Research On Preference Information Aggregation Methods Based On Spatial Steiner-Weber Point

In recent years,group decision-making has played an important role in modern government,management,science and technology,military,and other major decision-making issues.Preference information aggregation is the core link in multi-attribute group decisionmaking,and it is also the focus of current research.Therefore,it is of great significance to study an efficient preference information aggregation method to optimize the group opinions and obtain a scientific and practical result of group-decision.However,with the in-depth advancement of the digital economy,preference information aggregation is faced with new technical and application problems,such as the heterogeneity of preference information,the multiplicity of decision-making objectives,and the variability of decision-making environment.Most of the existing preference information aggregation methods are difficult to effectively aggregate the preference information of group members,and it is difficult for decision makers to reach a consensus.Therefore,how to put forward a scientific and effective aggregation method to aggregate different preference information into a group of representative opinions has become the core problem to be solved in group decision-making research.In solving the problem of preference information aggregation,how to map preference information into points on the plane or space,how to build the plane optimization aggregation model or spatial optimization aggregation model,and how to quickly solve the plane optimal aggregation model or spatial optimal aggregation model have become the key issuess in this thesis.To solve these problems,based on the spatial Steiner-Weber point theory,this thesis proposes a preference information aggregation method for planar and spatial Steiner-Weber point,aiming to improve the accuracy of planar and spatial preference information aggregation.The main research contents are as follows:(1)A preference information aggregation method is proposed based on two-dimensional Steiner-Weber point.Most of the existing two-dimensional preference information aggregation methods are extended or mixed by using classical aggregation operators.Once the aggregation of preference information is far from the mean,the aggregation results will have a large deviation,and the aggregation points obtained still have Pareto improvement.In order to solve these problems,a preference information aggregation method based on two-dimensional Steiner-Weber point is proposed.First,the two-dimensional preference information is preprocessed,and the preference information is mapped to two-dimensional points according to weighted Euclidian distance relation between multiple points on the plane.Then,on the basis of analyzing the prototype of the planar Steiner-Weber point,a two-dimensional plane optimization aggregation model is constructed.Aiming at the problem of solving planar Steiner-Weber point,the plant growth simulated algorithm(PGSA)is used to solve the optimal aggregation point of two-dimensional plane.On this basis,the framework of preference information aggregation method based on two-dimensional planar Steiner-Weber point is established.The selection of Fangcang hospital is analyzed,and the comparison with particle swarm optimization(PSO)method verifies the effectiveness and rationality of the proposed method.(2)A preference information aggregation method is proposed based on three-dimensional spatial Steiner-Weber point.Different from the preference information aggregation method of planar Steiner-Weber point,when the attribute value cannot be transformed into the aggregation problem of the two-dimensional plane,most of the existing three-dimensional aggregation methods still have some challenges,such as spatial mapping of three-dimensional preference information,constructing three-dimensional spatial optimization model,and solving three-dimensional spatial optimization model.To solve these problems,a preference information aggregation method based on three-dimensional Steiner-Weber point is proposed.For those aggregation problems that can convert attribute values into three-dimensional point coordinates,the three-dimensional preference information is preprocessed,and the preference information is mapped into preference points in three-dimensional space according to the three-dimensional space mapping rules proposed in this thesis.Then,the two-dimensional planar Steiner-Weber point theory is extended to the three-dimensional spatial Steiner-Weber point theory.In order to solve the problem of three-dimensional spatial Steiner-Weber point,the PGSA algorithm is adopted to solve the optimal aggregation point in three-dimensional space.Besides,the framework of preference information aggregation method is formed based on Steiner-Weber point in three-dimensional space.The selection of renewable energy in Pakistan is analyzed,and the comparison with spherical fuzzy weighted averaging(SFWA)results show that the proposed method is effective.(3)A preference information aggregation method is proposed based on multidimensional spatial Steiner-Weber point.Different from the above methods,the practical preference information aggregation problems are not only the preference information aggregation problems of two-dimensional and three-dimensional space but also the preference information aggregation problems of multi-attributes and multi-dimensions.When attribute values cannot be converted into the aggregation problem of the two-dimensional plane or three-dimensional space,most of the existing multi-dimensional aggregation methods still have problems such as spatial mapping of multi-dimensional preference information,construction of multi-dimensional spatial optimization model,and solution of multi-dimensional spatial optimization model.In order to solve the above problems,a method of preference information aggregation based on Steiner-Weber point in multi-dimensional space is proposed,which can aggregate the preference information of any dimension given by experts into a comprehensive aggregation point of a group.In this method,the multi-dimensional preference information is preprocessed,and the preference information is mapped into preference points in multi-dimensional space according to the multi-dimensional mapping rules.Then,the optimal aggregation model of multi-dimensional space is constructed based on the spatial Steiner-Weber point theory,and the PGSA algorithm is used to solve the optimal aggregation point in multi-dimensional space.Besides,the framework of preference information aggregation method is formed based on Steiner-Weber point in multi-dimensional space.Finally,the selection of emergency material suppliers is analyzed,and the comparison results with the least squares distance method(LSDM)show that the method proposed in this paper can achieve good aggregation accuracy.