Important Facts and Observations about Pairwise Comparisons (the Special Issue Edition).

This study has been inspired by numerous requests for clarification from researchers who often confuse Saaty's Analytic Hierarchy Process (AHP) with the pairwise comparisons (PC) method, taking AHP as the only representation of PC. This study should be regarded as an interpretation and clarification of past investigations of PC. In addition, this article is a reflection on general PC research at a higher level of abstraction: the philosophy of science. It delves into the foundations and implications of pairwise comparisons. Some results of this study are based on a recently published work by Koczkodaj and Szwarc. Finally, open problems have also been reported for future research.