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One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to represent such subjective assessments and to process them by…
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction transforms an inconsistent pairwise comparisons (PC) matrix into…
The pairwise winning indices, computed in the Stochastic Multicriteria Acceptability Analysis, give the probability with which an alternative is preferred to another taking into account all the instances of the assumed preference model…
Processing information, acquired by subjective assessments, involves inconsistency analysis in most (if not all) applications of which some are of considerable importance at a national level (see, Koczkodaj/Kulakowski/Ligenza,…
This paper recalls the definition of consistency for pairwise comparison matrices and briefly presents the concept of inconsistency index in connection to other aspects of the theory of pairwise comparisons. By commenting on a recent…
This paper examines the differences in ordinal rankings obtained from a pairwise comparison matrix using the eigenvalue method and the geometric mean method. First, we introduce several propositions on the (dis)similarity of both rankings…
Pairwise comparison matrices are increasingly used in settings where some pairs are missing. However, there exist few inconsistency indices for similar incomplete data sets and no reasonable measure has an associated threshold. This paper…
A distance-based inconsistency indicator, defined by the third author for the consistency-driven pairwise comparisons method, is extended to the incomplete case. The corresponding optimization problem is transformed into an equivalent…
Several methods of preference modeling, ranking, voting and multi-criteria decision making include pairwise comparisons. It is usually simpler to compare two objects at a time, furthermore, some relations (e.g., the outcome of sports…
Pairwise comparison matrices are frequently applied in multi-criteria decision making. A weight vector is called efficient if no other weight vector is at least as good in approximating the elements of the pairwise comparison matrix, and…
Incomplete pairwise comparison matrices offer a natural way of expressing preferences in decision making processes. Although ordinal information is crucial, there is a bias in the literature: cardinal models dominate. Ordinal models usually…
Efficiency is a core concept of multi-objective optimization problems and multi-attribute decision making. In the case of pairwise comparison matrices a weight vector is called efficient if the approximations of the elements of the pairwise…
Incomplete pairwise comparison matrices are increasingly employed to save resources and reduce cognitive load by collecting only a subset of all possible pairwise comparisons. We present their graph representation and some completion…
The article describes the main problems concerned with using expert assessment method in consumer preference researches. The author proved the expediency of using a 3-point measurement scale. The author suggested an algorithm for…
The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…
Efficiency, the basic concept of multi-objective optimization is investigated for the class of pairwise comparison matrices. A weight vector is called efficient if no alternative weight vector exists such that every pairwise ratio of the…
We consider a simple model of imprecise comparisons: there exists some $\delta>0$ such that when a subject is given two elements to compare, if the values of those elements (as perceived by the subject) differ by at least $\delta$, then the…
The eigenvalue method, suggested by the developer of the extensively used Analytic Hierarchy Process methodology, exhibits right-left asymmetry: the priorities derived from the right eigenvector do not necessarily coincide with the…
A principled approach to cyclicality and intransitivity in paired comparison data is developed. The proposed methodology enables more precise estimation of the underlying preference profile and facilitates the identification of all cyclic…
Analyzing the consistency of preferences is an important step in decision making with pairwise comparison matrices, and several indices have been proposed in order to estimate it. In this paper we prove the proportionality between some…