Consensus Reaching Process With Multiobjective Optimization for Large-Scale Group Decision Making With Cooperative Game

Abstract

Large-scale group decision making (LSGDM) is a common decision-making activity in which experts elicit their preferences through preference relations with consistencies based on additive properties. LSGDM has become a popular topic in decision making because of its necessity and applicability in multiple fields. In LSGDM, the consensus reaching process (CRP) ensures that decision makers (DMs) agree on the final decision-making results. Therefore, it is significant to investigate the CRP to improve the LSGDM process. In this article, a new method for LSGDM that includes a clustering algorithm, a weight determination method, and a CRP is developed. First, based on the consensus and the consistency of the additive preference relation, the DMs are classified into different subgroups by using the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> -means clustering algorithm. Then, because different subgroups have distinct decision-making interests, a weight determination method based on a cooperative game is proposed. Furthermore, to measure the consensus of each subgroup more comprehensively, the intra- and interconsensus levels are defined. These consensus levels are divided into four scenarios (acceptable–acceptable, acceptable–unacceptable, unacceptable–acceptable, and unacceptable–unacceptable) according to predetermined thresholds. Furthermore, different feedback mechanisms based on multiobjective optimization models corresponding to different CRP scenarios are presented. Finally, an illustrative example and comparative analyses are provided to verify the feasibility and validity of the proposed method.