Advances in Pairwise Comparisons: Detection, Evaluation and Reduction of Inconsistency

The objective of modern decision making methods is a selection of the best alternative (option, action, etc.) from a finite non-empty set of alternatives based on preferences of an individual-expert or a group of experts. To make informed and precise decisions less vulnerable to various limits of human thinking (cognitive bias), one current direction of operational research focuses on the investigation of various aspects of decision making methods, and, in particular, on the problem of inconsistency of preferences. A number of published studies indicate that inconsistency of preferences is a ubiquitous problem that cannot be ignored and requires thorough investigation. This monograph focuses on the problem of inconsistency (cardinal and ordinal) in the field of the multiplicative system of pairwise comparisons, which is probably the most popular theoretical framework for pairwise comparisons at the moment and includes, for example, the AHP (Analytical Hierarchy Process) method. The main problems in this area are the detection, evaluation and reduction of inconsistency, which is mirrored both in the title of the monograph and in its structure. The monograph brings a condensed "state-of-the-art" of the discipline supplemented by the author's new findings mainly in areas related to the properties of inconsistency indices, comparisons of inconsistency indices using numerical (Monte Carlo) methods, or the mutual relationship between cardinal and ordinal inconsistency.