Atlantis Press Paper Details: Construction of a Choquet integral and the value functions without any commensurateness assumption in multi-criteria decision making

title:

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

publication:

EUSFLAT

part of series:

Advances in Intelligent Systems Research

pages:

90 - 97

DOI:

To be assigned soon (how to use a DOI)

author(s):

Christophe Labreuche

publication date:

July 2011

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.

© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.

full text:

eusflatlfa2011_S2_1.pdf (1201 K)

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title:		Construction of a Choquet integral and the value functions without any commensurateness assumption in multi-criteria decision making
publication:		EUSFLAT
part of series:		Advances in Intelligent Systems Research
pages:		90 - 97
DOI:		To be assigned soon (how to use a DOI)
author(s):		Christophe Labreuche
publication date:		July 2011
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.
copyright:		© Atlantis Press. This article is distributed under the terms of the Creative Commons Attribution License, which permits non-commercial use, distribution and reproduction in any medium, provided the original work is properly cited.
full text:		eusflatlfa2011_S2_1.pdf (1201 K)