Abstract
Sugeno integrals can be viewed as multiple criteria aggregation functions which take into account a form of synergy between criteria. As such, Sugeno integrals constitute an important family of tools for modeling qualitative preferences defined on ordinal scales. The elicitation of Sugeno integrals starts from a set of data that associates a global evaluation assessment to situations described by multiple criteria values. A consistent set of data corresponds to a non-empty family of Sugeno integrals with which the data are compatible. This elicitation process presents some similarity with the revision process underlying the version space approach in concept learning, when new data are introduced. More precisely, the elicitation corresponds to a graded extension of version space learning, recently proposed in the framework of bipolar possibility theory. This paper establishes the relation between these two formal settings.
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
Dubois, D., Marichal, J.-L., Prade, H., Roubens, M., Sabbadin, R.: The use of the discrete Sugeno integral in decision making: A survey. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 9, 539–561 (2001)
Dubois, D., Prade, H., Smets, P.: Not impossible vs. guaranted possible in fusion and revision. In: Proc. of the 6th European Conference (ESCQARU 2001), Toulouse, France, September 19-21, pp. 522–531. Springer, Heidelberg (2001)
Greco, S., Matarazzo, B., Slowinski, R.: Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules. European Journal of Operational Research 158(2), 271–292 (2004)
Kandel, A., Byatt, W.J.: Fuzzy sets, fuzzy algebra, and fuzzy statistics. Proceedings of IEEE 66, 1619–1639 (1978)
Mitchell, T.: Generalization as search. Artificial intelligence 18, 203–226 (1982)
Prade, H., Rico, A., Serrurier, M., Raufaste, E.: Elicitating sugeno integrals: Methodology and a case study. In: Proc. of the 10th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty, ECSQARU 2009 (to appear, 2009)
Prade, H., Serrurier, M.: Bipolar version space learning. International Journal of Intelligent Systems, Bipolar Representations of Information and Preference (Part 2: reasoning and learning) 23(10), 1135–1152 (2008)
Rico, A., Labreuche, C., Grabisch, M., Chateauneuf, A.: Preference modeling on totally ordered sets by the Sugeno integral. Discrete Applied Mathematics 147 (2005)
Sugeno, M.: Theory of fuzzy integrals and its applications. PhD thesis, Tokyo Institute of technology (1974)
Sugeno, M.: Fuzzy measures and fuzzy integrals: A survey. In: Gupta, M.M., Saridis, G.N., Gaines, B.R. (eds.) Fuzzy Automa and Decision Processes, pp. 89–102. North-Holland, Amsterdam (1977)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Prade, H., Rico, A., Serrurier, M. (2009). Elicitation of Sugeno Integrals: A Version Space Learning Perspective. In: Rauch, J., Raś, Z.W., Berka, P., Elomaa, T. (eds) Foundations of Intelligent Systems. ISMIS 2009. Lecture Notes in Computer Science(), vol 5722. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04125-9_42
Download citation
DOI: https://doi.org/10.1007/978-3-642-04125-9_42
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-04124-2
Online ISBN: 978-3-642-04125-9
eBook Packages: Computer ScienceComputer Science (R0)