Abstract
The concept of universal integral has been recently proposed in order to generalize the Choquet, Shilkret and Sugeno integrals. We present two axiomatic foundations of the universal integral. The first axiomatization is expressed in terms of aggregation functions, while the second is expressed in terms of preference relations.
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
Debreu, G.: Representation of a preference ordering by a numerical function. In: Decision Processes, pp. 159–165 (1954)
Figueira, J., Greco, S., Ehrgott, M.: Multiple criteria decision analysis: state of the art surveys, vol. 78. Springer (2005)
Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation functions: means. Information Sciences 181(1), 1–22 (2011)
Klement, E., Mesiar, R., Pap, E.: A universal integral as common frame for Choquet and Sugeno integral. IEEE Transactions on Fuzzy Systems 18(1), 178–187 (2010)
Klement, E.P., Kolesárová, A., Mesiar, R., Stupnanová, A.: A generalization of universal integrals by means of level dependent capacities. Knowledge-Based Systems 38, 14–18 (2013), http://www.sciencedirect.com/science/article/pii/S0950705112002419 , doi:10.1016/j.knosys.2012.08.021
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Greco, S., Mesiar, R., Rindone, F. (2013). Axiomatic Foundations of the Universal Integral in Terms of Aggregation Functions and Preference Relations. In: Bustince, H., Fernandez, J., Mesiar, R., Calvo, T. (eds) Aggregation Functions in Theory and in Practise. Advances in Intelligent Systems and Computing, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39165-1_46
Download citation
DOI: https://doi.org/10.1007/978-3-642-39165-1_46
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39164-4
Online ISBN: 978-3-642-39165-1
eBook Packages: EngineeringEngineering (R0)