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 prefere...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.展开更多
基金partially supported by the National Natural Science Foundation of China under Grant No.71871106the Fundamental Research Funds for the Central Universities under Grant Nos. JUSRP1809ZD,2019JDZD06, JUSRP321016+5 种基金sponsored by the Major Projects of Educational Science Fund of Jiangsu Province in 13th Five-Year Plan under Grant No. A/2016/01the Key Project of Philosophy and Social Science Research in Universities of Jiangsu Province under Grant No. 2018SJZDI051the Major Projects of Philosophy and Social Science Research of Guizhou Province under Grant No. 21GZZB32Project of Chinese Academic Degrees and Graduate Education under Grant No. 2020ZDB2Major research project of the 14th Five-Year Plan for Higher Education Scientific Research of Jiangsu Higher Education Association under Grant No. ZDGG02the Henan University of Technology High-level Talents Scientific Research Fund (2022BS043)
文摘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.
