Belief functions and rough sets: Survey and new insights

Rough set theory and belief function theory, two popular mathematical frameworks for uncertainty representation, have been widely applied in different settings and contexts. Despite different origins and mathematical foundations, the fundamental concepts of the two formalisms (i.e., approximations in rough set theory, belief and plausibility functions in belief function theory) are closely related. In this survey article, we review the most relevant contributions studying the links between these two uncertainty representation formalisms. In particular, we discuss the theoretical relationships connecting the two approaches, as well as their applications in knowledge representation and machine learning. Special attention is paid to the combined use of these formalisms as a way of dealing with imprecise and uncertain information. The aim of this work is, thus, to provide a focused picture of these two important fields, discuss some known results and point to relevant future research directions.