Personalized Individual Semantics-Based Consistency Control and Consensus Reaching in Linguistic Group Decision Making

Abstract

Consistency and consensus are important issues for linguistic group decision making (GDM), which have been extensively studied by scholars. Nevertheless, most of previous consensus reaching models focus on adjusting decision makers’ preference relations and ignore the individual consistency, which results in that individual consistency may be destroyed by using these consensus reaching models. Moreover, it has been accepted that words mean different things for different people and thus, it is also necessary to model decision makers’ personalized individual semantics (PISs) in linguistic GDM. This work focuses on developing some PIS-based consistency control and consensus reaching models for linguistic GDM. First, we analyze the problems existing in previous PIS models and then develop a minimum adjustment-based optimization model to test and improve the individual consistency for a linguistic preference relation (LPR). Followed by this, a PIS-based individual consensus-level maximization model and a PIS-based minimum adjustment model are established for consensus reaching in linguistic GDM, in which individual consistency control is considered. Furthermore, an algorithm for consensus reaching is proposed based on these models. To justify the proposed models and algorithm, some numerical results and simulation analysis are provided eventually.