基于最优一致性矩阵的灰色层次分析法研究

Grey analytic hierarchy process using optimal transfer matrix

针对传统层次分析法中存在的专家难以把握评判尺度,一致性检验难以通过的问题,提出3标度法,建立专家判断矩阵,将专家判断矩阵转化为最优传递矩阵,最终转化为最优一致性矩阵,得到相对重要度,再与灰色系统理论相结合,对带有灰色、模糊性质的部分信息已知、部分信息未知的决策问题进行建模。以课堂活跃度评价作为具体实例,说明上述方法的应用过程,然后与传统灰色层次分析法以及同类方法进行对比。对比结果表明,将最优一致性矩阵应于灰色层次分析法专家就能够更准确地把握比较对象的重要性程度,同时简化了传统繁琐的一致性检验步骤。

In view of the problem that the evaluation scale is hard to grasp and the consistency check is difficult to pass inthe traditional analytic hierarchy process,this paper puts forward the3scale method,builds the experts judgment matrix,which is transformed into the optimal transfer matrix,finally into the optimal consistency matrix to obtain the relativeimportant degree.It can model the grey and fuzzy decision problem whose information is partial known while the informationis partial unknown combined with grey system theory.The model uses the evaluation of classroom liveness as a specificexample to demonstrate the application process of above method,which is compared with the traditional grey analytichierarchy process and similar method.The contrast shows that the ratio degree of importance is more accurately graspedby experts after the optimal consistency matrix is imported into grey analytic hierarchy process,the complicated steps ofconsistency check is also clearly simplified.