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.

Keywords: Decision analysis; Genetic algorithms; Multiple criteria analysis; Linear programming; Non-additive measures; k-additivity; p-symmetry; Vertices

Article Outline

1. Introduction

2. Basic concepts on non-additive measures

3. Genetic algorithms

4. Vertices of k-additive measures

5. The case of p-symmetric measures

6. Conclusions and future research

Acknowledgements

References