An optimisation-based method to conduct consistency and consensus in group decision making under probabilistic uncertain linguistic preference relations

Abstract

The use of probabilistic uncertain linguistic preference relations (PULPRs) enriches the flexibility of decision makers (DMs) in group decision making (GDM). However, the GDM models under PULPRs are mainly focussed on the consensus reaching process rather than the individual consistent improvement. The goal of this paper is to manage the consistency and consensus in GDM based on PULPRs, and provide a feasible method for minimising the preference information loss by optimisation model. First, according to DMs’ psychological preferences (optimistic, pessimistic, and neutral characteristics), we proposed a conversion function to fit uncertain linguistic terms in PULPRs, which may be transformed into probabilistic linguistic preference relations. Second, to preserve as much as possible the original preference information of DMs, a consensus model based on optimisation is established, which not only obtains the acceptable group consensus but also guarantees that the consistency level of individuals is acceptable. Finally, we validated the proposed method through a case study of an investment project selection for central enterprises’ poverty alleviation fund. The proposed method provides a new way to deal with GDM problems under PULPRs, and help DMs to reach a certain level of consensus on basis of acceptable consistent level of individuals.

Keywords:

• Group decision making
• probabilistic uncertain linguistic preference relation
• consistency
• consensus
• mathematical programming
• psychological preference

Disclosure statement

No potential conflict of interest was reported by the author.

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was supported in part by grants from the National Natural Science Foundation of China (#71601032, 71774134), the Special Funds of Taishan Scholars Project of Shandong Province (#tsqn201909149) and Fundamental Research Funds for the Central Universities (#ZYGX2019J133).