# Continuous Belief Functions: Focal Intervals Properties

#### Abstract

The set of focal elements resulting from a conjunctive or disjunctive combination of consonant belief functions is regretfully not consonant and is thus very difficult to represent. In this paper, we propose a graphical representation of the cross product of two focal sets originating from univariate Gaussian pdfs. This representation allows to represent initial focal intervals as well as focal intervals resulting from a combination operation. We show in case of conjunctive or disjunctive combination operations, that the whole domain can be separated in four subsets of intervals having same properties. At last, we focus on identical length focal intervals resulting from a combination. We show that such intervals are organized in connected line segments on our graphical representation.

DOI: 10.1007/978-3-642-29461-7_11

### Cite this paper

@inproceedings{Vannobel2012ContinuousBF, title={Continuous Belief Functions: Focal Intervals Properties}, author={Jean-Marc Vannobel}, booktitle={Belief Functions}, year={2012} }