概率语言术语集(PLTS)包含了语言术语信息及其相应的概率信息, 使得原始决 策信息得到充分利用, 大大提高了语言术语多属性决策的科学性. 文章研究了一种基于 概率语言术语集类Pearson 综合相关系数的TOPSIS多属性决策方法. 首先考虑了PLTSs的3个特征因素:均值、方差和长度, 然后基于传统Pearson 相关系数的思想, 提出了一种新的概率语言术语集类Pearson综合相关系数, 其 特征是可从完整性、分布情况和犹豫性3个方面描述PLTSs, 且取值大小介于区间$[-1,1]$, 从 而可度量变量之间的正负相关关系, 改进了现有方法存在的缺陷. 为融合属性指标的不同权重, 提出了概率语言术语集加权类Pearson综合相关系数, 其考虑了属性权重的重要性, 拓宽了适 用范围. 进一步地, 构建了基于类Pearson综合相关系数的概率语言术语相对贴近 度指标, 并在此基础上提出了一种基于类Pearson综合相关系数的概率语言术语TOPSIS多属性方法. 最后, 通过数值算例和比较分析, 说明该方法的有效性和适用性.

The probabilistic linguistic term set (PLTS) contains linguistic term information and corresponding probabilistic information, which makes full use of the original decision-making information and greatly improves the scientificity of linguistic terms multiple attribute decision-making. Therefore, we develop a PLTS Pearson-like synthetic correlation-based TOPSIS approach in this paper for dealing with multiple attribute decision-making (MADM) problems. Three characteristic factors of PLTS: The mean, the variance and the length are firstly considered, and based on the traditional Pearson correlation coefficient, a novel concept called PLTS Pearson-like synthetic correlation coefficient is defined, whose significant features include two aspects: It can express the integrality, the distribution and the hesitance of the PLTSs and lies in the interval $[-1,1]$, so that the positive and negative correlation between variables can be measured, which overcomes the shortcomings of existing measurements. In order to integrate the different weights of the attributes, a PLTS weighted Pearson-like synthetic correlation coefficient is defined, which takes into account the importance of attribute weights and expands the scope of application. A relative closeness index is further constructed based on the developed PLTS Pearson-like synthetic correlation coefficient, and based on which, a Pearson-like synthetic correlation-based TOPSIS approach for PLTS MADM problems is proposed. Finally, the effectiveness and applicability of the proposed method are illustrated by numerical examples and comparative analysis.}