Related papers: Inconsistency thresholds for incomplete pairwise c…
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group $G$, non necessarily abelian. A necessary and sufficient criterion for pairwise comparisons matrices to be consistent is provided.…
This study presents special cases of inconsistent pairwise comparisons PC matrices and analysis of their eigenvalue-based inconsistency index using mathematical methods. All studied special cases of PC matrices are Toeplitz matrices with…
We describe a framework for random pairwise comparisons matrices, inspired by selected constructions releted to the so called inconsistency reduction of pairwise comparisons (PC) matrices. In to build up structures on random pairwise…
This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. However, it wrongly assumes that an inconsistency indicator can take values in any abelian linearly ordered group. The followup publication…
The article is devoted to the problem of inconsistency in the pairwise comparisons based prioritization methodology. The issue of "inconsistency" in this context has gained much attention in recent years. The literature provides us with a…
Mathematical analysis of the analytic hierarchy process (AHP) led to the development of a mathematical function, usually called the inconsistency index, which has the center role in measuring the inconsistency of the judgements in AHP.…
Pairwise comparisons are used in a wide variety of decision situations where the importance of alternatives should be measured on a numerical scale. One popular method to derive the priorities is based on the right eigenvector of a…
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…
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…
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…
We examine the notion of inconsistency in pairwise comparisons and propose an axiomatization which is independent of any method of approximation or the inconsistency indicator definition (e.g., Analytic Hierarchy Process, AHP). It has been…
Estimating missing judgements is a key component in many multi-criteria decision making techniques, especially in the Analytic Hierarchy Process. Inspired by the Koczkodaj inconsistency index and a widely used solution concept of…
This paper considers the matrix completion problem. We show that it is not necessary to assume joint incoherence, which is a standard but unintuitive and restrictive condition that is imposed by previous studies. This leads to a sample…
This study proposes revised axioms for defining inconsistency indicators in pairwise comparisons. It is based on the new findings that "PC submatrix cannot have a worse inconsistency indicator than the PC matrix containing it" and that…
This study demonstrates that incorrect data are entered into a pairwise comparisons matrix for processing into weights for the data collected by a rating scale. Unprocessed rating scale data lead to a paradox. A solution to it, based on…
Pairwise comparison models have been widely used for utility evaluation and rank aggregation across various fields. The increasing scale of modern problems underscores the need to understand statistical inference in these models when the…
In this study, we provide mathematical and practice-driven justification for using $[0,1]$ normalization of inconsistency indicators in pairwise comparisons. The need for normalization, as well as problems with the lack of normalization,…
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…
The pairwise comparisons method is a convenient tool used when the relative order of preferences among different concepts (alternatives) needs to be determined. There are several popular implementations of this method, including the…
We investigate an application of a mathematically robust minimization method -- the gradient method -- to the consistencization problem of a pairwise comparisons (PC) matrix. Our approach sheds new light on the notion of a priority vector…