The Symmetric Sugeno Integral
AbstractWe propose an extension of the Sugeno integral for negative numbers, in the spirit of the symmetric extension of Choquet integral, also called \Sipos\ integral. Our framework is purely ordinal, since the Sugeno integral has its interest when the underlying structure is ordinal. We begin by defining negative numbers on a linearly ordered set, and we endow this new structure with a suitable algebra, very close to the ring of real numbers. In a second step, we introduce the Möbius transform on this new structure. Lastly, we define the symmetric Sugeno integral, and show its similarity with the symmetric Choquet integral.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00272084.
Date of creation: 2003
Date of revision:
Publication status: Published, Fuzzy Sets and Systems, 2003, 139, 473-490
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00272084/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dubois, Didier & Prade, Henri & Sabbadin, Regis, 2001. "Decision-theoretic foundations of qualitative possibility theory," European Journal of Operational Research, Elsevier, vol. 128(3), pages 459-478, February.
- David Schmeidler, 1989.
"Subjective Probability and Expected Utility without Additivity,"
Levine's Working Paper Archive
7662, David K. Levine.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
- Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
- Michel Grabisch & Christophe Labreuche, 2002.
"The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making,"
- Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January.
- Michel Grabisch, 2004. "The Möbius transform on symmetric ordered structures and its application to capacities on finite sets," Post-Print hal-00188158, HAL.
- Michel Grabisch & Bernard De Baets & Janos Fodor, 2004. "The quest for rings on bipolar scales," Post-Print hal-00271217, HAL.
- Dieter Denneberg & Michel Grabisch, 2004. "Measure and integral with purely ordinal scales," Post-Print hal-00272078, HAL.
- Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.