RT Book, Section
T1 Finding the set of k-additive dominating measures viewed as a flow problem
A1 Miranda Menéndez, Pedro
A1 Grabisch, Michel
A2 Carvalho, Joao Paulo
A2 Lesot, Marie-Jeanne
A2 Kaymak, Uzay
A2 Vieira, Susana
A2 Bouchon-Meunier, Bernadette
A2 Yager, Ronald R.
AB n this paper we deal with the problem of obtaining the set of k-additive measures dominating a fuzzy measure. This problem extends the problem of deriving the set of probabilities dominating a fuzzy measure, an important problem appearing in Decision Making and Game Theory. The solution proposed in the paper follows the line developed by Chateauneuf and Jaffray for dominating probabilities and continued by Miranda et al. for dominating k-additive belief functions. Here, we address the general case transforming the problem into a similar one such that the involved set functions have non-negative Möbius transform; this simplifies the problem and allows a result similar to the one developed for belief functions. Although the set obtained is very large, we show that the conditions cannot be sharpened. On the other hand, we also show that it is possible to define a more restrictive subset, providing a more natural extension of the result for probabilities, such that it is possible to derive any k-additive dominating measure from it.
PB Springer Verlag
SN 978-331940595-7
YR 2016
FD 2016
LK https://hdl.handle.net/20.500.14352/24891
UL https://hdl.handle.net/20.500.14352/24891
LA eng
NO 16th International Conference, IPMU 2016 Eindhoven, The Netherlands, June 20–24, 2016 Proceedings, Part I
NO Ministerio de Economía y Competitividad (MINECO)
DS Docta Complutense
RD 8 may 2024