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  

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

作　　者：常娟[1] 杜迎雪[1] 刘卫锋[1] CHANG Juan;DU Yingxue;LIU Weifeng(School of Maihemaiics,Zhengzhou U?riversiiy of Aeronauiics,Zhengzhou 450046,China)

机构地区：[1]郑州航空工业管理学院数学学院,河南郑州450046

出　　处：《浙江大学学报（理学版）》2021年第3期304-313,共10页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11501525);河南省高等学校重点科研项目(20A110035);河南省高等学校重点科研项目计划基础研究专项(20ZX003);河南省科技攻关计划项目(212102110206).

摘　　要：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。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.

关 键 词：毕达哥拉斯犹豫模糊集 混合加权距离测度 毕达哥拉斯犹豫模糊指数熵 多属性决策 

分 类 号：C934[经济管理—管理学] O223[理学—运筹学与控制论]