Abstract
Classical complete preorders can be characterized in several ways. However, when we work with complete fuzzy preorders this equivalences do not hold in general. In previous works we have proven some connections among them when using the minimum and the Łukasiewicz t-norms. In this contribution we generalize the study and we work with two important families (nilpotent and strict t-norms) when defining the fuzzy counterparts of the characterizations of a crisp complete preorder.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
De Baets, B., Fodor, J.: Generator triplets of additive fuzzy preference structures. In: Proc. of 6th. Internat. Workshop on Relational Methods in Computer Sicence, Tilburg, The Netherlands (2001)
De Baets, B., Van De Walle, B., Kerre, E.: Fuzzy preference structures without incomparability. Fuzzy Sets and Systems 76, 333–348 (1995)
Dasgupta, M., Deb, R.: Factoring fuzzy transitivity. Fuzzy Sets and Systems 118, 489–502 (2001)
Díaz, S., De Baets, B., Montes, S.: On the transitivity of indifference in the framework of additive fuzzy preference structures. In: De Baets, B., Kaynak, O., Bilgiç, T. (eds.) IFSA 2003. LNCS, vol. 2715, pp. 87–94. Springer, Heidelberg (2003)
Díaz, S., De Baets, B., Montes, S.: On some characterizations of complete fuzzy preorders. In: Proceedings of the fourth conference of the EUSFLAT, Barcelona, Spain, pp. 1039–1044 (2005)
Díaz, S., De Baets, B., Montes, S.: General results on the decomposition of transitive fuzzy relations. Fuzzy Decision and Decision Making 9, 1–29 (2010)
Díaz, S., Martinetti, D., Montes, I., Montes, S.: Connection among some characterizations of complete fuzzy preorders. In: Proceedings of the ninth conference of the ISDA, Pisa, Italy, pp. 839–844 (2009)
Díaz, S., Montes, S., De Baets, B.: Transitivity bounds in additive fuzzy preference structures. IEEE Transactions on Fuzzy Systems 15(2), 275–286 (2007)
Fodor, J., Roubens, M.: Fuzzy Preference Modelling and Multicriteria Decision Support. Kluwer Academic Publishers, Dordrecht (1994)
García-Lapresta, J.L., Rodríguez-Palmero, C.: Some algebraic characterizations of preference structures. Journal of Interdisciplinary Mathematics 7, 233–254 (2004)
Klement, E.P., Mesiar, R., Pap, E.: Triangular norms. Kluwer Academic Publishers, Dordrecht (2000)
Pirlot, M., Vincke, P.: Semiorders: Properties, Representations, Applications. Kluwer Academic Publishers, Dordrecht (1997)
Van de Walle, B., De Baets, B., Kerre, E.: Characterizable fuzzy preference structures. Ann. Oper. Res. 80, 105–136 (1998)
Wang, X., Xue, Y.: Notes on transitivity, negative transitivity, semitransitivity and Ferrers property. Journal of Fuzzy Mathematics 12, 323–330 (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Montes, I., Martinetti, D., Díaz, S., Montes, S. (2010). Characterization of Complete Fuzzy Preorders Defined by Archimedean t-Norms. In: Hüllermeier, E., Kruse, R., Hoffmann, F. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. Theory and Methods. IPMU 2010. Communications in Computer and Information Science, vol 80. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14055-6_17
Download citation
DOI: https://doi.org/10.1007/978-3-642-14055-6_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-14054-9
Online ISBN: 978-3-642-14055-6
eBook Packages: Computer ScienceComputer Science (R0)