%0 Journal Article
%A Miranda Menéndez, Pedro
%A Combarro, Elías F.
%A Gil Álvarez, Pedro
%T Extreme points of some families of non-additive measures
%D 2006
%@ 0377-2217
%U https://hdl.handle.net/20.500.14352/50187
%X 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.
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