An extended VIKOR method based on particle swarm optimization and novel operations of probabilistic linguistic term sets for multicriteria group decision‐making problem

This paper proposes an extended VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method based on the particle swarm optimization (PSO) algorithm for solving multicriteria group decision‐making problems with probabilistic linguistic information. First, we define the novel operations of probabilistic linguistic term sets and then prove the corresponding properties. Second, we apply a modified PSO algorithm to the consensus reaching process to improve the collective consensus level. In the context of probabilistic linguistic information, each participant can be recognized as a particle moving towards the best position. The consensus level can be regarded as the objective function that is used to construct the fitness function. In the update function, the trust relationship and the similarity measure between experts are exploited to determine the adjustment coefficient. The new consensus model based on PSO can ensure that the ultimate evaluation achieves a high level of consensus. Afterward, we propose the extended VIKOR method to obtain the optimal solution, which not only avoids the loss of decision information, but also considers the separation of each alternative from the positive ideal solution and the negative ideal solution when criteria are interactive. The advantages of the proposed method are highlighted through a numerical example. Finally, we perform a comparative analysis and a sensitivity analysis to reveal the effectiveness and applicability of the method.