A geometrical method for consensus building in GDM with incomplete heterogeneous preference information
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Group decision makingConsensus reachingIncomplete heterogeneous preference structuresGeometrical method
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]
SponsorshipNational Natural Science Foundation of China (NSFC) 71874023 71725001 71910107002 71771037 71971042; European Regional Development Fund (FEDER), European Union 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.