In this paper, we investigate the probabilistic linguistic multiple attribute group decision-making (MAGDM) with incomplete weight information. In this method, the linguistic term sets (LTSs) is converted into probabilistic linguistic term sets (PLTSs). For deriving the weight information of the attribute, an optimization model is built on the basis of the fundamental idea of conventional TOPSIS method, by which the attribute weights can be decided. In addition, the optimal alternative(s) is decided by computing the shortest distance from the probabilistic linguistic positive ideal solution (PLPIS) and on the other side the farthest distance of the probabilistic linguistic negative ideal solution (PLNIS). The method has precise trait in probabilistic linguistic information processing. The information distortion and losing was avoided which happen formerly in the probabilistic linguistic information processing. In the end, a case study for green supplier selection is given to demonstrate the merits of the developed method. The results display that the approach is uncomplicated, valid and simple to compute.

中文翻译：

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利用概率语言信息开发供应商选择的TOPSIS方法

在本文中，我们研究了权重信息不完整的概率语言多属性群决策（MAGDM）。在这种方法中，将语言术语集（LTS）转换为概率语言术语集（PLTS）。为了获得属性的权重信息，在传统TOPSIS方法的基本思想的基础上建立了一个优化模型，可以确定属性权重。另外，通过计算距概率语言否定理想解（PLPIS）的最短距离，以及另一方面，概率语言否定理想解（PLNIS）的最远距离，来确定最佳替代方案。该方法在概率语言信息处理中具有精确的特点。避免了以前在概率语言信息处理中发生的信息失真和丢失。最后，对绿色供应商选择进行了案例研究，以证明所开发方法的优点。结果表明，该方法简单，有效且易于计算。