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Constructive Consistent Approximations in Pairwise Comparisons
 
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1
Institute of Information Technology, Warsaw University of Life Sciences - SGGW, ul. Nowoursynowska 159, 02-776 Warsaw, Poland
 
2
Institute of Mathematics and Cryptology, Cybernetics Faculty, Military University of Technology, S. Kaliskiego 2, 00-908 Warsaw, Poland
 
 
Corresponding author
Ryszard Kozera   

Institute of Information Technology, Warsaw University of Life Sciences - SGGW, ul. Nowoursynowska 159, 02-776 Warsaw, Poland
 
 
Adv. Sci. Technol. Res. J. 2022; 16(4):243-255
 
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ABSTRACT
In this paper we investigate groups which admit the existence of weighted consistent approximations for pairwise comparisons matrices. These approximations are defined by extending the classical matrix projection for R_{+} to abstract weighted projections on the non-linear sets of transitive group-valued matrices. It is of interest that all of them are represented by general explicit formulae dependent on an abstract logarithmic function. This general approach is applied to the groups Z^{∗}_{p} and F^{∗}_{2m} which are of fundamental importance in in cryptography. Finally, we use our unified mathematical model of pairwise comparisons for continuous one-parameter unitary groups, which play a fundamental role in physics.
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