Controling the Number of Focal Elements

Abstract

A basic belief assignment can have up to 2ⁿ 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.