Manipulating Focal Sets on the Unit Simplex: Application to Plastic Sorting

Belief functions are quite generic models when it comes to represent uncertain data, as it extends a wide range of uncertainty models (possiblity and probability distributions, among others). Usually, belief functions are defined over finite spaces, however many real word problems require to deal with beliefs over a continuous space while maintaining computational efficiency. This paper discusses the case of focal sets on the unit simplex, and proposes efficient inference tools to manipulate them. Such sets can be used to represent unknown proportions that one may face in various fields like soil contamination managing, plastic sorting or image reconstruction. In this paper, we illustrate their use on an industrial problem of plastic sorting, where the proportion of material impurities must not go over a limit while minimizing the rejection of sorted materials, whose nature is uncertain.