状态离散的确定性多阶段群体满意决策最优的算法

为了解决状态离散的确定性多阶段群体决策问题，将群体满意决策问题的多阶段与图的点集、边集对应起来，应用图论知识建立了多阶段群体决策问题的模型．将多阶段群体满意决策问题转换成一个在多部赋权图中找一条最长路径的问题．依据一条最长路径上的任意两个不相邻的顶点之间是不可以被由不在这一条路径上的两个顶点组成的更长的路所替代这一事实，提出了一种多部赋权图中最长路径的算法．最后给出计算实例．

Optimal Algorithm of Multistage Group Decision-making under Discrete Determinate Status

In this paper, we investigate the problem of multistage group decision making under discrete deter- minate status. The problem of multistage group decision making is corresponded to the vertex sets and the edge sets of a graph. According to principle of graph theory, the mathematical model of that problem is estab- lished. Then the problem of multistage group decision-making under discrete determinate status is translated into find a longest path in a multi-partite graph with eighted-vector. Based on that the longest path between any two nonadjacent vertices of a longest path can not be replaced the longer path which is composed of the two vertices of the longest path, an algorithm for the longest path problem with k-partite graph with weigh- ted-vector is presented. Finally a computing example is given.