A geometrical method for consensus building in GDM with incomplete heterogeneous preference information Kou, Gang Peng, Yi Chao, Xiangrui Herrera Viedma, Enrique Alsaadi, Fawaz E. Group decision making Consensus reaching Incomplete heterogeneous preference structures Geometrical method This work was supported in part by grants from the National Natural Science Foundation of China (#71874023, #71725001, #71910107002, #71771037, #71971042), and European Regional Development Fund (FEDER), European Union funds in the project TIN2016-75850-R. In real-life group decision-making (GDM) problems, the preferences given by decision-makers(DMs) are often incomplete, because the complexity of decision-making problems and the limitation of knowledge of DM make it difficult for DMs to take a determined evaluation of alternatives. In addition, preference relations provided by DMs are often heterogeneous because they always have different decision habits and hobbies. However, the consensus method for GDM under incomplete heterogeneous preference relations is rarely studied. For four common preference relations: utility values, preference orderings, and (incomplete) multiplicative preference relations and (incomplete) fuzzy preference relations, this paper proposes a geometrical method for consensus building in GDM. Specifically, we integrate incomplete heterogeneous preference structures using a similarity-based optimization model and set a corresponding geometrical consensus measurement. Then, preference modification and weighting processes are proposed to improve consensus degree. Finally, we conduct a comparison analysis based on a qualitative analysis and algorithm complexity analysis of existing consensus reaching methods. Numerical analyses and convergence tests show that our method can promote the improvement of the consensus degree in GDM, and has less time complexity than the previous methods. The proposed geometrical method is a more explainable model due to operability and simplicity. 2021-07-06T07:33:59Z 2021-07-06T07:33:59Z 2021-02-27 info:eu-repo/semantics/article Gang Kou... [et al.], A geometrical method for consensus building in GDM with incomplete heterogeneous preference information, Applied Soft Computing, Volume 105, 2021, 107224, ISSN 1568-4946, [https://doi.org/10.1016/j.asoc.2021.107224] http://hdl.handle.net/10481/69532 10.1016/j.asoc.2021.107224 eng http://creativecommons.org/licenses/by-nc-nd/3.0/es/ info:eu-repo/semantics/openAccess Atribución-NoComercial-SinDerivadas 3.0 España Elsevier