A note on belief structures and S-approximation spaces

TL;DR

This paper explores the connections between evidence theory and S-approximation spaces, showing how belief structures can be derived from S-approximation spaces and their relations.

Contribution

It establishes a formal link between S-approximation spaces and belief structures, extending the understanding of their interplay in evidence theory.

Findings

An S-approximation space with a monotonicity condition induces a belief structure.

Belief structures can be transferred between related sets via partial monotone S-approximation spaces.

The work deepens the theoretical understanding of the relationship between rough sets, evidence theory, and S-approximation spaces.

Abstract

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.