MACBETH is a multicriteria decision analysis approach that requires only non-numerical judgments about differences in attractiveness between options to help the decision maker DM measure the relative attractiveness or value of options Bana e Costa et al. Within a multicriteria value measurement framework, MACBETH has been most commonly used to build value functions and weight criteria in additive models.
During this questioning protocol, a matrix with the categorical judgments of the DM is populated. After the consistency verification, the software derives, by mathematical programming, an interval numerical scale which has to be analysed and validated by the DM Bana e Costa et al.
As mentioned in Edwards et al. For cases of interdependent EC, there has been an increase in studies using procedures with operators of CI family that belong to the non-additive measure family.
These CI operators are represented by a mathematical expression that aggregates impact values of multiple interdependent EC into a single global score Mayag et al. Some of these studies lack information about the questioning protocol applied and do not explain how to convert impacts into value or how to determine the CI parameters Feyziog lu et al.
Other studies convert quantitative impacts into values linearly and therefore presuppose that a unit of impact has always the same value, which is a strong assumption in other words, problems on the interpretation of commensurate scales - see section 3. Other studies weight EC based only on the notion of importance Labreuche et al.
Some studies require a direct elicitation of numerical information about the overall value of each option from the DM Grabisch et al. By local judgment we mean a judgment involving one EC alone; matrx eness for binary options reviews global judgment we mean a judgment involving the interrelated EC all together.
However, if there exist interdependencies between EC, that judgment may change with the impacts in the remaining EC and therefore these should be fixed before the questioning a further explanation on this is provided in sections 2. Even if the local judgments, present in the first matrix, were asked to the DM in the form of global judgments, the use of two matrices could entail incoherence and inconsistency problems.