  We study relations between evidence theory and S-approximation spaces. Both
theories have their roots in the analysis of Dempster's multivalued mappings
and lower and upper probabilities and have close relations to rough sets. We
show that an S-approximation space, satisfying a monotonicity condition, can
induce a natural belief structure which is a fundamental block in evidence
theory. We also demonstrate that one can induce a natural belief structure on
one set, given a belief structure on another set if those sets are related by a
partial monotone S-approximation space.
