基于符号距离和交叉熵的概率犹豫模糊多属性决策方法  

Probabilistic hesitant fuzzy multi-attribute decision method based on signed distance and cross entropy

作　　者：朱峰 徐济超 刘玉敏[2] 孙静静 ZHU Feng;XU Ji-chao;LIU Yu-min;SUN Jing-jing(School of Management Engineering,Zhengzhou University,Zhengzhou 450001,China;Business of School,Zhengzhou University,Zhengzhou 450001,China)

机构地区：[1]郑州大学管理工程学院,郑州450001 [2]郑州大学商学院,郑州450001

出　　处：《控制与决策》2020年第8期1977-1986,共10页Control and Decision

基　　金：国家自然科学基金项目(71672182;71711540309;U1604262)。

摘　　要：针对概率犹豫模糊环境下属性权重完全未知的多属性决策问题,提出基于符号距离和交叉熵的多属性决策方法.首先,定义用于测量决策者犹豫程度的3种概率犹豫模糊元的犹豫度:数值犹豫度,信息不完全度和总犹豫度,基于3种犹豫度提出概率犹豫模糊符号距离;然后,为了避免人为添加元素,定义调和概率犹豫模糊元,并结合信息不完全度提出概率犹豫模糊元的交叉熵;最后,根据概率犹豫模糊元的符号距离和交叉熵构建多属性决策模型,并通过算例验证了该模型的有效性和合理性.A multi-attribute decision making method based on signed distance and cross entropy is proposed for multiattribute decision making problems in which the attribute weights are completely unknown under the probabilistic hesitant fuzzy environment.Firstly,the three kinds hesitation degree of probability hesitant fuzzy elements used to measure the degree of hesitancy of decision makers is proposed:Numerical hesitation degree,information incomplete degree and total hesitation degree.The probability hesitant fuzzy signed distance is proposed based on three hesitation degrees.Then,in order to avoid artificially adding elements,the adjusted probabilistic hesitant fuzzy element is defined,it combines with the incomplete degree of information to propose the cross entropy of the probabilistic hesitant fuzzy element.Finally,the multi-attribute decision model is constructed based on the signed distance and cross entropy of the probabilistic hesitant fuzzy element,and the e?ectiveness and rationality of the model are illustrated by an example.

关 键 词：多属性决策 概率犹豫模糊元 犹豫度 符号距离 交叉熵 信息不完全度 调和概率犹豫模糊元 

分 类 号：C934[经济管理—管理学]