基于区间运算的随机多准则决策方法

Journal of Systems Engineering and Electronics ›› 2010, Vol. 32 ›› Issue (2): 308-312.

基于区间运算的随机多准则决策方法

任剑1,2, 高阳1

(1. 中南大学商学院, 湖南长沙 410083; 2. 湖南农业大学科学技术师范学院, 湖南长沙 410128)

出版日期:2010-02-03 发布日期:2010-01-03

Stochastic multicriterion decisionmaking method based on interval operation

REN Jian1,2， GAO Yang1

（1. Business School, Central South Univ., Changsha 410083, China；
2. Normal School of Science Technology, Hunan Agriculture Univ., Changsha 410128, China）

Online:2010-02-03 Published:2010-01-03

摘要/Abstract

摘要：

针对准则权重信息不完全且准则值为正态分布随机变量的多准则决策问题，提出一种基于区间运算的随机多准则决策方法。该方法将正态分布准则值转化为区间数，利用离差最大化原理和不完全准则权重信息建立区间参数线性规划模型，将其转化为最优模型。通过对最优模型进行求解,得到最优准则权重向量，从而构造加权规范化区间决策矩阵。然后计算每个方案到区间理想点的区间距离,并根据其大小确定方案集的带有可能度的排序。最后算例说明该方法的有效性和可行性。

Abstract:

Accoding to multicriterion decisionmaking problems with incomplete certain information of the weights on criterions and normal distribution evaluations of alternatives on criterions, a new method based on interval operation is proposed.Firstly, the normal distribution evaluations of alternatives on criterions are transformed into interval numbers.Secondly, a linear programming model with interval parameters is constructed based on maximal deviations and incomplete certain information of the weights on criterions.Then, the optimal form of the front model is worked out in order to get the optimal weight vector.Thirdly, a weighted normalized interval decisionmaking matrix is given.And then, the ranking with possibility degree of alternatives appears with the help of the interval distances between alternatives and ideal interval point.Finally, an example is given to prove the feasibility and availability of the method.

任剑1,2, 高阳1. 基于区间运算的随机多准则决策方法[J]. Journal of Systems Engineering and Electronics, 2010, 32(2): 308-312.

REN Jian1,2， GAO Yang1. Stochastic multicriterion decisionmaking method based on interval operation[J]. Journal of Systems Engineering and Electronics, 2010, 32(2): 308-312.