在继承传统层次分析/网络分析方法的基础上提出一种新的决策方法——基于有限状态齐次马尔科夫链的网络决策方法MC-ANP. 该方法使用有向图定义决策准则及准则之间的支配关系,通过对准则的两两比较量化支配关系,用马氏链的状态转移描述支配关系. 该方法突出了准则支配关系的合成过程,提供了两种合成模型(其中积合成模型可以彻底解决传统层次分析中出现的逆序问题), 指出传统网络分析中无条件使用Cesaro平均极限求解存在的问题.新方法将决策问题分为两类:有方案的决策问题,解是对方案的排序, 求解过程就是求马氏链状态转移概率方阵的属于特征根1的特定的左特征向量;无方案决策问题,解是对准则的排序,解是马氏链状态转移概率方阵的属于特征根1的右特征向量.
Abstract
On the basis of the traditional AHP/ANP, a new decision making approach — MC-ANP (analytic Network Process based on finite state homogeneous Markov chain) — was proposed. In this approach we have used a direct graph to define the criteria and the dominance relations among them, have quantified the relations of dominations through comparison of criteria, and have~described criteria dominance relations~using the matrix of state transition of the Markov chain. This approach has focused on the synthesis of the dominance relations, has provided two synthetic models (among which the multiply model can be used to solve rank reverse problem throughly), and has pointed out the confusion existed in the traditional ANP using Cesaro mean limit. In the MC-ANP, the decision problems are classified in two categories: i) ranking the alternatives, the process of the solution is to find the specific left eigenvectors of eigenvalue 1 of matrix of state transition probability of the Markov chain; ii) ranking the criteria (no alternative), the solution is the right eigenvector of eigenvalue 1 of matrix of state transition probability of the Markov chain.
关键词
决策方法 /
层次分析(AHP) /
网络分析(ANP) /
Markov链 /
邻接方阵
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Key words
decision making /
AHP (analytic hierarchy process) /
ANP (analytic network process) /
Markov chains /
adjacency matrix
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中图分类号：
C934
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