基于曲边梯形面积刻画毕达哥拉斯模糊数的排序方法

Ranking method of Pythagorean fuzzy numbers characterized by curved trapezoidal area

毕达哥拉斯模糊集(Pythagorean fuzzy set,PFS)是传统直觉模糊集(intuitionistic fuzzy set,IFS)的扩展,能在更广泛区域处理多属性信息决策问题。首先,针对某文献毕达哥拉斯模糊数(Pythagorean fuzzy number,PFN)排序方法存在的错误,分析了其产生原因。其次,在毕达哥拉斯模糊环境下,基于可靠信息量所对应的曲边梯形面积(curved trapezoidal area,CTA)提出了新的得分函数公式,进而给出了PFN的排序准则,并讨论了该得分函数的基本性质。最后,用实例说明给出的排序方法克服了其他方法的某些缺陷,具有一定优势。

Pythagorean fuzzy set(PFS)is an extension of traditional intuitionistic fuzzy set(IFS).It can deal with decision-making problems with multi-attribute information in a wider area.In this paper,we first point out errors in the ranking criterion of Pythagorean fuzzy number(PFN)proposed in a paper,and analyze the reasons that cause these errors through the derivation of reliable information(accuracy function).Then,we propose a new score function through the curved trapezoidal area(CTA)corresponding to the reliable information,which provides a ranking criterion of PFN.The basic properties of the score function are discussed.Finally,we show an example indicating the effectiveness and advantage of the new ranking method.