Miranda Menéndez, PedroCombarro, Elías F.Gil Álvarez, Pedro2023-06-202023-06-202006Miranda 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.2005.03.005.0377-221710.1016/j.ejor.2005.03.005https://hdl.handle.net/20.500.14352/50187Non-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.engjournal articlehttps//doi.org/10.1016/j.ejor.2005.03.005http://www.sciencedirect.com/science/article/pii/S0377221705002730restricted access519.816Decision analysisGenetic algorithmsMultiple criteria analysisLinear programmingNon-additive measuresk-additivityp-symmetryVerticesInvestigación operativa (Matemáticas)1207 Investigación Operativa