Some awkward issues on pairwise comparison matrices

Many decision-making techniques use pairwise comparisons (PCs) elicited by one or more stakeholders involved in a given corresponding decision-making process. In very complex problems, the number of criteria or options to be compared may be too large, thus limiting PC applicability to large-scale decision problems due to the so-called curse of dimensionality, that is, a large number of pairwise comparisons need to be produced from a decision maker. For example, in AHP, Saaty [1] recommends that to obtain a reasonable and consistent PC matrix, the number of comparing elements should be at most seven. In [2] and [3], arguing on limitations of the human capabilities, the maximum number of elem…