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Extreme points of some families of non-additive measures

Miranda Menéndez, Pedro and Combarro, Elías F. and Gil, Pedro (2006) Extreme points of some families of non-additive measures. European journal of operational research, 174 (3). pp. 1865-1884. ISSN 0377-2217

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Abstract

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.

Item Type:Article
Uncontrolled Keywords:Decision analysis; Genetic algorithms; Multiple criteria analysis; Linear programming; Non-additive measures; k-additivity; p-symmetry; Vertices
Subjects:Sciences > Mathematics > Operations research
ID Code:17069
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