极大熵准则下的群决策AHP-DEA模型研究

Research on Group Decision Making ModelAHP-DEA Based on the Maximum Entropy Criterion

摘要:

传统带有AHP约束锥的DEA模型,其约束锥的构建是在单一决策者的环境之下,无法解决多个决策偏好存在时的问题,因此具有很大的风险性和不可靠性。如今一个决策问题的解决往往需要综合多方的意见,而群决策的概念能够充分考虑多决策者情况下决策偏好的选择。因此,在本文中,将群决策思想融入该模型,通过对多决策者不同偏好的基于欧式距离的聚类、基于判断矩阵hardmard积的集结以及基于极大熵准则的合成,形成含有群决策思想的DEA偏好约束锥,置于DEA模型中,从而形成了极大熵准则下的群决策下的AHP约束锥的DEA模型,最后结合算例,论证了该方法的可行性。

关键词:极大熵;群决策DEA;Hardmard积;AHP约束锥

Abstract:

The construction of traditional DEA model with AHP restraint cone is under the environment of a single decision maker, unable to solve the problem when multiple decision preference exist, so it has a great deal of risks and uncertainties. Now solving a decision problem often need to consider various opinions. So, in this paper, through composing different preferences of decision makers that based on the clustering of Euclidean Distance, the mass of Hadamard product of judgment matrix and the Maximum Entropy Criterion, integrate the concept of group decision making into the AHP-DEA model and form the DEA constraint cone that contains the concept of group decision making and put it into DEA model. So we get the DEA model based on the maximum entropy criterion, group decision making and the constraint cone of AHP. Finally, in combination with numerical example, we demonstrate the feasibility of this method.

Key words:maximum entropy, group decision making of DEA, Hadamard product, constraint cone of AHP