Indistinguishability relations in Dempster–Shafer theory of evidence Original Research Article

Each theory or model implicitly defines its inherent notion of equality for the objects in question. In turn, this equality, and its counterpart, the mathematical concept of equivalence, provides the basis on which to establish classification mechanisms for the domain at hand. Nevertheless, equivalence relations have not been proved to be sufficiently suited to capturing the underlying structure when dealing with domains pervaded with uncertainty. Therefore, the need for a more flexible definition of equality brings the concept of T-indistinguishability operator on to the scene. In this paper, we study the notion of indistinguishability within the context of the Dempster–Shafer theory of evidence and provide effective definitions and procedures for computing the T-indistinguishability operator associated with a given body of evidence. We also show how these procedures could also be adapted in order to provide a new method for tackling the problem of belief function approximation based on the concept of T-preorder.