Mahmood Tahir, Emam Walid, Ahmmad Jabbar, Iftikhar Muhammad, Rehman Ubaid Ur, Pamucar Dragan
Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan.
Department of Statistics and Operations Research, Faculty of Science, King Saud University, P.O. Box 2455, 11451, Riyadh, Saudi Arabia.
Sci Rep. 2025 May 13;15(1):16538. doi: 10.1038/s41598-025-99297-x.
Business engineering creates novel business solutions using a social and technological system. Business engineering is facing several challenges like (1) complexity management (2) rapid technological advancements (3) Resource constraints (4) Interdisciplinary collaboration etc., and there is a need to classify the solutions for these issues faced by the business community. To cover more advanced data and overcome the chance of data loss, in this article, we have developed the idea of a complex Pythagorean fuzzy rough set based on Tamir's idea of a complex fuzzy set. We have developed basic operational laws for the proposed idea under the notion of Yager's t-norm and t-conorm. Additionally, we have initiated the theory of complex Pythagorean fuzzy rough Yager weighted average and geometric aggregation operators. To discuss the utilization of the initiated work, we have introduced the WASPAS technique that can help us tackle the MADM problems. Moreover, we have provided an illustrative example for the classification of the solutions regarding the problems in business engineering. Also, a comparative analysis of the initiated theory shows the advantages of the introduced work.
商业工程利用社会和技术系统创造新颖的商业解决方案。商业工程面临着若干挑战，如（1）复杂性管理（2）技术的快速进步（3）资源限制（4）跨学科协作等，并且需要对商业界所面临的这些问题的解决方案进行分类。为了涵盖更高级的数据并克服数据丢失的可能性，在本文中，我们基于塔米尔的复模糊集思想，提出了一种复毕达哥拉斯模糊粗糙集的概念。我们在耶格的三角模和余三角模的概念下，为所提出的概念开发了基本运算定律。此外，我们还开创了复毕达哥拉斯模糊粗糙耶格加权平均和几何聚合算子理论。为了讨论所开创工作的应用，我们引入了WASPAS技术，它可以帮助我们解决多属性决策问题。此外，我们为商业工程中的问题解决方案分类提供了一个示例。同时，对所开创理论的比较分析显示了所介绍工作的优势。
