Extending stochastic ordering to belief functions on the real line

Thierry Denoeux (1)

1 Heudiasyc - Heuristique et Diagnostic des Systèmes Complexes [Compiègne]

In this paper, the concept of stochastic ordering is extended to belief functions on the real line defined by random closed intervals. In this context, the usual stochastic ordering is shown to break down into four distinct ordering relations, called credal orderings, which correspond to the four basic ordering structures between intervals. These orderings are characterized in terms of lower and upper expectations. We then derive the expressions of the least committed (least informative) belief function credally less (respectively, greater) than or equal to a given belief function. In each case, the solution is a consonant belief function that can be described by a possibility distribution. A simple application to reliability analysis is used as an example throughout the paper.

Mots clés: Dempster-Shafer theory; Evidence theory; Random intervals; Ordering relation; Possibility distribution

Domaines: Intelligence artificielle [cs.AI]

Thierry Denoeux. Extending stochastic ordering to belief functions on the real line. Information Sciences, 2009, 179, pp.1362-1376. ⟨10.1016/j.ins.2009.01.009⟩. ⟨hal-00448368⟩