2024 Jul 30.
Multiple-Attribute Group Decision-Making (MAGDM) is a significant area of research in decision-making, and its principles and methodologies are widely implemented. A Pythagorean Fuzzy Set (PFS) is an extension of an Intuitionistic Fuzzy Set (IFS) that is highly valuable for representing uncertain information in real-world scenarios. The 2-Tuple Linguistic Pythagorean Fuzzy Number (2TLPFN) is a specific type of Pythagorean Fuzzy Number (PFN) that can be used to represent uncertainty in real-world decision making through the use of 2-Tuple Linguistic Terms (2TLTs). This paper focuses on the examination of Multiple Attribute Group Decision Making (MAGDM) using 2TLPFNs. Dombi's t-norm and t-conorm operations were commonly referred to as Dombi operations, which might have been greater degree of applicability if offered in a new form of flexibility within the general parameter. In this research, we implement Dombi operations to construct some 2-Tuple Linguistic Pythagorean Fuzzy (2TLPF) Dombi Aggregation operators. These operators include the 2TLPF Dombi Weighted Averaging (2TLPFDWA) operator, 2TLPF Dombi Ordered Weighted Averaging (2TLPFDOWA) operator, 2TLPF Dombi Weighted Geometric (2TLPFDWG) operator, and 2TLPF Dombi Ordered Weighted Geometric (2TLPFDOWA) operator. An analysis is conducted to examine the unique characteristics of these suggested operators. Subsequently, we leveraged the proposed operators to develop a model aimed at tackling the MAGDM problems in the 2TLPF environment. Eventually, a suitable instance has been demonstrated to validate the formation of the model as well as exhibit its implementation and resilience.
多属性群决策（MAGDM）是决策领域的一个重要研究方向，其原理和方法得到了广泛应用。毕达哥拉斯模糊集（PFS）是直觉模糊集（IFS）的扩展，在表示现实世界场景中的不确定信息方面具有很高的价值。二元组语言毕达哥拉斯模糊数（2TLPFN）是毕达哥拉斯模糊数（PFN）的一种特殊类型，可通过使用二元组语言术语（2TLT）来表示现实世界决策中的不确定性。本文重点研究使用2TLPFN进行多属性群决策（MAGDM）。Dombi的t - 范数和t - 余范数运算通常称为Dombi运算，如果能以一种在通用参数内具有新的灵活性形式提供，可能具有更高的适用性。在本研究中，我们运用Dombi运算构建了一些二元组语言毕达哥拉斯模糊（2TLPF）Dombi聚合算子。这些算子包括2TLPF Dombi加权平均（2TLPFDWA）算子、2TLPF Dombi有序加权平均（2TLPFDOWA）算子、2TLPF Dombi加权几何（2TLPFDWG）算子和2TLPF Dombi有序加权几何（2TLPFDOWG）算子。对这些建议算子的独特特性进行了分析。随后，我们利用所提出的算子开发了一个模型，旨在解决2TLPF环境下的MAGDM问题。最后，通过一个合适的实例验证了模型的形成，并展示了其实现过程和适用性。
