Reference : On the entropy of non-additive weights
Scientific congresses, symposiums and conference proceedings : Unpublished conference
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
On the entropy of non-additive weights
Marichal, Jean-Luc mailto [University of Liège, Belgium > Institute of Mathematics]
Roubens, Marc [University of Liège, Belgium > Institute of Mathematics]
17th Eur. Conf. on Operational Research (EURO XVII)
from 16-07-2000 to 19-07-2000
Jakob Krarup (Programme Committee Chair)
[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.
University of Liège, Belgium
Researchers ; Professionals ; Students

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