Abstract
In this paper we first consider the problem of extending fuzzy (weak and strict) preference relations, represented by fuzzy preorders on a set to a fuzzy preferences on subsets, and we characterise different possibilities. Based on their properties, we then semantically define and axiomatize several two-tiered graded modal logics to reason about the corresponding different notions of fuzzy preferences.
This paper is our humble contribution to the tribute, in the occasion of his 65th birthday, to José Luis “Curro” Verdegay. Excellent researcher and better person, he has been one of the pioneers of fuzzy logic in Spain and founder and driving force of the research group on Decision Making and Optimization at the University of Granada. Our contribution is devoted to logic and fuzzy preferences, a topic that, although it is not central on the research of Curro, is ubiquitous in fuzzy decision making models and we hope it may be of his interest. Along many years, we have jointly participated in many events around the world with Curro and with our friends from Granada, we have learnt a lot from his research ideas and organizational competences, but more importantly, we have enjoyed his friendship and shared many unforgettable moments. Thanks for all Curro, and congratulations for this well-deserved homage!
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
This is the strict order companion defined and studied in [7].
References
van Benthem, J., Girard, P., Roy, O.: Everything else being equal: a modal logic for ceteris paribus preferences. J. Philos. Logic 38, 83–125 (2009)
Bodenhofer, U.: Orderings of fuzzy sets based on fuzzy orderings part I: the basic approach. Mathw. Soft Comput. 15(2), 201–218 (2008)
Bodenhofer, U.: Orderings of fuzzy sets based on fuzzy orderings part II: generalizations. Mathw. Soft Comput. 15(3), 219–249 (2008)
Bodenhofer, U., Demirci, M.: Strict fuzzy orderings with a given context of similarity. Int. J. Uncertain. Fuzziness Knowl. Based Syst. 16(2), 147–178 (2008)
Domshlak, C., Hüllermeier, E., Kaci, S., Prade, H.: Preferences in AI: an overview. Artif. Intell. 175, 1037–1052 (2011)
Fodor, J., Roubens, M.: Fuzzy Preference Modeling and Multicriteria Decision Support. Kluwer Academic Publishers (1994)
Díaz, S., De Baets, B., Montes, S.: Additive decomposition of fuzzy pre-orders. Fuzzy Sets Syst. 158(8), 830–842 (2007)
Díaz, S., De Baets, B., Montes, S.: General results on the decomposition of transitive fuzzy relations. Fuzzy Optim. Decis. Making 9(1), 1–29 (2010)
Díaz, S., Montes, S., De Baets, B.: Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum. Kybernetika 40(1), 71–88 (2004)
Díaz, S., De Baets, B., Montes, S.: On the compositional characterization of complete fuzzy pre-orders. Fuzzy Sets Syst. 159(17), 2221–2239 (2008)
Díaz, S., García-Lapresta, J.L., Montes, S.: Consistent models of transitivity for reciprocal preferences on a finite ordinal scale. Inf. Sci. 178(13), 2832–2848 (2008)
Esteva, F., Godo, L., Rodriguez, R.O., Vetterlein, T.: Logics for approximate and strong entailments. Fuzzy Sets Syst. 197, 59–70 (2012)
Esteva, F., Godo, L., Vidal, A.: On a graded modal logic approach to reason with fuzzy preferences. In: Proceedings of CCIA 2017 (to appear)
Fono, L.A., Andjiga, N.G.: Fuzzy strict preference and social choice. Fuzzy Sets Syst. 155, 372–389 (2005)
Halpern, J.Y.: Defining relative likelihood in partially-ordered preference structures. J. Artif. Intell. Res. 7, 1–24 (1997)
Liu, F.: Von Wright’s “The Logic of Preference” revisited. Synthese 175(1), 69–88 (2010)
Hansson, S.O., Grüne-Yanoff, T.: Preferences. In: Zalta, E.N. (ed.) The Stanford Encyclopedia of Philosophy (Winter 2012 Edition). https://plato.stanford.edu/archives/win2012/entries/preferences/ (2012)
Kaci, S.: Working with Preferences: Less is More. Springer (2011)
Mayor, G., Torrens, J.: On a class of operators for expert systems. Int. J. Intell. Syst. 8, 771–778 (1993)
Sören, H.: On the logic of better. Library of Theoria, no. 2, Uppsala (1957)
Vidal, A., Esteva, F., Godo, L.: On finite-valued bimodal logics with an application to reasoning about preferences In: Proceedings of EUSFLAT 2017 (to appear)
von Wright, G.H.: The Logic of Preference. Edinburgh University Press (1963)
von Wright, G.H.: The logic of preference reconsidered. Theory Decis. 3(2), 140–169 (1972)
Acknowledgements
Esteva and Godo acknowledges partial support by the Spanish FEDER/MINECO project TIN2015-71799-C2-1-P. Vidal acknowledges partial support by the joint project of the Austrian Science Fund (FWF) I1897-N25 and the Czech Science Foundation (GACR) 15-34650L, and by the institutional grant RVO:67985807.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Esteva, F., Godo, L., Vidal, A. (2018). A Modal Account of Preference in a Fuzzy Setting. In: Pelta, D., Cruz Corona, C. (eds) Soft Computing Based Optimization and Decision Models. Studies in Fuzziness and Soft Computing, vol 360. Springer, Cham. https://doi.org/10.1007/978-3-319-64286-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-64286-4_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-64285-7
Online ISBN: 978-3-319-64286-4
eBook Packages: EngineeringEngineering (R0)