Average consistency index based consensus model for a group decision making problem dealing with ELICIT expressions

Abstract

A group decision making (GDM) problem is often modeled by using a reciprocal preference relation (RPR) structure. Linguistic information is widely used in RPRs to depict its components because it facilitates its understanding and management of uncertainty. Among the existing linguistic representation models, the extended comparative linguistic expressions with symbolic translation (ELICIT) model improves the accuracy of computational processes and maintains the comprehensibility and interpretability of the results. Therefore, we introduce a new linguistic RPR (L-RPR) structure using ELICIT information, denoted as ELICIT-RPR, whose elements are uniformed as 2-tuple linguistic intervals to simplify and facilitate computations between ELICIT expressions. In addition, the average consistency index (ACI) of ELICIT-RPR is proposed together an algorithm for improving the ACI values of ELICIT-RPRs based on their best and worst consistency indices. To avoid conflicts and obtain agreed solutions, consensus reaching processes (CRPs) have been widely used in GDM. Thus, a novel CRP based on ACI values is developed using a new distance between linguistic intervals. Finally, a case study and a comparison analysis are presented to demonstrate the validity and applicability of the proposal.