Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology (EUSFLAT-11)

Construction of a Choquet integral and the value functions without any commensurateness assumption in multi-criteria decision making

Authors
Christophe Labreuche
Corresponding Author
Christophe Labreuche
Available Online August 2011.
DOI
https://doi.org/10.2991/eusflat.2011.130How to use a DOI?
Keywords
Choquet integral, capacity, value functions, commensurateness.
Abstract
We consider a multi-criteria evaluation function U defined over a Cartesian product of attributes. We assume that U is written as the combination of an aggregation function and one value function over each attribute. The aggregation function is assumed to be a Choquet integral w.r.t. an unknown capacity. The problem we wish to address in this paper is the following one: if U is known, can we construct both the value functions and the capacity? The approaches that have been developed so far in the literature to answer this question in an analytical way assume some commensurateness hypothesis. We propose in this paper a method to construct the value functions and the capacity without any commensurateness assumption. Moreover, we show that the construction of the value functions is unique up to an affine transformation.
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Proceedings
Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
Part of series
Advances in Intelligent Systems Research
Publication Date
August 2011
ISBN
978-90-78677-00-0
ISSN
1951-6851
DOI
https://doi.org/10.2991/eusflat.2011.130How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Christophe Labreuche
PY  - 2011/08
DA  - 2011/08
TI  - Construction of a Choquet integral and the value functions without any commensurateness assumption in multi-criteria decision making
BT  - Proceedings of the 7th conference of the European Society for Fuzzy Logic and Technology
PB  - Atlantis Press
SP  - 90
EP  - 97
SN  - 1951-6851
UR  - https://doi.org/10.2991/eusflat.2011.130
DO  - https://doi.org/10.2991/eusflat.2011.130
ID  - Labreuche2011/08
ER  -