Ma Xiuqin, Niu Xuli, Qin Hongwu, Ren Dong, Lei Siyue, Tang Kexin
College of Computer Science and Engineering, Northwest Normal University, Lanzhou, 730020, Gansu, China.
Institute for Big Data Analytics and Artificial Intelligence (IBDAAI), Universiti Teknologi MARA, 40450, Shah Alam, Selangor, Malaysia.
Sci Rep. 2025 Mar 18;15(1):9343. doi: 10.1038/s41598-025-89324-2.
Water ecological civilization construction (WECC) is regarded as the core and cornerstone of ecological civilization construction. However, a lot of uncertainty is involved in assessing the WECC level, which presents serious and intricate difficulties for the related multiple- attribute decision-making (MADM) processes. The interval-valued hesitant Fermatean fuzzy set (IVHFFS) is a powerful tool for handling uncertainty in MADM issues. However, in the existing MADM approaches, attribute weight calculation involves high data redundancy and low computational efficiency. The existing aggregation operators ignore the importance of the attributes and their ordered positions. In order to solve these problems, in this paper, we propose a novel MADM model using interval-valued hesitant Fermatean fuzzy (IVHFF) Hamacher aggregation operator (AO) and statistical variance (SV) weight calculation. Firstly, the SV weight calculation method is given under IVHFFSs, aiming to computing objective weights of attributes. This greatly reduces data redundancy and improves the computational complexity. Secondly, we propose some IVHFF Hamacher AOs, such as IVHFF Hamacher (ordered) weighted averaging operator, IVHFF Hamacher (ordered) weighted geometric operator, IVHFF Hamacher hybrid averaging operator and geometric operator which consider the significance of the attributes and their ordered positions. Thirdly, a new MADM model based on the above information AOs and SV weight calculation is proposed. Finally, a comparative study on the real-world application for WECC and randomly generated data sets is also carried out to further demonstrate that our method outperforms the existing methods.
水生态文明建设被视为生态文明建设的核心与基石。然而，在评估水生态文明建设水平时存在诸多不确定性，这给相关的多属性决策（MADM）过程带来了严峻且复杂的困难。区间值犹豫模糊集（IVHFFS）是处理MADM问题中不确定性的有力工具。然而，在现有的MADM方法中，属性权重计算存在数据冗余度高和计算效率低的问题。现有的聚合算子忽略了属性及其有序位置的重要性。为了解决这些问题，本文提出了一种使用区间值犹豫模糊（IVHFF）哈马赫聚合算子（AO）和统计方差（SV）权重计算的新型MADM模型。首先，给出了IVHFFS下的SV权重计算方法，旨在计算属性的客观权重。这大大降低了数据冗余度并提高了计算复杂度。其次，我们提出了一些IVHFF哈马赫AO，如IVHFF哈马赫（有序）加权平均算子、IVHFF哈马赫（有序）加权几何算子、IVHFF哈马赫混合平均算子和几何算子，这些算子考虑了属性及其有序位置的重要性。第三，提出了一种基于上述信息AO和SV权重计算的新MADM模型。最后，还对水生态文明建设的实际应用和随机生成的数据集进行了对比研究，以进一步证明我们的方法优于现有方法。
