Research on the Optimal Aggregation Method of Judgment Matrices Based on Spatial Steiner-Weber Point

This paper is to provide a novel approach for the spatial aggregation of judgment matrices. The optimal aggregation method of judgment matrices based on spatial Steiner-Weber point can effectively aggregate the preference information of group members and achieve the optimization of group preference. The method comprises three key elements: The spatial mapping of the judgment matrices, the spatial optimal aggregation model of the judgment matrices, and the plant growth simulation algorithm (PGSA) is used to find the optimal aggregation points. Firstly, the judgment matrices are mapped into a set of spatial multidimensional coordinates by using spatial mapping rules. Secondly, the spatial Steiner-Weber point is used as the prototype to construct the spatial aggregation model. Thirdly, the PGSA algorithm is used to find the spatial aggregation points, whose spatial weighted Euclidean distance to all the decision makers preference points is minimal. The optimal aggregation matrix is composed of these optimal aggregation points, which can accurately reflect the decision maker's comprehensive opinions. Finally, the effectiveness and rationality of this method are verified by comparing with the classical group preference aggregation methods.