Evidential clustering is an approach to clustering based on the use of Dempster-Shafer mass functions to represent cluster-membership uncertainty. In this paper, we introduce a neural-network based evidential clustering algorithm, called NN-EVCLUS, which learns a mapping from attribute vectors to mass functions, in such a way that more similar inputs are mapped to output mass functions with a lower degree of conflict. The neural network can be paired with a one-class support vector machine to make it robust to outliers and allow for novelty detection. The network is trained to minimize the discrepancy between dissimilarities and degrees of conflict for all or some object pairs. Additional terms can be added to the loss function to account for pairwise constraints or labeled data, which can also be used to adapt the metric. Comparative experiments show the superiority of N-EVCLUS over state-of-the-art evidential clustering algorithms for a range of unsupervised and constrained clustering tasks involving both attribute and dissimilarity data.

This paper discusses a new measure that is adaptable to certain intervalic probability frameworks, possibility theory, and belief theory. As such, it has the potential for wide use in knowledge engineering, expert systems, and related problems in the human sciences. This measure (denoted here by F) has been introduced in Smithson (1988) and is more formally discussed in Smithson (1989a)o Here, I propose to outline the conceptual basis for F and compare its properties with other measures of second-order uncertainty. I will argue that F is an indicator of nonspecificity or alternatively, of freedom, as distinguished from either ambiguity or vagueness.

A new entropy-like measure as well as a new measure of total uncertainty pertaining to the Dempster-Shafer theory are introduced. It is argued that these measures are better justified than any of the previously proposed candidates.