A Linguistic Metric for Consensus Reaching Processes Based on ELICIT Comprehensive Minimum Cost Consensus Models

Linguistic group decision making (LiGDM) aims at solving decision situations involving human decision makers (DMs) whose opinions are modeled by using linguistic information. To achieve agreed solutions that increase DMs' satisfaction toward the collective solution, linguistic consensus reaching processes (LiCRPs) have been developed. These LiCRPs aim at suggesting DMs to change their original opinions to increase the group consensus degree, computed by a certain consensus measure. In recent years, these LiCRPs have been a prolific research line, and consequently, numerous proposals have been introduced in the specialized literature. However, we have pointed out the nonexistence of objective metrics to compare these models and decide which one presents the best performance for each LiGDM problem. Therefore, this article aims at introducing a metric to evaluate the performance of LiCRPs that takes into account the resulting consensus degree and the cost of modifying DMs' initial opinions. Such a metric is based on a linguistic comprehensive minimum cost consensus (CMCC) model based on Extended Comparative Linguistic Expressions with Symbolic Translation information that models DMs' hesitancy and provides accurate Computing with Words processes. In addition, the linguistic CMCC optimization model is linearized to speed up the computational model and improve its accuracy.