基于广义梯形模糊数相似度的交叉效率集结

在不确定环境下,针对模糊数据的多样性和复杂性,本文结合广义梯形模糊数相似度理论将广义梯形模糊数的交叉效率矩阵转换为交叉互评相似度矩阵,并根据模糊信息检索系统中的布尔模型,以能最大程度还原信息本身为准则,构建满足"正相容性"的有序几何平均集结函数对交叉互评相似度矩阵进行集结,从而得到关于每个决策单元的同行评价综合相似度.根据决策单元的同行评价综合相似度,建立反映决策者偏好的模糊一致性偏好矩阵,并对决策单元进行集结权重的分配,根据分配结果计算决策单元的全局交叉效率值.本文的集结方法可以解决不确定环境下,交叉效率矩阵数据多样性的问题,有较高的适用性;并且其集结结果具有较高的一致性和稳定性.最后本文以梯形模糊数的交叉效率矩阵为算例,来说明该方法的合理性和适用性.

The aggregation of cross efficiency matrix by generalized trapezoid fuzzy similarity theory

In uncertain environment, the cross-efficiency matrix will be expressed by various and complex fuzzy data. In order to aggregate the cross-efficiency with different types of fuzzy data, the similarity theory of the generalized fuzzy numbers is introduced to change generalize fuzzy cross-efficiency matrix into the cross-evaluation similarity matrix. The comprehensive similarity of peer evaluation of each (decision making units DMU) is computed by ordered geometric mean function, which satisfied the proposition of "positively compensatory". Moreover, based on the comprehensive similarities of peer evaluation of DMUs, a fuzzy additive consist preference matrix is constructed to yield aggregation weights of DMUs. The final cross-efficiency of DMUs is obtained by aggregating the cross-efficiency matrix. The aggregation method in this paper has wide adaptability, and the results of it are highly consistent and stable. At last, this paper demonstrates the applicability of fuzzy cross efficiency aggregation based on the similarity by taking the example of 12 suppliers from semiconductor industry.