一种基于灰熵的区间数灰色局势决策方法  

A Decision-making Method of Interval Numbers' Grey Situation Based on Grey Entropy

作　　者：何其慧[1] 罗文刚 姚登宝[3] 曹雪萍[3] 毛军军[3] 

机构地区：[1]安徽经济管理学院基础部,合肥230059 [2]龙街中学,贵州毕节553109 [3]安徽大学数学科学学院,合肥230039

出　　处：《合肥学院学报（自然科学版）》2012年第1期16-20,30,共6页Journal of Hefei University :Natural Sciences

基　　金：国家自然科学基金(61073117);安徽大学学术创新团队(KJTD001B);安徽大学人才队伍建设经费;安徽高等学校青年基金项目(2011SQRL186);高等学校优秀青年人才基金项目(2011SQRL186)资助

摘　　要：基于区间数距离和灰熵分析,研究了灰色局势的多属性决策问题.首先给出了一种新的灰熵定义,并通过预处理得到一致效果测度矩阵.然后,提取正负理想值,结合灰熵定义建立多目标规划模型,通过拉格朗日乘数法给出了目标权重的计算公式,将多目标的一致效果测度矩阵集成为综合效果测度矩阵.最后,利用可能度和排序向量法找到各事件下的最优对策和各对策下的最优事件,从而得到最优局势,并通过实例分析验证了所提决策方法的有效性和实用性.Based on the interval numbers＇ distance and grey making problem of grey situation has been researched in entropy analysis＇, multi-attribute decision- this paper. Firstly, a new grey entropy definition has been proposed and uniform effect measure matrices have been obtained after pretreatment. Secondly, by extracting desired-undesired effect value and grey entropy definition, a multi-objective programming model has been constructed, and objective weights could be obtained by use of Lagrange multiplier method, uniform effect measure matrices of multi-objective have been aggregated into collective effect measure matrix. Finally, by use of possibility degree and ranking vectors method, the optimal decision of every event and the optimal event of every decision could be fund, consequently, the optimal situation could been obtained. And a practical example has been presented to verify the proposed method＇s effectiveness and practicability.

关 键 词：区间数 灰熵 灰色局势 规划 目标权重 可能度 

分 类 号：N941.5[自然科学总论—系统科学]