---
title: "The Canonical Decomposition of a Weighted Belief"
authors:
  - "Philippe Smets"
doi: ""
url: "https://ijcai.org/proceedings/1995/243"
pdf: "https://ijcai.org/proceedings/1995/0243.pdf"
venue: "Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"
year: 1995
pages: "1896-1900"
track: "Reasoning Under Uncertainty"
keywords:
---

# The Canonical Decomposition of a Weighted Belief

Philippe Smets

*Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence*, pages 1896-1900.

## Abstract

Any belief function can be decomposed into a confidence and a diffidence components . Each components is uniquely decomposable into simple support functions that represent the impact of the simplest form of evidence, the one that only partially supports a given subset of the frame of discernment. The nature of the inverse of Dempster's rule of combination is detailed. The confidence component translates the impact of ' good reasons to believe'. It is the component classically considered when constructing a belief. The diffidence component translates the impact of 'good reasons not to believe' .