Department of Statistics, Lahore Campus, COMSATS University Islamabad, Islamabad 45550, Pakistan.
Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, ul. Zołnierska 49, 71-210 Szczecin, Poland.
Sensors (Basel). 2022 Jul 31;22(15):5736. doi: 10.3390/s22155736.
A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e., considerable data loss. The probabilistic hesitant fuzzy set (PHFS) has been proposed to improve the HFS. It provides probability values to the HFS and has the ability to retain more information than the HFS. Previously, fuzzy regression models such as the fuzzy linear regression model (FLRM) and hesitant fuzzy linear regression model were used for decision making; however, these models do not provide information about the distribution. To address this issue, we proposed a probabilistic hesitant fuzzy linear regression model (PHFLRM) that incorporates distribution information to account for multi-criteria decision-making (MCDM) problems. The PHFLRM observes the input-output (IPOP) variables as probabilistic hesitant fuzzy elements (PHFEs) and uses a linear programming model (LPM) to estimate the parameters. A case study is used to illustrate the proposed methodology. Additionally, an MCDM technique called the technique for order preference by similarity to ideal solution (TOPSIS) is employed to compare the PHFLRM findings with those obtained using TOPSIS. Lastly, Spearman's rank correlation test assesses the statistical significance of two rankings sets.
近年来，一种称为犹豫模糊集（HFS）的模糊集扩展在决策中越来越受欢迎，特别是当专家在模糊环境中工作时，难以通过使用单个值评估来评估多个替代方案时。然而，它在使用中存在一个重大问题，即大量数据丢失。为了改进 HFS，提出了概率犹豫模糊集（PHFS）。它为 HFS 提供概率值，并具有比 HFS 保留更多信息的能力。以前，模糊回归模型（如模糊线性回归模型（FLRM）和犹豫模糊线性回归模型）用于决策；但是，这些模型不提供有关分布的信息。为了解决这个问题，我们提出了一种概率犹豫模糊线性回归模型（PHFLRM），它结合了分布信息以解决多准则决策（MCDM）问题。PHFLRM 将输入-输出（IPOP）变量视为概率犹豫模糊元素（PHFE），并使用线性规划模型（LPM）来估计参数。通过案例研究说明了所提出的方法。此外，使用称为相似理想解排序技术（TOPSIS）的多准则决策技术来比较 PHFLRM 的结果与使用 TOPSIS 获得的结果。最后，Spearman 秩相关检验评估了两个排序集的统计显著性。
