广义毕达哥拉斯犹豫模糊集混合加权距离测度及决策应用

在毕达哥拉斯犹豫模糊数的距离基础上，定义毕达哥拉斯犹豫模糊集（Pythagorean hesitant fussy set，PHFS）的加权距离测度和有序加权距离测度，在兼顾属性权重和位置权重的基础上，提出广义PHFS混合加权距离测度（D_GPHFHWA），并研究其性质和特殊形式。针对属性值为毕达哥拉斯犹豫模糊数且属性权重未知的多属性决策问题，利用毕达哥拉斯犹豫模糊指数熵确定属性权重，并结合逼近理想解排序法（technique for order preference by similarity to an ideal solution，TOPSIS）思想，提出基于D_GPHFHWA测度的决策方法。最后，通过实例验证所提方法是有效、合理的。

Generalized Pythagorean hesitant fuzzy set hybrid weighted distance measure and its application to decision making

Based on the distance of Pythagorean hesitant fuzzy numbers,the weighted distance measure and the ordered weighted distance measure of Pythagorean hesitant fuzzy set are defined.Then accounting for both the attribute weights and the position weights,the Pythagorean hesitant fuzzy set generalized hybrid weighted distance measure (D_GPHFHWA) is proposed, and the properties and several special forms of D_GPHFHWA are studied.In view of the multi-attribute decision problem in which the value of attribute is in the form of Pythagorean hesitant fuzzy numbers and the attribute weights are unknown,the attribute weights are determined by using the Pythagorean hesitant fuzzy exponential entropy,and the decision method based on the D_GPHFHWA is proposed combining with TOPSIS thought.Finally,an example is given to show that the proposed method is effective and reasonable.