A note on belief structures and S-approximation spaces
This work provides theoretical insights linking two mathematical frameworks used in uncertainty modeling, but it is incremental as it builds on existing relations without introducing new applications or broad advancements.
The paper establishes connections between evidence theory and S-approximation spaces by showing that an S-approximation space with monotonicity can induce a belief structure, and that belief structures can be transferred between sets via partial monotone S-approximation spaces.
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.