Vimala J, Surya A N, Kausar Nasreen, Pamucar Dragan, Simic Vladimir, Salman Mohammed Abdullah
Department of Mathematics, Alagappa University, Karaikudi, Tamilnadu, 630003, India.
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, 34220, Esenler, Istanbul, Turkey.
Sci Rep. 2025 Jan 2;15(1):69. doi: 10.1038/s41598-024-81785-1.
The introduction of (p, q)-rung linear Diophantine fuzzy set into the field of fuzzy set theory is a significant advancement, providing a broader perspective to address complicated decision-making scenarios. Alongside, the preference ranking organization method for enrichment of evaluation (PROMETHEE) emerges as a widely recognized tool for tackling multi-criteria decision-making challenges. This study contributes theoretically to the decision-making field by integrating (p, q)-rung linear Diophantine fuzzy sets into the PROMETHEE framework, improving (p, q)-rung linear Diophantine fuzzy sets adaptability and efficiency in practical aspects, the proposed framework can effectively address various intricate decision-making challenges encountered in real-world scenarios. This enhancement enables the (p, q)-rung linear Diophantine fuzzy sets to be more capable of handling a wide range of complex problems that arise in practical situations, making it a valuable tool for decision-makers looking to tackle real-life issues with precision and reliability. By illustrating the application of this extended method in the context of robot selection problem, the study showcases the practical utility and relevance of the proposed method. Furthermore, a comprehensive evaluation and discussion of the proposed PROMETHEE method is presented, emphasizing its validity, sensitivity, superiority, robustness, and adaptability in addressing real-world decision-making complexities.
将（p，q）- rung线性丢番图模糊集引入模糊集理论领域是一项重大进展，为解决复杂的决策场景提供了更广阔的视角。与此同时，用于丰富评价的偏好排序组织方法（PROMETHEE）成为解决多准则决策挑战的广泛认可的工具。本研究通过将（p，q）- rung线性丢番图模糊集集成到PROMETHEE框架中，在理论上为决策领域做出了贡献，在实际方面提高了（p，q）- rung线性丢番图模糊集的适应性和效率，所提出的框架能够有效解决现实场景中遇到的各种复杂决策挑战。这种改进使（p，q）- rung线性丢番图模糊集更有能力处理实际情况中出现的各种复杂问题，使其成为希望精确且可靠地解决现实生活问题的决策者的宝贵工具。通过说明这种扩展方法在机器人选择问题背景下的应用，该研究展示了所提出方法的实际效用和相关性。此外，还对所提出的PROMETHEE方法进行了全面评估和讨论，强调了其在解决现实世界决策复杂性方面的有效性、敏感性、优越性、稳健性和适应性。
