摘要
首先提出几种基于兰氏距离的犹豫模糊集距离测度.然后针对两个犹豫模糊数中的隶属度个数不相等问题,提出新的犹豫模糊数降维方案.该方案不需要反复添加最大最小隶属度数值到犹豫模糊数中,不仅很好地保留了数据的原始信息,而且减少了计算距离时的计算量.针对属性权重信息完全未知的情况,采用实际数据信息构造犹豫模糊指数熵,并利用信息熵最小化原则计算得到属性权重.最后利用指数熵加权的降维犹豫模糊兰氏距离测度,结合实际的医疗诊断数据进行实例分析.结果表明,所提出的基于指数熵加权的降维犹豫模糊兰氏距离测度不仅在λ取不同值时诊断结果一致,而且减少了计算量,提高了诊断效率,对实时、有效的医疗诊断具有一定的应用价值.
This paper proposes several distance measures about hesitant fuzzy sets based on the Lance distance at first.Then,aiming at the unequal number of membership numbers in two hesitant fuzzy elements,a new dimension reduction scheme of hesitant fuzzy elements is introduced.The scheme does not need to add the maximum or minimum membership value to the hesitant fuzzy element,which not only preserves the original information of the data well,but also reduces the computation of the calculated distance.In the case that the information of attribute weights are completely unknown,the hesitant fuzzy exponential entropy is constructed by using the actual data information.This paper uses the principle of entropy minimization to calculate attribute weights.Finally,a medical diagnosis example is provided to illustrate the weighted hesitant fuzzy Lance distance measure of dimension reduction based on the exponential entropy.The results show that,the proposed distance measure not only achieves the consistent diagnosis results whenλtakes different values,but also reduces the computation and improves the diagnostic efficiency,which has certain application value for real-time and effective medical diagnosis.
作者
沙秀艳
尹传存
徐泽水
SHA Xiu-yan;YIN Chuan-cun;XU Ze-shui(School of Statistics,Qufu Normal University,Qufu 273165,China;Business School,Sichuan University,Chengdu 610064,China)
出处
《控制与决策》
EI
CSCD
北大核心
2020年第3期728-734,共7页
Control and Decision
基金
国家自然科学基金项目(11171179,11571198,61273209).
关键词
犹豫模糊集
兰氏距离
降维
指数熵
hesitant fuzzy set
Lance distance
dimension reduction
exponential entropy
作者简介
沙秀艳(1977-),女,讲师,博士生,从事决策分析、数据预测的研究,E-mail:shaxiuyan@sina.com;通讯作者:尹传存(1963-),男,教授,博士生导师,从事决策分析和概率统计等研究,E-mail:ccyin@qfnu.edu.cn;徐泽水(1968-),男,教授,博士生导师,从事决策分析、信息融合等研究,E-mail:xuzeshui@263.net.
