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In various fields of evaluation, selection, and prioritization processes decision makers try to find the best alternative(s) from a feasible set of alternatives. In many cases, the comparison of different alternatives according to their desirability in decision problems cannot be done using only a single criterion or one decision maker. Here, procedures have been established to combine opinions about alternatives related to different points of view. These procedures are often based on pairwise comparisons, in the sense that processes are linked to some degree of preference for one alternative over another. The presented monograph consists of two parts: in the first part, theoretical aspects of pairwise comparisons are investigated from various point of views. The pairwise comparisons matrix, a fundamental tool for further investigation, is firstly viewed as a deterministic matrix with given elements. Then, in the following three chapters, it is investigated under uncertainty, either as a matrix with vague elements (fuzzy and/or intuitionistic fuzzy ones), and also as random elements. In the second part, theoretical results are applied in the three most popular multicriteria decision making methods: the Analytic Hierarchy Process (AHP), PROMETHEE and TOPSIS. In these methods pairwise comparisons play a leading role with a decisive impact. From this point of view, all well known methods are reconsidered in new and broader perspectives.