The polygonal fuzzy set is an effective tool to approximate the general fuzzy set by means of a finite number of ordered real numbers. It not only overcomes the shortcomings (which does not satisfy the closeness) of arithmetic operations of fuzzy sets based on Zadeh extension principle, but also realizes the non-linear operation of general fuzzy sets by an ordered representation of the polygonal fuzzy set. In this paper, the definition, geometric interpretation, ordered representation and arithmetic operations of the polygonal fuzzy sets are introduced for the first time, and the method of solving polygonal fuzzy sets and their ordered representation based on convex fuzzy sets are given by an example. Second, a new Euclidean metric of polygonal fuzzy sets is proposed, and the approximation accuracy of polygonal fuzzy sets to convex fuzzy sets is discussed. In addition, the linear function describing transportation cost index information of logistics companies is obtained through the ordered representation of Gauss membership function, and according to the ordered representation a new normalization method for the polygonal decision matrix is given. Finally, the method of solving the positive (negative) ideal solution and degree of relative closeness of the polygonal decision matrix is suggested by the weighted Euclidean distance. Then a new TOPSIS evaluation system is established, and the effectiveness of the proposed method is illustrated by an example of logistics transportation.

中文翻译：

---

基于多边形模糊集有序表示的物流运输TOPSIS评价系统

多边形模糊集是通过有限数量的有序实数来逼近通用模糊集的有效工具。它不仅克服了基于Zadeh扩展原理的模糊集的算术运算的缺点（不满足紧密性），而且通过多边形模糊集的有序表示实现了通用模糊集的非线性运算。本文首次介绍了多边形模糊集的定义，几何解释，有序表示和算术运算，并举例说明了基于凸模糊集的多边形模糊集及其有序表示的求解方法。其次，提出了一种新的多边形模糊集的欧氏度量，讨论了多边形模糊集对凸模糊集的逼近精度。另外，通过高斯隶属度函数的有序表示获得描述物流公司运输成本指标信息的线性函数，并根据有序表示为多边形决策矩阵给出了一种新的归一化方法。最后，通过加权欧几里得距离，提出了求解多边形决策矩阵的正（负）理想解和相对接近度的方法。然后建立了一个新的TOPSIS评估系统，并以物流运输为例说明了该方法的有效性。通过高斯隶属度函数的有序表示获得描述物流公司运输成本指标信息的线性函数，并根据有序表示给出了一种新的多边形决策矩阵归一化方法。最后，通过加权欧几里得距离，提出了求解多边形决策矩阵的正（负）理想解和相对接近度的方法。然后建立了一个新的TOPSIS评估系统，并以物流运输为例说明了该方法的有效性。通过高斯隶属度函数的有序表示获得描述物流公司运输成本指标信息的线性函数，并根据有序表示给出了一种新的多边形决策矩阵归一化方法。最后，通过加权欧几里得距离，提出了求解多边形决策矩阵的正（负）理想解和相对接近度的方法。然后建立了一个新的TOPSIS评估系统，并以物流运输为例说明了该方法的有效性。通过加权欧几里得距离，提出了求解多边形决策矩阵的正（负）理想解和相对接近度的方法。然后建立了一个新的TOPSIS评估系统，并以物流运输为例说明了该方法的有效性。通过加权欧几里得距离，提出了求解多边形决策矩阵的正（负）理想解和相对接近度的方法。然后建立了一个新的TOPSIS评估系统，并以物流运输为例说明了该方法的有效性。