A global optimization feedback model with PSO for large scale group decision making in hesitant fuzzy linguistic environments

In an increasingly complex and uncertain decision-making environment, large-scale group decision-making (LSGDM) can offer a more efficient method, allowing a large number of decision-makers (DMs) to truly participate in the decision-making process. The consensus-reaching process (CRP) is an effective method for resolving conflicting opinions among large-scale DMs. However, in the existing CRP of LSGDM, the new consensus state and the adjustment cost borne by inconsistent DMs after implementing feedback suggestions are not taken into consideration. To address this issue, this paper proposes a global optimization feedback model with particle swarm optimization (PSO) for LSGDM in hesitant fuzzy linguistic environments. An improved density-based spatial clustering of applications with noise (DBSCAN) on hesitant fuzzy linguistic term sets (HFLTSs) is introduced to classify large-scale DMs into several clusters, and a weight determination method that combines cluster size and intra-cluster tightness is also presented. The consensus degree of clusters is calculated at two levels: intra-consensus and inter-consensus. To improve the global consensus level with minimum cost, a global optimization feedback model is established to generate recommendation advice for inconsistent DMs, and the model is solved by PSO. A numerical example related to "COVID-19" and some comparisons are provided to verify the feasibility and advantages of the proposed method.