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 complexity of problems and limitation knowledge DM make it difficult for DMs to take a determined evaluation alternatives. addition, preference relations provided heterogeneous they always have different decision habits hobbies. However, consensus method GDM under incomplete is rarely studied. For four common relations: utility values, orderings, (incomplete) multiplicative fuzzy relations, this paper proposes geometrical building in GDM. Specifically, we integrate structures using similarity-based optimization model set corresponding measurement. Then, modification weighting processes proposed improve degree. Finally, conduct comparison analysis based on qualitative algorithm existing reaching methods. Numerical analyses convergence tests show that our can promote improvement degree GDM, has less time than previous The more explainable due operability simplicity. • Propose with relations. Integrate model. A various measurements representative