A Group Decision-Making Method With Probabilistic Linguistic Preference Relations Based on Additive Consistency and Its Application

How to evaluate the citizens' sense of gain (CSG) is an essential problem in the new smart city. To solve the problem, this paper investigates a group decision making (GDM) method with probabilistic linguistic preference relations (PLPRs). First, the additive consistency of PLPR is defined by the linguistic hybrid weighted average (LHWA) operator. The LHWA-based linguistic preference relation is extracted from a PLPR to derive the priority weights. For the GDM problem in the linguistic environment, combining the linguistic evaluations and their probability of different citizens, i.e, decision makers (DMs), the PLPRs of DMs' subsets (DMSes) are formed to obtain the corresponding priority weights. The similarity divergences and the proximity divergences of DMSes are introduced to derive DMSes' weights. Using the relative entropy, the comprehensive priority weights are generated for ranking alternatives. Thus, a GDM method with PLPRs is proposed and validated.