Gul Rizwan, Al-Shami Tareq M, Ayub Saba, Shabir Muhammad, Hosny M
Department of Mathematics, Quaid-i-Azam University, Islamabad, 44230, Pakistan.
Department of Mathematics, Sana'a University, Sana'a, Yemen.
Heliyon. 2024 Aug 12;10(16):e35942. doi: 10.1016/j.heliyon.2024.e35942. eCollection 2024 Aug 30.
Aczel-Alsina t-norm and t-conorm are intrinsically flexible and endow Aczel-Alsina aggregation operators with greater versatility and robustness in the aggregation process than operators rooted in other t-norms and t-conorm families. Moreover, the linear Diophantine fuzzy set (LD-FS) is one of the resilient extensions of the fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), Pythagorean fuzzy sets (PyFSs), and q-rung orthopair fuzzy sets (q-ROFSs), which has acquired prominence in decision analysis due to its exceptional efficacy in resolving ambiguous data. Keeping in view the advantages of both LD-FSs and Aczel-Alsina aggregation operators, this article aims to establish Aczel-Alsina operation rules for LD-FSs, such as Aczel-Alsina sum, Aczel-Alsina product, Aczel-Alsina scalar multiplication, and Aczel-Alsina exponentiation. Based on these operation rules, we expose the linear Diophantine fuzzy Aczel-Alsina weighted average (LDFAAWA) operator, and linear Diophantine fuzzy Aczel-Alsina weighted geometric (LDFAAWG) operator and scrutinize their distinctive characteristics and results. Additionally, based on these aggregation operators (AOs), a multi-criteria decision-making (MCDM) approach is designed and tested with a practical case study related to forecasting weather under an LD-FS setting. The developed model undergoes a comparative analysis with several prevailing approaches to demonstrate the superiority and accuracy of the proposed model. Besides, the influence of the parameter Λ on the ranking order is successfully highlighted.
阿采尔 - 阿尔西纳三角模与三角余模本质上具有灵活性，相较于源于其他三角模和三角余模族的算子，阿采尔 - 阿尔西纳聚合算子在聚合过程中具有更强的通用性和稳健性。此外，线性丢番图模糊集（LD - FS）是模糊集（FSs）、直觉模糊集（IFSs）、毕达哥拉斯模糊集（PyFSs）和q - 阶正交对模糊集（q - ROFSs）的弹性扩展之一，由于其在处理模糊数据方面的卓越功效，在决策分析中备受瞩目。鉴于LD - FSs和阿采尔 - 阿尔西纳聚合算子的优势，本文旨在为LD - FSs建立阿采尔 - 阿尔西纳运算规则，如阿采尔 - 阿尔西纳和、阿采尔 - 阿尔西纳积、阿采尔 - 阿尔西纳数乘以及阿采尔 - 阿尔西纳指数运算。基于这些运算规则，我们给出线性丢番图模糊阿采尔 - 阿尔西纳加权平均（LDFAAWA）算子和线性丢番图模糊阿采尔 - 阿尔西纳加权几何（LDFAAWG）算子，并审视它们的独特特性和结果。此外，基于这些聚合算子（AOs），设计了一种多准则决策（MCDM）方法，并通过一个与LD - FS设置下的天气预测相关的实际案例进行测试。将所开发的模型与几种流行方法进行比较分析，以证明所提模型的优越性和准确性。此外，成功突出了参数Λ对排序顺序的影响。
