A Defect in Dempster-Shafer Theory

TL;DR

This paper identifies a fundamental inconsistency in Dempster-Shafer theory related to belief functions and proposes a new approach to uncertainty management that avoids these issues.

Contribution

The paper reveals an inconsistency in Dempster-Shafer theory and introduces a new method for managing uncertainty that aligns with intuitive ideas but resolves the identified problems.

Findings

Identifies inconsistency in Dempster-Shafer theory

Proposes a new approach for uncertainty management

Avoids fundamental postulate conflicts

Abstract

By analyzing the relationships among chance, weight of evidence and degree of beliefwe show that the assertion "probability functions are special cases of belief functions" and the assertion "Dempster's rule can be used to combine belief functions based on distinct bodies of evidence" together lead to an inconsistency in Dempster-Shafer theory. To solve this problem, we must reject some fundamental postulates of the theory. We introduce a new approach for uncertainty management that shares many intuitive ideas with D-S theory, while avoiding this problem.