层次分析法中基于SVDD群体信息提取方法  

Extracting Method for Group Information Based on SVDD in Analytic Hierarchy Process

作　　者：刘万里[1] 卫宗礼[1] 

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471022

出　　处：《数学的实践与认识》2008年第22期117-123,共7页Mathematics in Practice and Theory

基　　金：国家自然基金项目(60574075);河南省教育厅自然科学研究项目(2004601013)

摘　　要：针对层次分析法中群决策问题提出一种基于支持向量域描述(SVDD)的集结方法.首先利用生成树的方法把判断矩阵进行一致性剖分;然后利用支持向量域描述的方法排除干扰信息,找出群体公共信息,引入群体相容性,最优解等概念,提出并证明了关于群体信息球的特性;根据最大特征值法把群体信息球中的向量合成为群决策最优解,即关于方案的排序向量.并通过一个具体示例给出该方法的算法步骤同时显示了该方法的可行性和有效性.An extraction method is proposed based on support vector domain description （SVDD） for group decision making in analytic hierarchy process. Firstly, a consistency dissection is performed for every judgment matrix by means of the spanning-tree method. Secondly, the disturbance information is removed and the group information is found by using the SVDD, and several concepts such as group compatibility, optimal solution are introduced. Thirdly, the performance of the group-information sphere is proposed and proved. Finally,. the optimal solution for group decision making, i. e. order vector, is obtained by aggregating the vectors in group informational sphere based on the maximal eigenvalue method. The algorithm steps, the feasibility and efficiency of the method are illustrated with an example.

关 键 词：层次分析法 群决策 生成树 群体一致性 支持向量域描述(SVDD) 特征值 

分 类 号：O225[理学—运筹学与控制论] S763.33[理学—数学]