一种基于灰色关联分析和超效率DEA的MCDM模型

MCDM model based on gray correlation analysis and super-efficiency DEA

针对多属性决策问题(MCDM)权重难以客观确定的缺陷,提出一种基于灰色关联分析和超效率数据包络分析(DEA)的混合算法研究MCDM。对MCDM进行建模,利用灰色关联分析计算各属性的点关联度,为了得到各属性的相对最优灰关联度并将其充分排序,利用超效率DEA改进灰色关联分析模型。该混合算法能够更加客观地确定权重向量,并且突破权重和为1的限制,使得均一的权重更加灵活;同时,可以得到各属性的相对最优灰色关联度,超效率DEA能够增强模型对灰关联度的分辨能力。通过北京市商品房空置影响因素的实例分析验证了该混合算法的有效性。

In view of the defect that the weights of multiple criteria decision making （MCDM） are hard to determine objectively, this paper proposed a hybrid model combined gray correlation analysis with super-efficiency DEA （ data envelopment analysis）. On the basis of gray correlation analysis, it calulated the point correlation degree of each criterion. In order to obtain relative optimal gray correlation degree of each criterion and rank them completely, suggested the super-efficiency DEA method. The hybrid model could ascertain the weight vector more objectively. It broke through the constraint that the sum of each weight vector was equal to 1, thus the homogeneous weight could be more flexible. The improved model could lead to relative optimal gray correlation degree of each criterion. Super-efficiency DEA could enhance the discernment ability as well. It studied the influence factors of vacant commercial housing in Beijing city. The results show that the correlation order of influence factors. The numerical example illustrates the availability and efficiency of the hybrid model.