# Basic Formal Properties of A Relational Model of The Mathematical Theory of Evidence

## TL;DR

This paper offers a new relational and rough-set based interpretation of Dempster-Shafer belief functions, linking belief combination to database join operations and emphasizing diversity over frequency.

## Contribution

It introduces a novel qualitative interpretation of belief functions using relational data and rough sets, connecting belief operators with database operations.

## Key findings

- Dempster rule corresponds to relational join
- Belief measures can be derived through domain operations
- Interpretation emphasizes diversity over frequency

## Abstract

The paper presents a novel view of the Dempster-Shafer belief function as a measure of diversity in relational data bases. It is demonstrated that under the interpretation The Dempster rule of evidence combination corresponds to the join operator of the relational database theory. This rough-set based interpretation is qualitative in nature and can represent a number of belief function operators. The interpretation has the property that Given a definition of the belief measure of objects in the interpretation domain we can perform operations in this domain and the measure of the resulting object is derivable from measures of component objects via belief operator. We demonstrated this property for Dempster rule of combination, marginalization, Shafer's conditioning, independent variables, Shenoy's notion of conditional independence of variables. The interpretation is based on rough sets (in connection with decision tables), but differs from previous interpretations of this type in that it counts the diversity rather than frequencies in a decision table.