Partial classification in the belief function framework

TL;DR: In this paper, the utility of set-valued predictions is defined using an Ordered Weighted Average (OWA) operator, which allows to model the decision maker's attitude towards imprecision using a single parameter.

Abstract: Partial, or set-valued classification assigns instances to sets of classes, making it possible to reduce the probability of misclassification while still providing useful information. This paper reviews approaches to partial classification based on the Dempster–Shafer theory of belief functions. To define the utility of set-valued predictions, we propose to extend the utility matrix using an Ordered Weighted Average operator, allowing us to model the decision maker’s attitude towards imprecision using a single parameter. Various decision criteria are analyzed comprehensively. In particular, two main strategies are distinguished: partial classification based on complete preorders among partial assignments, and partial preorders among complete assignments. Experiments with UCI and simulated Gaussian data sets show the superiority of partial classification in terms of average utility, as compared to single-class assignment and classification with rejection.