基于改进Gini-Simpson指数的指标及权重均为混合属性的广义灰靶决策方法  

Generalised Grey Target Decision Method with Index and Weight both Containing Mixed Attribute Values based on Improved Gini-Simpson Index

作　　者：马金山[1] MA Jin-shan(School of Energy Science and Engineering,Henan Polytechnic University,Jiaozuo 454000,China)

机构地区：[1]河南理工大学能源科学与工程学院,河南焦作454000

出　　处：《统计与信息论坛》2019年第2期28-34,共7页Journal of Statistics and Information

基　　金：河南理工大学博士基金<不确定性广义灰靶决策方法及其在煤矿安全管理中的应用>(B2016-53)

摘　　要：提出了一种新的以改进的Gini-Simpson指数为决策依据的指标及权重均为混合属性值的广义灰靶决策方法。该方法构造权重函数将不确定性混合指标权重确定化,并以改进的综合加权Gini-Simpson指数作为方案决策的依据。首先将各方案的混合属性指标值转化为二元联系数,并分解为确定项和不确定项以组成(确定,不确定)二元组数;其次,分别获得各属性下靶心指标的(确定,不确定)二元组数;然后,构造权重函数将不确定性权重确定化,继而求得各方案的综合加权Gini-Simpson指数;最后以综合加权的Gini-Simpson指数为依据对各方案进行决策,以其值越小方案越优。案例分析的结果验证了该法的可行性。A novel improved Gini-Simpson index based generalised grey target decision method with index and weight both containing mixed attribute values is proposed.This method builds the weight function to transform the mixed attribute-based weights into the certain number-based weights and takes the improved comprehensive weighted Gini-Simpson indices to rank the alternatives.This method first transforms all alternatives'indices into binary connection numbers and divides them into the deterministic terms and uncertain terms to compose the two-tuple(determinacy,uncertainty)numbers.Then the target centre indices of two-tuple(determinacy,uncertainty)number are determined.Next the certain number-based weights can be determined by the weight function.Following this,the comprehensive weighted Gini-Simpson index of all alternatives can be obtained.Finally,the alternatives ranking is easy to be made with the Gini-Simpson index the smaller the better.A case study illustrates the proposed approach.

关 键 词：Gini-Simpson指数 混合属性 广义灰靶决策方法 权重函数 二元联系数 

分 类 号：O212[理学—概率论与数理统计] F224[理学—数学]