Boulaaras Salah, Mostafa Ghada E, Jan Rashid, Mekawy Ibrahim
Department of Mathematics, College of Science, Qassim University, Buraydah, 51452, Saudi Arabia.
Department of Mathematics, Faculty of Science, Al-Azhar University [Girls Branch], Nasr City, Cairo, Egypt.
Sci Rep. 2024 Oct 31;14(1):26214. doi: 10.1038/s41598-024-75687-5.
This paper introduces a novel distance measure for dual hesitant fuzzy sets (DHFS) and weighted dual hesitant fuzzy sets (WDHFS), with a rigorous proof of the triangular inequality to ensure its mathematical validity. The proposed measure extends the normalized Hamming, generalized, and Euclidean distance measures to dual hesitant fuzzy elements (DHFE), offering a broader framework for handling uncertainty in fuzzy environments. Additionally, the utilization of a score function is shown to simplify the computation of these distance measures. The practical relevance of the proposed measure is demonstrated through its application in medical diagnosis and decision-making processes. A comparative analysis between the newly introduced distance measure denoted as , and an existing measure, is performed to underscore the superiority and potential advantages of the new approach in real-world scenarios.
本文介绍了一种针对对偶犹豫模糊集（DHFS）和加权对偶犹豫模糊集（WDHFS）的新型距离度量方法，并对三角不等式进行了严格证明以确保其数学有效性。所提出的度量方法将归一化汉明距离、广义距离和欧几里得距离度量扩展到对偶犹豫模糊元素（DHFE），为处理模糊环境中的不确定性提供了更广泛的框架。此外，还表明使用得分函数可简化这些距离度量的计算。通过将所提出的度量方法应用于医学诊断和决策过程，证明了其实际相关性。对新引入的记为 的距离度量与现有度量 进行了比较分析，以强调新方法在实际场景中的优越性和潜在优势。
