Azim Ahmad Bin, Ali Asad, Khan Abdul Samad, Awwad Fuad A, Ali Sumbal, Ismail Emad A A
Department of Mathematics and Statistics, Hazara University Mansehra, 21300, Khyber Pakhtunkhwa, Pakistan.
Research Center for Computational Science, School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an, 710129, China.
Heliyon. 2024 Jul 20;10(15):e34698. doi: 10.1016/j.heliyon.2024.e34698. eCollection 2024 Aug 15.
This study introduces innovative operational laws, Einstein operations, and novel aggregation algorithms tailored for handling q-spherical fuzzy rough data. The research article presents three newly designed arithmetic averaging operators: q-spherical fuzzy rough Einstein weighted averaging, q-spherical fuzzy rough Einstein ordered weighted averaging, and q-spherical fuzzy rough Einstein hybrid weighted averaging. These operators are meticulously crafted to enhance precision and accuracy in arithmetic averaging. By thoroughly examining their characteristics and interrelations with existing aggregate operators, the article uncovers their distinct advantages and innovative contributions to the field. Furthermore, the study illustrates the actual implementation of these newly constructed operators in a variety of attribute decision-making scenarios employing q-SFR data, yielding useful insights. Our suite of decision-making tools, including these operators, is specifically designed to address complex and uncertain data. To validate our approach, this study offers a numerical example showcasing the real-world applicability of the proposed operators. The results not only corroborate the efficacy of the proposed method but also underscore its potential significance in practical decision-making processes dealing with intricate and ambiguous data. Additionally, comparative and sensitivity analyses are presented to assess the effectiveness and robustness of our proposed work relative to other approaches. The acquired knowledge enriches the current understanding and opens new avenues for future research.
本研究介绍了创新的运算定律、爱因斯坦运算以及为处理q-球面模糊粗糙数据量身定制的新型聚合算法。该研究文章提出了三种新设计的算术平均算子：q-球面模糊粗糙爱因斯坦加权平均、q-球面模糊粗糙爱因斯坦有序加权平均和q-球面模糊粗糙爱因斯坦混合加权平均。这些算子经过精心设计，以提高算术平均的精度和准确性。通过深入研究它们的特性以及与现有聚合算子的相互关系，文章揭示了它们的独特优势以及对该领域的创新贡献。此外，该研究还说明了这些新构建的算子在使用q-SFR数据的各种属性决策场景中的实际应用，得出了有用的见解。我们包括这些算子在内的一套决策工具专门设计用于处理复杂和不确定的数据。为了验证我们的方法，本研究提供了一个数值示例，展示了所提出算子在现实世界中的适用性。结果不仅证实了所提方法的有效性，还强调了其在处理复杂和模糊数据的实际决策过程中的潜在重要性。此外，还进行了比较分析和敏感性分析，以评估我们所提工作相对于其他方法的有效性和稳健性。所获得的知识丰富了当前的理解，并为未来的研究开辟了新途径。
