# A Multiple Criteria Decision Analysis Framework for Dispersed Group Decision-Making Contexts
## 2 Literature Review
[PERSON], [PERSON] [22] developed a Consistency Consensus Matrix (CCM) for GDM to measure the consistency in judgement elicitation using the Analytic Hierarchic Process (AHP). To do so, first the authors considered the definitions developed in [23,24] regarding both preference structures (which corresponds to possible rankings of a set of alternatives) and stability intervals (which corresponds to the interval in which a judgment can vary while still being consistent). Then, the authors defined a row geometric mean as a prioritization procedure and a geometric consistency index to measure the inconsistency level of each judgement. The authors referred to CCM as a tool that could be used as an initial step of a participatory dialogue GDM process and applied to scenarios requiring the interaction between few or several decision-makers. Furthermore, the authors referred that their work could be extended to other multi-criteria decision-making techniques that consider the concept of consistency, and that could allow one to extract valuable knowledge to help achieve consensus. [PERSON], [PERSON] [2] studied the relation between consensus and consistency and proposed a web-based multi-criteria group decision support system to solve multi-criteria ranking problems. The two main contributions of their work are (1) the use of multi-objective evolutionary algorithms and multi-criteria aggregation-disaggregation to identify alternatives and criteria parameters that less contribute to the consensus level and (2) the definition of a consistency mechanism based on multi-objective combinatorial optimization to help decision-makers maintain a high consistency level regarding their preferences avoiding self-contradiction and decreasing the significance of rank reversal and incompleteness. [PERSON], [PERSON] [25] proposed an approach to support GDM processes using a multi-agent system where each agent's preferences are represented through a set of linguistic preferences relations. This approach is divided into two steps: in the first step, linguistic terms are transformed into intervals using a performance index that considers the consensus among the group of agents and the consistency of each individual agent assessments. In the second step, all the alternatives are ranked by defining a degree of relation between the alternatives and then transforming that degree into a classification from the best alternative to the worst. The authors recognized that one limitation of their approach was the fact of only considering static sets of alternatives, and that it should be adapted to consider dynamic scenarios with the possibility to include and remove alternatives over time. [PERSON], [PERSON] [26] explained how most of the existing frameworks that consider consensus degree and individual consistency include a consistency improving process and a consensus reaching process. In the first process, it is ensured that the preferences of the decision-maker are not inconsistent or random. In the second process, it is ensured that the group of decision-makers agree with the preferences given for each alternative. However, the authors refer to the fact that the individual consistency improving process is applied before the consensus reaching process, which can lead to an inconsistent adjustment of preferences before the consensus reaching process. As a result, the consistency improving process is often repeated during the consensus reaching process. Furthermore, they argued that the available frameworks that do not consider these two processes, and manage both consensus and consistency simultaneously, are based on automatic consensus processes that do not consider the decision-makers' opinions. Then, to avoid repeating the consistency improving process during the consensus reaching process, the authors proposed an approach using a consensus reaching process with individual consistency control.