[en] We consider a Choquet capacity, that is a set function which describes the importance of every subset of criteria in a MCDA problem. The following question is approached: what is the generalized counterpart of the Shannon entropy (defined for a probabilistic measure) for such a capacity? The extension that is proposed depends on the scale type.
In the cardinal case, the entropy is defined in terms of the first derivatives of the non-additive measures.
In the ordinal case, it refers to the cardinality of the scale values that appear in the set of all capacities.
Both generalized entropies are symmetric functions of the capacities and their extreme values (max entropy and min entropy) are characterized.
An application to the determination of weights is given when interacting criteria are considered.
Disciplines :
Quantitative methods in economics & management Mathematics
Author, co-author :
MARICHAL, Jean-Luc ; University of Liège, Belgium > Institute of Mathematics
Roubens, Marc; University of Liège, Belgium > Institute of Mathematics
Language :
English
Title :
On the entropy of non-additive weights
Publication date :
July 2000
Number of pages :
1
Event name :
17th Eur. Conf. on Operational Research (EURO XVII)
