Abstract
This paper presents several variants of Sugeno integral, and in particular the idea of (qualitative) desintegrals, a dual of integrals. When evaluating an item, desintegrals are maximal if no defects at all are present, while integrals are maximal if all advantages are sufficiently present. This idea leads to a bipolar representation of preferences, by means of a pair made of an integral and a desintegral, whose possibilistic logic counterparts are outlined (in the case where criteria are binary).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Benferhat, S., Dubois, D., Kaci, S., Prade, H.: Modeling positive and negative information in possibility theory. Int. J. of Intellig. Syst. 23(10), 1094–1118 (2008)
Benferhat, S., Kaci, S.: Logical representation and fusion of prioritized information based on guaranteed possibility measures: Application to the distance-based merging of classical bases. Artificial Intelligence 148, 291–333 (2003)
de Cooman, G., de Baets, B.: Implicator and coimplicator integrals. In: Proc. 6th Inter. Conf. on Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU 1996), Granada, July 1-5, vol. III, pp. 1433–1438 (1996)
Domshlak, C., Hüllermeier, E., Kaci, S., Prade, H.: Preferences in AI: An overview. Artif. Intell. 175(7-8), 1037–1052 (2011)
Dubois, D., Fargier, H., Bonnefon, J.F.: On the comparison of decisions having positive and negative features. J. of Artif. Intellig. Res. 32, 385–417 (2008)
Dubois, D., Le Berre, D., Prade, H., Sabbadin, R.: Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms. Fund. Inform. 37, 1–30 (1999)
Dubois, D., Prade, H.: Possibilistic logic: a retrospective and prospective view. Fuzzy Sets and Systems 144, 3–23 (2004)
Dubois, D., Prade, H., Rico, A.: A Possibilistic Logic View of Sugeno Integrals. In: Melo-Pinto, P., Couto, P., Serôdio, C., Fodor, J., De Baets, B. (eds.) Eurofuse 2011. AISC, vol. 107, pp. 19–30. Springer, Heidelberg (2011)
Dubois, D., Prade, H., Rico, A.: Qualitative Integrals and Desintegrals: How to Handle Positive and Negative Scales in Evaluation. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds.) IPMU 2012, Part III. CCIS, vol. 299, pp. 306–316. Springer, Heidelberg (2012)
Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals of Oper. Res. 175, 247–286 (2010)
Hadjali, A., Kaci, S., Prade, H.: Database preference queries - A possibilistic logic approach with symbolic priorities. Ann. Math. in AI (2012)
Marichal, J.-L.: Aggregation Operations for Multicriteria Decision Aid. Ph.D.Thesis, University of Liège, Belgium (1998)
Prade, H., Rico, A.: Describing acceptable objects by means of Sugeno integrals. In: Proc. 2nd Inter. IEEE Conf. on Soft Computing and Pattern Recognition (SoCPaR 2010), Cergy-Pontoise, pp. 6–11 (December 2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dubois, D., Prade, H., Rico, A. (2012). Qualitative Integrals and Desintegrals – Towards a Logical View. In: Torra, V., Narukawa, Y., López, B., Villaret, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2012. Lecture Notes in Computer Science(), vol 7647. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34620-0_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-34620-0_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34619-4
Online ISBN: 978-3-642-34620-0
eBook Packages: Computer ScienceComputer Science (R0)