The polygonal fuzzy set is an effective tool to express a class of fuzzy information with the help of finite ordered real numbers. It can not only guarantee the closeness of arithmetic operation of the polygonal fuzzy sets, but also has good linearity and intuitiveness. Firstly, the concept of then-intuitionistic polygonal fuzzy set (n-IPFS) is proposed based on the intuitionistic fuzzy set and the polygonal fuzzy set. The ordered representation and arithmetic operation of n-IPFS are given by an example. Secondly, a new aggregation method for multi attribute fuzzy information is given based on the n-IPFS operations and the weighted arithmetic average operator, and the ranking criteria of n-IPFS are obtained by using the score function and the accuracy function. Finally, a new group decision making method is proposed for urban residents to choose the livable city problem based on the decision matrix of the n-IPFS, and the effectiveness of the proposed method is explained by an actual example.

中文翻译：

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n直觉多边形模糊集描述的居民选择宜居城市的群体决策方法

多边形模糊集是在有限有序实数的帮助下表达一类模糊信息的有效工具。它不仅可以保证多边形模糊集算术运算的紧密性，而且具有良好的线性和直观性。首先，基于直觉模糊集和多边形模糊集，提出了直觉多边形模糊集（n-IPFS）的概念。一个示例给出了n-IPFS的有序表示和算术运算。其次，基于n-IPFS操作和加权算术平均算子，提出了一种新的多属性模糊信息聚合方法，并利用得分函数和精度函数获得了n-IPFS的排序准则。最后，