基于灰色关联系数和D-S证据理论的区间数投资决策方法  

Approach to interval numbers investment decision-making based on grey incidence coefficients and D-S theory of evidence

作　　者：王育红[1,2] 党耀国[1] 

机构地区：[1]南京航空航天大学经济与管理学院,南京210016 [2]Department of Industrial Engineering,University of Arkansas,Fayetteville,AR 72701,USA

出　　处：《系统工程理论与实践》2009年第11期128-134,共7页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金(70473037);国家留学基金(2008104757);江苏省软科学基金(BR2006025);南京航空航天大学科研创新基金(Y0811-091)

摘　　要：主要研究投资方案的指标值为区间数时的投资方案选择问题.定义了效益型和成本型指标下的理想属性区间数,并且通过理想属性偏离度定义把指标值为区间数的矩阵转化为以理想属性偏离度为测度的矩阵,把不确定性问题转化为确定性问题处理.在此基础上把灰色关联分析方法与证据理论相结合,构造了一种新的信息不确定度提取方法和基本概率分配函数,探讨了不同子集间信度函数和基本概率分配函数之间的数量关系;通过对各投资方案对应于不同指标下基本概率分配函数的确定,利用Dempster法则进行信息融合,确定最佳投资方案.算例结果表明,文中提出的方法可以得到满意的决策结果并显著降低决策的不确定性.This paper focuses mainly on problems of selecting investment cases when attribute values of corresponding alternatives fall into intervals.Ideal attribute interval numbers for benefit type indices and cost type indices are defined respectively.The concept of ideal attribute deviation is also defined in this paper. A matrix of interval numbers is converted into the matrix of measures with ideal attribute deviations by above definitions.Then an uncertain problem is converted into the certain problem which can be addressed relatively easier.A combination of the grey incidence analysis method and the theory of evidence is presented based on the understanding of problems.A novel method extracting the degree of ignorance for information and a new method for basic probability assignment function are constructed to combine distinct pieces of information in accordance with the Dempster combination rule.A conversion relationship between a belief function and a basic probability assignment function is also discussed in this paper.After all required steps completed for information fusion the Dempster combination rule is applied and the optimal investment case is derived in terms of the largest belief function value.A numerical example is utilized to illustrate the method proposed in this paper.The result indicates that a satisfied case can be obtained through applying the method and an obvious decrease can be observed in the uncertainty of decision-making.

关 键 词：灰色关联分析 证据理论 理想属性偏离度 数据融合 决策 

分 类 号：N941.5[自然科学总论—系统科学]