Abstract
CPTS-integrals (Cumulative Prospect Theory Sugeno integral) are agregation functions that return a global rating when the evaluations are given on a bipolar scale. This paper presents the problem of the elicitation of CPTS-integrals agreeing with a data set composed of pairs concerning some criteria and a global evaluation. Moreover the set of fuzzy measures which are solutions of this inverse problem is identified. When the elicitation of one CPTS-integral is not possible, a set of family of CPTS-integrals is proposed.
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
Preview
Unable to display preview. Download preview PDF.
References
Pap, E., Mihailović, B.P.: A representation of a comonotone-\(\textcircled{V}\)-additive and monotone functional by two Sugeno integrals. Fuzzy Sets and Systems 155, 77–88 (2005)
Rico, A., Grabisch, M., Labreuche, C., Chateauneuf, A.: Preference modelling on totally ordered sets by the Sugeno integral. Discrete Applied Mathematics 147, 113–124 (2005)
Prade, H., Rico, A., Serrurier, M., Raufaste, E.: Elicitating Sugeno Integrals: Methodology and a Case Study. In: Sossai, C., Chemello, G. (eds.) ECSQARU 2009. LNCS, vol. 5590, pp. 712–723. Springer, Heidelberg (2009)
Sugeno, M.: Ordinal Preference Models Based on S-Integrals and Their Verification. In: Li, S., Wang, X., Okazaki, Y., Kawabe, J., Murofushi, T., Guan, L., et al. (eds.) Nonlinear Mathematics for Uncertainty and its Applications. AISC, vol. 100, pp. 1–18. Springer, Heidelberg (2011)
Sugeno, M.: Theory of fuzzy integrals and its applications, Ph.D. Thesis, Tokyo Institute of Technology (1974)
Grabisch, M., Labreuche, C.: A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid. Annals OR 175(1), 247–286 (2010)
Dubois, D., Prade, H.: Bipolar Representations in Reasoning, Knowledge Extraction and Decision Processes. In: Greco, S., Hata, Y., Hirano, S., Inuiguchi, M., Miyamoto, S., Nguyen, H.S., Słowiński, R. (eds.) RSCTC 2006. LNCS (LNAI), vol. 4259, pp. 15–26. Springer, Heidelberg (2006)
Grabisch, M.: The symmetric Sugeno integral. Fuzzy Sets and Systems 139, 473–490 (2003)
Marichal, J.-L.: Weighted lattice polynomials. Discrete Mathematics 309, 814–820 (2009)
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
Rico, A., Sugeno, M. (2012). Eliciting CPTS-Integrals on Bipolar Scale. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances in Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31724-8_28
Download citation
DOI: https://doi.org/10.1007/978-3-642-31724-8_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31723-1
Online ISBN: 978-3-642-31724-8
eBook Packages: Computer ScienceComputer Science (R0)