Paper Info
Title
An axiomatization of the Choquet integral in the context of multiple criteria decision making without any commensurability assumption.
Abstract
An axiomatization of the Choquet integral is proposed in the context of multiple criteria decision making without any commensurability assumption. The most essential axiom—named Commensurability Through Interaction—states that the importance of an attribute i takes only one or two values when a second attribute k varies. When the importance takes two values, the point of discontinuity is exactly the value on the attribute k that is commensurate to the fixed value on attribute i. If the weight of criterion i does not depend on criterion k, for any value of the other criteria than i and k, then criteria i and k are independent. Applying this construction to any pair i, k of criteria, one obtains a partition of the set of criteria. In each block, the criteria interact one with another, and it is thus possible to construct vectors of values on the attributes that are commensurate. There is complete independence between the criteria of any two blocks in this partition. Hence one cannot ensure commensurability between two blocks in the partition. But this is not a problem since the Choquet integral is additive between subsets of criteria that are independent.
Year
DOI
Venue
2018
10.1007/s10479-018-3046-1
Annals OR
Keywords
Field
DocType
Choquet integral, Capacity, Commensurability, Interaction between criteria
Discrete mathematics,Multiple criteria,Discontinuity (linguistics),Choquet integral,Partition (number theory),Mathematics,Commensurability (philosophy of science)
Journal
Volume
Issue
ISSN
271
2
0254-5330
Citations 
PageRank 
References 
0
0.34
10
Authors
1
Name
Order
Citations
PageRank
Christophe Labreuche170965.78