On Strict Ranking by Pairwise Comparisons

Jean-Pierre Magnot

doi:10.2478/amsil-2026-0005

.blurhash-client-img { display: none !important; }

On Strict Ranking by Pairwise Comparisons

Annales Mathematicae Silesianae

Volume 40 (2026): Issue 2 (September 2026)

By: Jean-Pierre Magnot

Open Access

|Apr 2026

Abstract

This paper addresses the problem of obtaining a strict ranking (i.e., a ranking without equally ranked items) of n items based on a pairwise comparisons matrix. The basic structures are described and a heuristic approach based on a condition, the ℛ-condition is proposed. The limitations of this ranking procedure are analyzed.

References

D. Bartl and J. Ramík, A new algorithm for computing priority vector of pairwise comparisons matrix with fuzzy elements, Inform. Sci. 615 (2022), 103–117.
Search in Google Scholar Back to article
S. Bozóki and T. Rapcsák, On Saaty’s and Koczkodaj’s inconsistencies of pairwise comparison matrices, J. Global Optim. 42 (2008), no. 2, 157–175.
Search in Google Scholar Back to article
E.U. Choo and W.C. Wedley, A common framework for deriving preference values from pairwise comparison matrices, Comput. Oper. Res. 31 (2004), no. 6, 893–908.
Search in Google Scholar Back to article
J.M. Colomer, Ramon Llull: from ‘Ars electionis’ to social choice theory, Soc. Choice Welf. 40 (2013), no. 2, 317–328.
Search in Google Scholar Back to article
A. Darko, A.P.C. Chan, E.E. Ameyaw, E.K. Owusu, E. Pärn, and D.J. Edwards, Review of application of analytic hierarchy process (AHP) in construction, Int. J. Constr. Manag. 19 (2019), no. 5, 436–452.
Search in Google Scholar Back to article
A. Ellingsen, D. Lundholm, and J.-P. Magnot, “The six blind men and the elephant”: an interdisciplinary selection of measurement features, in: P. Kielanowski et al. (eds.), Geometric Methods in Physics XL,Workshop, Białowieża, Poland, 2023, Trends Math., Birkhäuser/Springer, Cham, 2024, pp. 275–307.
Search in Google Scholar Back to article
E.R. Fadell and S.Y. Husseini, Geometry and Topology of Configuration Spaces, Springer Monogr. Math., Springer-Verlag, Berlin, 2001.
Search in Google Scholar Back to article
J. Fülöp, A method for approximating pairwise comparison matrices by consistent matrices, J. Global Optim. 42 (2008), no. 3, 423–442.
Search in Google Scholar Back to article
M. Gromov, Metric Structures for Riemannian and Non-Riemannian Spaces, 2nd ed., Mod. Birkhäuser Class., Birkhäuser Boston, Inc., Boston, MA, 2007.
Search in Google Scholar Back to article
K. Ilinski, Gauge geometry of financial markets, J. Phys. A 33 (2000), no. 1, L5–L14.
Search in Google Scholar Back to article
W.W. Koczkodaj, A new definition of consistency of pairwise comparisons, Math. Comput. Modelling 18 (1993), no. 7, 79–84.
Search in Google Scholar Back to article
W.W. Koczkodaj, J.-P. Magnot, J. Mazurek, J.F. Peters, H. Rakhshani, M. Soltys, D. Strzałka, J. Szybowski, and A. Tozzi, On normalization of inconsistency indicators in pairwise comparisons, Internat. J. Approx. Reason. 86 (2017), 73–79.
Search in Google Scholar Back to article
W.W. Koczkodaj and M. Orlowski, An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix, Comput. Math. Appl. 34 (1997), no. 10, 41–47.
Search in Google Scholar Back to article
W.W. Koczkodaj, R. Smarzewski, and J. Szybowski, On orthogonal projections on the space of consistent pairwise comparisons matrices, Fund. Inform. 172 (2020), no. 4, 379–397.
Search in Google Scholar Back to article
K. Kułakowski, K. Grobler-Dębska, and J. Wąs, Heuristic rating estimation: geometric approach, J. Global Optim. 62 (2015), no. 3, 529–543.
Search in Google Scholar Back to article
K. Kułakowski, J. Mazurek, and M. Strada, On the similarity between ranking vectors in the pairwise comparison method, J. Oper. Res. Soc. 73 (2022), no. 9, 2080–2089.
Search in Google Scholar Back to article
M. Lahby, L. Cherkaoui, and A. Adib, Network selection decision based on handover history in heterogeneous wireless networks, Int. J. Comput. Sci. Telecom. 3 (2012), no 2, 21–25.
Search in Google Scholar Back to article
J.-P. Magnot, From configurations to branched configurations and beyond, Res. Rep. Math. 1 (2017), no. 1, Art. ID 1000105, 6 pp.
Search in Google Scholar Back to article
J.-P. Magnot, A mathematical bridge between discretized gauge theories in quantum physics and approximate reasoning in pairwise comparisons, Adv. Math. Phys. 2018, Art. ID 7496762, 5 pp.
Search in Google Scholar Back to article
J.-P. Magnot, On mathematical structures on pairwise comparisons matrices with coefficients in an abstract group arising from quantum gravity, Heliyon 5 (2019), no. 6, Art. ID e01821, 12 pp.
Search in Google Scholar Back to article
J.-P. Magnot, On random pairwise comparisons matrices and their geometry, J. Appl. Anal. 30 (2024), no. 2, 345–361.
Search in Google Scholar Back to article
J.-P. Magnot, J. Mazurek, and V. Čerňanová, A gradient method for inconsistency reduction of pairwise comparisons matrices, Internat. J. Approx. Reason. 152 (2023), 46–58.
Search in Google Scholar Back to article
J. Mazurek, C. Pérez Rico, C. Fernández, J.-P. Magnot, and T. Magnot, The 5-item Likert scale and percentage scale correspondence with implications for the use of models with (fuzzy) linguistic variables, Rev. Métodos Cuantitativos Econ. Empresa 31 (2001), 3–16.
Search in Google Scholar Back to article
T.L. Saaty, A scaling method for priorities in hierarchical structures, J. Mathematical Psychology 15 (1977), no. 3, 234–281.
Search in Google Scholar Back to article
S.E. Vázquez and S. Farinelli, Gauge invariance, geometry and arbitrage, J. Invest. Strateg. 1 (2012), no. 2, 23–66.
Search in Google Scholar Back to article

Articles in this issue

DOI: https://doi.org/10.2478/amsil-2026-0005 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

Journal RSS Feed

Language: English

Page range: 242 - 257

Submitted on: Mar 31, 2025

Accepted on: Mar 2, 2026

Published on: Apr 4, 2026

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Keywords:

90B50,

81T13,

91B06

Related subjects:

Mathematics,

General mathematics

© 2026 Jean-Pierre Magnot, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 40 (2026): Issue 2 (September 2026)