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

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Abstract

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.

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Authors and Affiliations

  1. School of Internet of Things Engineering, Jiangnan University, Wuxi, 214122, China

    Wei Liu

  2. School of Management, Henan University of Technology, Zhengzhou, 450001, China

    Wei Liu

  3. School of Business, Jiangnan University, Wuxi, 214122, China

    Yuhong Wang & Lei Li

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  1. Wei Liu
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  2. Yuhong Wang
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  3. Lei Li
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Correspondence to Yuhong Wang.

Additional information

The research was partially supported by the National Natural Science Foundation of China under Grant No. 71871106 and the Fundamental Research Funds for the Central Universities under Grant Nos. JUSRP1809ZD, 2019JDZD06, JUSRP321016. The work was also sponsored by the Major Projects of Educational Science Fund of Jiangsu Province in 13th Five-Year Plan under Grant No. A/2016/01; the Key Project of Philosophy and Social Science Research in Universities of Jiangsu Province under Grant No. 2018SJZDI051; the Major Projects of Philosophy and Social Science Research of Guizhou Province under Grant No. 21GZZB32; Project of Chinese Academic Degrees and Graduate Education under Grant No. 2020ZDB2; Major research project of the 14th Five-Year Plan for Higher Education Scientific Research of Jiangsu Higher Education Association under Grant No. ZDGG02; the Henan University of Technology High-level Talents Scientific Research Fund (2022BS043).

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Liu, W., Wang, Y. & Li, L. Research on the Optimal Aggregation Method of Judgment Matrices Based on Spatial Steiner-Weber Point. J Syst Sci Complex 36, 1228–1249 (2023). https://doi.org/10.1007/s11424-023-1257-2

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  • DOI: https://doi.org/10.1007/s11424-023-1257-2

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