Warianty tytułu
Języki publikacji
Abstrakty
In this study, the orthogonalization process for different inner products is applied to pairwise comparisons. Properties of consistent approximations of a given inconsistent pairwise comparisons matrix are examined. A method of a derivation of a priority vector induced by a pairwise comparison matrix for a given inner product has been introduced. The mathematical elegance of orthogonalization and its universal use in most applied sciences has been the motivating factor for this study. However, the finding of this study that approximations depend on the inner product assumed, is of considerable importance.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
379--397
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
- Computer Science, Laurentian University, Sudbury, Ontario P3E 2C6, Canada, wkoczkodaj@cs.laurentian.ca
autor
- Institute of Mathematics and Cryptology, Faculty of Cybernetics, Military University of Technology, ul. Kaliskiego 2, 00-908 Warsaw, Poland, ryszard.smarzewski@gmail.com
autor
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Krakow, Poland, szybowsk@agh.edu.pl
Bibliografia
- [1] Balazs P, Ozsva Z, Tasi TS, Nyul LG. A Measure of Directional Convexity Inspired by Binary Tomography. Fundamenta Informaticae, 2015. 141(2-3): 151-167. doi:10.3233/FI-2015-1269.
- [2] Barcucci E, Brocchi S. Solving Multicolor Discrete Tomography Problems by Using Prior Knowledge. Fundamenta Informaticae, 2013. 125(3-4): 313-328. doi:10.3233/FI-2013-866.
- [3] Goupy A, Pagani SMC. Probabilistic Reconstruction of hv-convex Polyominoes from Noisy Projection Data. Fundamenta Informaticae, 2014. 135(1-2): 117-134.
- [4] Wichert A, Moreira C., On Projection Based Operators in l(p) Space for Exact Similarity Search. Fundamenta Informaticae, 2015. 136(4): 461-474. doi:10.3233/FI-2015-1166.
- [5] Llull R. Artifitium electionis personarum. Available at The Augsburg Web Edition of Llull’s Electoral Writings, https://www.math.uni-augsburg.de/htdocs/emeriti/pukelsheim/llull/.
- [6] Koczkodaj WW, Mikhailov M, Redlarski G, Soltys M, Szybowski J, Tamazian G, Wajch E, Yuen KEF. Important facts and observations about pairwise comparisons. Fundamenta Informaticae, 2016. 144(3-4): 291-307. doi:10.3233/FI-2016-1336.
- [7] Koczkodaj WW, Orlowski M. Computing a consistent approximation to a generalized pairwise comparisons matrix. Computers & Mathematics with Applications, 1999. 37(3): 79-85. URL https://doi.org/10.1016/S0898-1221(99)00048-6.
- [8] Crawford G, Williams C. A note on the analysis of subjective judgement matrices. Journal of Mathematical Psychology, 1985, 29:387-405. URL https://doi.org/10.1016/0022-2496(85)90002-1.
- [9] Koczkodaj WW, Szybowski J. Pairwise comparisons simplified. Applied Mathematics and Computation, 2015. 253:387-394. URL https://doi.org/10.1016/j.amc.2014.12.069.
- [10] Gerard HB, Shapiro HN. Determining the Degree of Inconsistency in a Set of Paired Comparisons. Psychometrika, 1958. 23(1): 33-46.
- [11] Hill RJ. A note on inconsistency in paired comparison judgments. American Sociological Review, 1953. 18(5): 564-566.
- [12] Kendall MG, Babington-Smith B. On the method of paired comparisons. Biometrika, 1940. 31(3-4): 324-345.
- [13] Slater P. Inconsistencies in a schedule of paired comparisons. Biometrika, 1961. 48(3-4):303-310.
- [14] Choo EU, Wedley WC, Wijnmalen DJD. Mathematical Support for the Geometric Mean when Deriving a Consistent Matrix from a Pairwise Ratio Matrix. Fundamenta Informaticae, 2016. 144(3-4): 263-278. doi:10.3233/FI-2016-1334.
- [15] Koczkodaj WW, Szybowski J. The Limit of Inconsistency Reduction in Pairwise Comparisons. International Journal of Applied Mathematics and Computer Science, 2016. 26(3):721-729. URL https://doi.org/10.1515/amcs-2016-0050Openaccess.
- [16] Koczkodaj WW, Kosiek M, Szybowski J, Xu D. Fast Convergence of Distance-based Inconsistency in Pairwise Comparisons. Fundamenta Informaticae, 2015. 137(3):355-367. doi:10.3233/FI-2015-1184.
- [17] Holsztynski, W., Koczkodaj WW. Convergence of Inconsistency Algorithms for the Pairwise Comparisons. Information Processing Letters, 1996. 59: 197-202. URL https://doi.org/10.1016/0020-0190(96)00113-5.
- [18] Koczkodaj WW, Szarek, SJ. On distance-based inconsistency reduction algorithms for pairwise comparisons. Logic Journal of the IGPL, 2010. 18(6): 859-869. doi:10.1093/jigpal/jzp062.
- [19] Koczkodaj WW, Urban R. Axiomatization of inconsistency indicators for pairwise comparisons. International Journal Journal of Approximate Reasoning, 2018. 94:18-29. URL https://doi.org/10.1016/j.ijar.2017.12.001.
- [20] Koczkodaj WW, Orlowski M., An orthogonal basis for computing a consistent approximation to a pairwise comparisons matrix. Computers & Mathematics with Applications, 1997. 34(10):41-47. URL https://doi.org/10.1016/S0898-1221(97)00205-8.
- [21] Martinez-Avendaño RA, Rios-Cangas JI. Inner products on the space of complex square matrices. Linear Algebra and its Applications, 2013. 439(11):3620-3637. URL https://doi.org/10.1016/j.laa.2013.09.030.
- [22] Lang S. Algebra. Revised third edition. Graduate Texts in Mathematics. 211 Springer-Verlag, New York, 2002. ISBN: 978-0-387-95385-4, 978-1-4612-6551-1.
- [23] Rutka P, Smarzewski R. Difference inequalities and barycentric identities for classical discrete iterated weights. Mathematics of Computations, 2018. 318:1791-1804. URL https://doi.org/10.1090/mcom/3396.
Uwagi
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu
"Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja
sportu (2020).
"Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja
sportu (2020).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.baztech-31e1398e-c96a-48f6-8c52-b6e9ca965e6f