An adaptive consensus model for multi-criteria sorting under linguistic distribution group decision making considering decision-makers’ attitudes

Group multiple criteria sorting (MCS) has become a trend in dealing with a variety of practical problems. During the process of managing group MCS, it is critical to reduce conflicts among decision-makers (DMs). Given the key role of DMs’ attitudes in affecting consensus level, this study aims to propose a novel consensus-based approach to solve group MCS problems considering DMs’ attitudes with flexible expression linguistic distribution assessments (LDAs) that can capture massive DMs’ qualitative preferences. To achieve this goal, first, a minimum adjustment-based optimization model is built to guide individuals in revising their preferences, and a maximum assignment interval-based optimization model is constructed to derive consistent and possible assignments of each alternative while maintaining the accuracy levels of the original assignments. An attitudinal consensus index is then defined to measure the group consensus level, by which group DMs’ attitudes can be well considered in MCS problems. A sophisticated adaptive feedback adjustment mechanism is also developed and inserted into the consensus model, which provides support for consensus-reaching based on the advantages of both types of adaptive feedback adjustment mechanism strategies. Afterwards, to generate more straightforward and scientific assignment solutions, this study proposes a minimum information loss-based optimization model to identify the final categories of each alternative. Finally, an illustrative example for evaluating livable cities, followed by sensitivity and comparative analyses, is presented to demonstrate the applicability and advantages of the proposed MCS approach.