Abstract
When a non-numerical ranking is created using Pairwise Comparisons paradigm, its first estimation is a binary relation which may not even be a partial order. In the paper four different partial order approximations of an arbirary binary relation are introduced and discussed.
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References
Arrow, K.J.: Social Choice and Individual Values. J. Wiley, Chichester (1951)
Dyer, J.S.: Remarks on the Analytic Hierarchy Process. Management Sci. 36, 244–258 (1990)
Fishburn, P.C.: Interval Orders and Interval Graphs. J. Wiley, New York (1985)
French, S.: Decision Theory. Ellis Horwood, New York (1986)
Janicki, R.: Pairwise Comparisons, Incomparability and Partial Orders. In: Proc. of ICEIS 2007 (Int. Conf. on Enterprise Information Systems), Funchal, Portugal, vol. 2, pp. 297–302 (2007)
Janicki, R.: Ranking with Partial Orders and Pairwise Comparisons. In: Wang, G., Li, T., Grzymała-Busse, J.W., Miao, D., Skowron, A., Yao, Y. (eds.) RSKT 2008. LNCS (LNAI), vol. 5009, pp. 442–451. Springer, Heidelberg (2008)
Janicki, R., Koczkodaj, W.W.: Weak Order Approach to Group Ranking. Computers Math. Applic. 32(2), 51–59 (1996)
Pawlak, Z.: Rough Sets. Kluwer, Dordrecht (1991)
Rosen, K.H.: Discrete Mathematics and Its Applications. McGraw-Hill, New York (1999)
Saaty, T.L.: A Scaling Methods for Priorities in Hierarchical Structure. Journal of Mathematical Psychology 15, 234–281 (1977)
Schröder, E.: Algebra der Logik, 2nd edn., Teuber, Leipzig, vol. 1895. Chelsea (1966)
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Janicki, R. (2008). Some Remarks on Approximations of Arbitrary Binary Relations by Partial Orders. In: Chan, CC., Grzymala-Busse, J.W., Ziarko, W.P. (eds) Rough Sets and Current Trends in Computing. RSCTC 2008. Lecture Notes in Computer Science(), vol 5306. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88425-5_9
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DOI: https://doi.org/10.1007/978-3-540-88425-5_9
Publisher Name: Springer, Berlin, Heidelberg
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