Khan Salma, Abujabal Hamza Ali, Rahim Muhammad, Almutairi A, Alburaikan Alhanouf, Khalifa Hamiden Abd El-Wahed
Department of Mathematics, Women University, Mardan, KPK, 23200, Pakistan.
Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589, Jeddah, Saudi Arabia.
Sci Rep. 2025 Aug 7;15(1):28868. doi: 10.1038/s41598-025-12354-3.
This study proposes novel operational laws that extend the Frank t-norm and t-conorm to develop a new class of aggregation operators (AOs), namely the [Formula: see text] quasirung orthopair fuzzy Frank weighted average, weighted geometric, ordered weighted average, and ordered weighted geometric operators. These operators are specifically designed to manage uncertain and imprecise information within multi-attribute group decision-making (MGADM) environments. The proposed operators exhibit desirable mathematical properties such as flexibility, robustness, and compatibility, making them highly suitable for complex fuzzy decision contexts. Flexibility is notably enhanced through the independent tuning of the parameters [Formula: see text], [Formula: see text], and τ, allowing for more refined control over membership (MD), non-membership (NMD), and interaction behaviors. An entropy-based approach is employed to objectively determine unknown attribute weights, minimizing subjective bias. A real-world case study on the selection of an optimal investment location demonstrates the practical applicability of the proposed method. The results show an improvement in decision-making accuracy by approximately 7.5% compared to traditional approaches. Sensitivity analysis confirms the stability and reliability of the proposed operators under varying conditions. Comparative results further highlight the method's superiority in terms of accuracy, interpretability, and adaptability to input variations. The paper concludes by outlining special cases and acknowledging certain limitations, offering directions for future research.
本研究提出了新颖的运算定律,将弗兰克三角模和三角余模进行扩展,以开发一类新的聚合算子(AO),即[公式:见原文]准梯形正交对模糊弗兰克加权平均、加权几何、有序加权平均和有序加权几何算子。这些算子专门设计用于处理多属性群体决策(MGADM)环境中的不确定和不精确信息。所提出的算子具有诸如灵活性、鲁棒性和兼容性等理想的数学性质,使其非常适合复杂的模糊决策情境。通过对参数[公式:见原文]、[公式:见原文]和τ的独立调整,灵活性得到显著增强,从而能够对隶属度(MD)、非隶属度(NMD)和交互行为进行更精细的控制。采用基于熵的方法客观地确定未知属性权重,将主观偏差降至最低。一个关于选择最佳投资地点的实际案例研究证明了所提方法的实际适用性。结果表明,与传统方法相比,决策准确性提高了约7.5%。敏感性分析证实了所提算子在不同条件下的稳定性和可靠性。比较结果进一步突出了该方法在准确性、可解释性以及对输入变化的适应性方面的优越性。本文最后概述了特殊情况并承认了某些局限性,为未来研究提供了方向。