RT Journal Article
T1 Dominance of capacities by k-additive belief functions
A1 Miranda Menéndez, Pedro
A1 Grabisch, Michel
A1 Gil Álvarez, Pedro
AB In this paper we deal with the set of k-additive belief functions dominating a given capacity. We follow the line introduced by Chateauneuf and Jaffray for dominating probabilities and continued by Grabisch for general k-additive measures. First, we show that the conditions for the general k-additive case lead to a very wide class of functions and this makes that the properties obtained for probabilities are no longer valid. On the other hand, we show that these conditions cannot be improved. We solve this situation by imposing additional constraints on the dominating functions. Then, we consider the more restrictive case of k-additive belief functions. In this case, a similar result with stronger conditions is proved. Although better, this result is not completely satisfactory and, as before, the conditions cannot be strengthened. However, when the initial capacity is a belief function, we find a subfamily of the set of dominating k-additive belief functions from which it is possible to derive any other dominant k-additive belief function, and such that the conditions are even more restrictive, obtaining the natural extension of the result for probabilities. Finally, we apply these results in the fields of Social Welfare Theory and Decision Under Risk.
PB Elsevier Science
SN 0377-2217
YR 2006
FD 2006
LK https://hdl.handle.net/20.500.14352/50186
UL https://hdl.handle.net/20.500.14352/50186
LA eng
NO Miranda Menéndez, P., Grabisch, M. & Gil Álvarez, P. et al. «Dominance of Capacities by K-Additive Belief Functions». European Journal of Operational Research, vol. 175, n.o 2, diciembre de 2006, pp. 912-30. DOI.org (Crossref), https://doi.org/10.1016/j.ejor.2005.06.018
NO Fondo Europeo de Desarrollo Regional/Madrid Ciencia y Tecnología
DS Docta Complutense
RD 21 abr 2025