Multicriteria Decision Making: Scale, Polarity, Symmetry, Interpretability

In this study, we discuss the problem of interpretability of scale versus polarity in multicriteria decision-making problem. Decision making requires aggregation of premises of different characters and types. The influence of premises on a decision to be made may have a different characteristics as well. Some premises may have a positive character, i.e. they vote/agitate towards making a decision, others may fight against a decision. On the other hand, premises can be tempered by priorities, which may affect their character. Therefore, there is a need to discuss different configurations of premises and their priorities. This is the first aspect of our discussion on multicriteria decision making. The second one under discussion is the interpretability of all aspects mentioned so far. In this case, we discuss the representation problems of both premises and priorities. They are usually exhibited as numbers taken from some scale as, for instance, the unipolar unit interval [0,1] or the bipolar unit interval [-1,1]. On the other hand, there is a question raised about a character of premises/priorities, that is, whether they vote pro or contra a decision to be taken and what relations between scales and polarities are.