Department of Statistics, Comsats University Islamabad, Lahore, Pakistan.
Research Team on Intelligent Decision Support Systems, Department of Artificial Intelligence Methods and Applied Mathematics, Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin, Szczecin, Poland.
PLoS One. 2022 Aug 9;17(8):e0270414. doi: 10.1371/journal.pone.0270414. eCollection 2022.
Correlation is considered the most important factor in analyzing the data in statistics. It is used to measure the movement of two different variables linearly. The concept of correlation is well-known and used in different fields to measure the association between two variables. The hesitant 2-tuple fuzzy linguistic set (H2FLS) comes out to be valuable in addressing people's reluctant subjective data. The purpose of this paper is to analyze new correlation measures between H2FLSs and apply them in the decision-making process. First and foremost, the ideas of mean and variance of hesitant 2-tuple fuzzy linguistic elements (H2FLEs) are introduced. Then, a new correlation coefficient between H2FLSs is established. In addition, considering that different H2FLEs may have different criteria weights, the weighted correlation coefficient and ordered weighted correlation coefficient are further investigated. A practical example concerning the detailed procedure of solving problems is exemplified to feature the reasonableness and attainability of the proposed technique in situations where the criteria weights are either known or unknown. When the weight vector is unknown, the best-worst method (BWM) is used to acquire the criteria weights in the context of a hesitant 2-tuple fuzzy linguistic environment. Furthermore, a comparative study is undertaken with current techniques to provide a vision into the design decision-making process. Finally, it is verified that the proposed correlation coefficient between H2FLSs is more satisfactory than the extant ones, and the correlation coefficient with the weights of criteria being either known or unknown is applicable.
相关性被认为是统计学中分析数据的最重要因素。它用于衡量两个不同变量之间的线性运动。相关性的概念在不同领域中广为人知，并用于衡量两个变量之间的关联。犹豫 2-元模糊语言集 (H2FLS) 在处理人们犹豫不决的主观数据方面具有重要价值。本文旨在分析 H2FLS 之间的新相关度量标准，并将其应用于决策过程中。首先，引入了犹豫 2-元模糊语言元素 (H2FLE) 的均值和方差的概念。然后，建立了 H2FLS 之间的新相关系数。此外，考虑到不同的 H2FLE 可能具有不同的标准权重，进一步研究了加权相关系数和有序加权相关系数。通过一个涉及详细问题解决过程的实际例子，说明了在标准权重已知或未知的情况下，所提出的技术在实际情况中的合理性和可实现性。当权重向量未知时，在犹豫 2-元模糊语言环境中使用最佳最差方法 (BWM) 来获取标准权重。此外，还与当前技术进行了比较研究，为设计决策过程提供了一个视角。最后，验证了所提出的 H2FLS 之间的相关系数比现有系数更令人满意，并且具有已知或未知标准权重的相关系数是适用的。
