An Additive-Consistency- and Consensus-Based Approach for Uncertain Group Decision Making With Linguistic Preference Relations

Linguistic preference relations (LPRs) can indicate the decision makers (DMs)' qualitative pairwise judgments regarding a set of alternatives in uncertain multicriteria decision-making problems. This paper examines several goal programming models for managing the additive consistency and consensus of LPRs and then develops an additive-consistency- and consensus-based method for group decision making (GDM) with LPRs. First, this paper offers a consistency index to quantify the consistency level for LPRs and define acceptable consistent LPRs. For an LPR that is unacceptably additive consistent, several additive-consistency-based programming models are developed to address the inconsistency and to establish an acceptably consistent LPR. Then, an additive-consistency-based procedure to generate the priority weight vector from the LPR is offered. An additive-consistency-based algorithm for decision making with an LPR is presented. Subsequently, considering the consensus in GDM, a consensus index is proposed for gauging the agreement degree among individual LPRs. Regarding individual LPRs that do not exhibit acceptably additive consistency or acceptable consensus, several goal programming models to derive new LPRs with acceptable consistency and consensus are provided. Afterward, the DMs' weights are determined objectively, and individual LPRs are integrated into a collective LPR. An additive-consistency- and consensus-based GDM method with a group of LPRs is developed. Finally, two practical numerical examples are offered, and a comparative analysis is presented.