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Controling the Number of Focal Elements

Some Combinatorial Considerations
Part of the Advances in Intelligent and Soft Computing book series (AINSC, volume 164)

Abstract

A basic belief assignment can have up to 2 n focal elements, and combining them with a simple conjunctive operator will need \({\mathcal O}(2^{2n})\) operations. This article proposes some techniques to limit the size of the focal sets of the bbas to be combined while preserving a large part of the information they carry.

The first section revisits some well-known definitions with an algorithmic point of vue. The second section proposes a matrix way of building the least committed isopignistic, and extends it to some other bodies of evidence. The third section adapts the k-means algorithm for an unsupervized clustering of the focal elements of a given bba.

Keywords

Basic belief assignments Combinatorial complexity Focal elements k-means Pignistic probability Body of evidence Least commitment 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Lab-STICC UMR 3192ENSTA BretagneBretagneFrance

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