Zeeshan Muhammad, Khan Madad, Shafqat Ramsha, Althobaiti Ali, Althobaiti Saad, Bedada Tola Bekene
Department of Mathematics, The University of Agriculture, Dera Ismail Khan, Pakistan.
Department of Mathematics, COMSATS University Islamabad, Abbottabad Campus, Abbottabad, Pakistan.
Sci Rep. 2024 Jul 25;14(1):17129. doi: 10.1038/s41598-024-65324-6.
Complex fuzzy soft matrices play a crucial role in various applications, including decision-making, pattern recognition, signals processing, and image processing. The main objective of this study is to introduce the unique notions of complex Pythagorean fuzzy soft matrices (CPFSMs), which provide more flexibility and accuracy in modelling uncertainty. CPFSMs incorporate Pythagorean fuzzy soft matrices, allowing for more sophisticated uncertainty modeling. The key findings of CPFSMs, specific instances, and certain fundamental set-theoretic operations and principles were covered. A set of new distance metrics between two CPFSMs has been defined. In the context of complex Pythagorean fuzzy soft sets and complex Pythagorean fuzzy soft matrices, we created a CPFS decision-making technique. Moreover, the application's numerical example and comparison analysis have been effectively demonstrated. Thus, by integrating the concepts of Pythagorean fuzzy sets, soft matrices, and complex numbers, CPFSMs provide a robust framework with membership and non-membership degrees for complex decision-making modeling and analyzing uncertain data.
复模糊软矩阵在包括决策、模式识别、信号处理和图像处理等各种应用中起着至关重要的作用。本研究的主要目的是引入复毕达哥拉斯模糊软矩阵（CPFSMs）的独特概念，其在不确定性建模中提供了更大的灵活性和准确性。CPFSMs包含毕达哥拉斯模糊软矩阵，允许进行更复杂的不确定性建模。涵盖了CPFSMs的关键发现、具体实例以及某些基本的集合论运算和原理。定义了两个CPFSMs之间的一组新的距离度量。在复毕达哥拉斯模糊软集和复毕达哥拉斯模糊软矩阵的背景下，我们创建了一种CPFS决策技术。此外，有效地展示了该应用的数值示例和比较分析。因此，通过整合毕达哥拉斯模糊集、软矩阵和复数的概念，CPFSMs为复杂决策建模和分析不确定数据提供了一个具有隶属度和非隶属度的强大框架。
