A geometrical method for consensus building in GDM with incomplete heterogeneous preference information

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. (C) 2021 The Authors. Published by Elsevier B.V.

Automated summary

This paper proposes a geometrical method for consensus building in group decision-making under incomplete heterogeneous preference relations, which integrates incomplete preference structures, sets consensus measurement, and introduces preference modification and weighting processes to improve consensus degree. Comparative analysis shows that the method improves consensus degree with less time complexity compared to existing methods, making it a more explainable model due to its operability and simplicity.