Advanced Search
MyIDEAS: Login

The Symmetric Sugeno Integral

Contents:

Author Info

  • Michel Grabisch

    ()
    (LIP6 - Laboratoire d'Informatique de Paris 6 - CNRS : UMR7606 - Université Pierre et Marie Curie - Paris VI)

Abstract

We 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 Info

If 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.
File URL: http://hal.archives-ouvertes.fr/docs/00/27/20/84/PDF/fss01.pdf
Download Restriction: no

Bibliographic Info

Paper provided by HAL in its series Post-Print with number hal-00272084.

as in new window
Length:
Date of creation: 2003
Date of revision:
Publication status: Published, Fuzzy Sets and Systems, 2003, 139, 473-490
Handle: RePEc:hal:journl:hal-00272084

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/

Related research

Keywords:

References

References listed on IDEAS
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.:
as in new window
  1. 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.
  2. 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.
  3. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  4. Michel Grabisch & Christophe Labreuche, 2002. "The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making," Post-Print halshs-00273184, HAL.
  5. Michel Grabisch, 2004. "The Möbius transform on symmetric ordered structures and its application to capacities on finite sets," Post-Print hal-00188158, HAL.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
  2. Michel Grabisch & Bernard De Baets & Janos Fodor, 2004. "The quest for rings on bipolar scales," Post-Print hal-00271217, HAL.
  3. Dieter Denneberg & Michel Grabisch, 2004. "Measure and integral with purely ordinal scales," Post-Print hal-00272078, HAL.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:hal:journl:hal-00272084. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.