2026-06-28T10:38:36Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/501872024-09-16T14:26:05Zcom_20.500.14352_14col_20.500.14352_15

Extreme points of some families of non-additive measures Miranda Menéndez, Pedro Combarro, Elías F. Gil Álvarez, Pedro Non-additive measures are a valuable tool to model many different problems arising in real situations. However, two important difficulties appear in their practical use: the complexity of the measures and their identification from sample data. For the first problem, additional conditions are imposed, leading to different subfamilies of non-additive measures. Related to the second point, in this paper we study the set of vertices of some families of non-additive measures, namely k-additive measures and p-symmetric measures. These extreme points are necessary in order to properly apply a new method of identification of non-additive measures based on genetic algorithms, whose cross-over operator is the convex combination. We solve the problem through techniques of Linear Programming. 2023-06-20T09:41:21Z 2023-06-20T09:41:21Z 2023-06-20T09:41:21Z 2006 journal article https://hdl.handle.net/20.500.14352/50187 0377-2217 10.1016/j.ejor.2005.03.005 eng BFM2001-3515 TIC2001-3579 PR-01-GE-15 Miranda Menéndez, P., Combarro, E. F. & Gil Álvarez, P. «Extreme Points of Some Families of Non-Additive Measures». European Journal of Operational Research, vol. 174, n.o 3, noviembre de 2006, pp. 1865-84. DOI.org (Crossref), https://doi.org/10.1016/j.ejor.2005.03.005. restricted access Elsevier Science