In this study, we introduce pairwise comparisons matrix classification based on homology groups of graphs with unique vertices. Algebraic topology transforms a sequence of topological objects (such as graphs associated with pairwise comparison ...

The role of an expert in the decision-making process is crucial. If we ask an expert to help us to make a decision we assume their honesty. But what if the expert is dishonest? Then, the answer on how difficult it is for an expert to provide ...

In decision-making methods, it is common to assume that the experts are honest and professional. However, this is not the case when one or more experts in the pairwise-based group decision-making framework, such as the group analytic hierarchy ...

Apart from consistency, the completeness of information is one of the key factors influencing data quality. In the case of the pairwise comparisons (PC) method, much space in the literature is devoted to the quantitative analysis of ...

We define a new inconsistency index for tournament matrices and two tournaments-based indices for multiplicative pairwise comparison matrices. We compare them with the index defined by Kulakowski and illustrate the fundamental differences on ...

This study presents special cases of inconsistent pairwise comparisons PC matrices. The analysis of the selected inconsistency indicators is provided. One of the compared inconsistencies is the popular eigenvalue-based consistency index (CI) which fails ...

This article analyzes the question of reliability of entries collected in the pairwise comparison matrices used for prioritization of alternatives. The inappropriate input data may result in an invalid output hierarchy. Basing on the Geometric ...

The method of pairwise comparisons is widely applied in the decision making process. The inconsistency of data may significantly affect the final result. Since the notion of consistency is based on triads or cycles, there is a great need for defining ...

AbstractThis study provides a proof that the limit of a distance-based inconsistency reduction process is a matrix induced by the vector of geometric means of rows when a distance-based inconsistent pairwise comparisons matrix is transformed into a ...

This study presents an abelian group approach to analyzing inconsistency in pairwise comparisons. A notion of an inconsistency indicator map on a group, taking values in an abelian linearly ordered group, is introduced. For it, metrics and generalized ...

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 ...

This study presents theoretical proof and empirical evidence of the reduction algorithm convergence for the distance-based inconsistency in pairwise comparisons. Our empirical research shows that the convergence very quick. It usually takes less than 10 ...

This study examines the notion of generators of a pairwise comparisons matrix. Such approach decreases the number of pairwise comparisons from n ( n - 1 ) to n - 1 . An algorithm of reconstructing of the PC matrix from its set of generators is ...