85 citations · 279 across the 23 of their papers we have counts for
24 papers
Recursive Multilevel Decomposition of Pairwise Comparison Matrices: Algorithms and Inconsistency Diagnostics
Mert Çarboğa, Waldemar W. Koczkodaj, Yusuf Yaylı
Positive reciprocal pairwise comparison matrices are studied in entrywise logarithmic coordinates. Starting from the established consistent-residual split, we show that, for any fi…
A note on the theoretical approach to Grassmannians and Plücker coordinates for additive skew-symmetric pairwise comparisons matrices
Waldemar W. Koczkodaj, Witold Pedrycz, Alexander Pigazzini +2
Symmetry and antisymmetry are fundamental concepts in many strict sciences. Pairwise comparisons (PC) matrices are fundamental tools for representing pairwise relations in decision…
Computationally efficient orthogonalization for pairwise comparisons method
Julio Benitez, Waldemar W. Koczkodaj, Adam Kowalczyk
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is…
Combating harmful Internet use with peer assessment and differential evolution
W. W. Koczkodaj, M. Mazurek, W. Pedrycz +8
Harmful Internet use (HIU) is a term coined for the unintended use of the Internet. In this study, we propose a more accurate HIU measuring method based on the peer assessment and…
Pairwise Comparisons Matrix Decomposition into Approximation and Orthogonal Component Using Lie Theory
W. W. Koczkodaj, V. W. Marek, Y. Yayli
This paper examines the use of Lie group and Lie Algebra theory to construct the geometry of pairwise comparisons matrices. The Hadamard product (also known as coordinatewise, coor…
On Orthogonal Projections on the Space of Consistent Pairwise Comparisons Matrices
W. W. Koczkodaj, R. Smarzewski, J. Szybowski
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwi…
On the use of group theory to generalize elements of pairwise comparisons matrix: a cautionary note
W. W. Koczkodaj, F. Liu, V. W. Marek +11
This paper examines the constricted use of group theory in the studies of pairwise comparisons. The presented approach is based on the application of the famous Levi Theorems of 19…
RatingScaleReduction package: stepwise rating scale item reduction without predictability loss
Waldemar W. Koczkodaj, Alicja Wolny-Dominiak
This study presents an innovative method for reducing the number of rating scale items without predictability loss. The "area under the re- ceiver operator curve method" (AUC ROC)…
Special cases of pairwise comparisons matrices represented by Toeplitz matrices
Viera Čerňanová, Waldemar W. Koczkodaj
This study presents special cases of inconsistent pairwise comparisons PC matrices and analysis of their eigenvalue-based inconsistency index using mathematical methods. All studie…
On normalization of inconsistency indicators in pairwise comparisons
W. W. Koczkodaj, J. -P. Magnot, J. Mazurek +6
In this study, we provide mathematical and practice-driven justification for using normalization of inconsistency indicators in pairwise comparisons. The need for normaliza…
A Geometric Framework for the Inconsistency in Pairwise Comparisons
Waldemar W. Koczkodaj, Jean-Pierre Magnot
In this study, a pairwise comparison matrix is generalized to the case when coefficients create Lie group , non necessarily abelian. A necessary and sufficient criterion for pai…
Pairwise Comparisons Rating Scale Paradox
W. W. Koczkodaj
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…
Axiomatization of Inconsistency Indicators for Pairwise Comparisons
W. W. Koczkodaj, J. -P. Magnot
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 inconsisten…
A different perspective on a scale for pairwise comparisons
J. Fueloep, W. W. Koczkodaj, S. J. Szarek
One of the major challenges for collective intelligence is inconsistency, which is unavoidable whenever subjective assessments are involved. Pairwise comparisons allow one to repre…
Managing Null Entries in Pairwise Comparisons
W. W. Koczkodaj, M. W. Herman, M. Orlowski
This paper shows how to manage null entries in pairwise comparisons matrices. Although assessments can be imprecise, since subjective criteria are involved, the classical pairwise…
An Algorithm for the Optimal Consistent Approximation to a Pairwise Comparisons Matrix by Orthogonal Projections
W. W. Koczkodaj, M. Orlowski
The algorithm for finding the optimal consistent approximation of an inconsistent pairwise comparisons matrix is based on a logarithmic transformation of a pairwise comparisons mat…
An LP-based inconsistency monitoring of pairwise comparison matrices
S. Bozoki, J. Fulop, W. W. Koczkodaj
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…
A Monte Carlo Study of Pairwise Comparisons
M. W. Herman, W. W. Koczkodaj
Consistent approximations obtained by geometric means () and the principal eigenvector (), turned out to be close enough for 1,000,000 not-so-inconsistent pairwise comparis…
On the Convergence of the Pairwise Comparisons Inconsistency Reduction Process
Waldemar W. Koczkodaj, Jacek Szybowski
This study investigates a powerful model, targeted to subjective assessments, based on pairwise comparisons. It provides a proof that a distance-based inconsistency reduction trans…
The key properties of inconsistency indicators for a triad in pairwise comparison matrices
W. W. Koczkodaj, J. Szybowski
Processing information, acquired by subjective assessments, involves inconsistency analysis in most (if not all) applications of which some are of considerable importance at a nati…
How to reduce the number of rating scale items without predictability loss?
W. W. Koczkodaj, T. Kakiashvili, A. Szymańska +5
Rating scales are used to elicit data about qualitative entities (e.g., research collaboration). This study presents an innovative method for reducing the number of rating scale it…
Inconsistency indicator maps on groups for pairwise comparisons
W. W. Koczkodaj, J. Szybowski, E. Wajch
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…
Pairwise Comparisons Simplified
W. W. Koczkodaj, J. Szybowski
This study examines the notion of generators of a pairwise comparisons matrix. Such approach decreases the number of pairwise comparisons from to . An algorithm…
On Axiomatization of Inconsistency Indicators for Pairwise Comparisons
W. W. Koczkodaj, R. Szwarc
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 defi…