Probability theory and possibility theory seem to come from the same father: evidence theory. This is the reason why they both have similar properties, as shown in ``Comparison between possibility and probability theory'', and why they cannot be mixed up, as they are based on incompatible assertions.

The aim of belief theory is to give a formal representation of the inaccurate and uncertain aspect of information.

"Inaccuracy" and "uncertainty" can be considered as two antagonistic points of view concerning the same actual imperfection of the information:

• Inaccuracy concerns the content of information, whereas
  
  
• uncertainty is connected to insufficient knowledge of its truth. Uncertainty of information is considered with the help of qualifiers such as " probable ", " possible ", " necessary ", " plausible ", " credible " [Dubois and Prade, 1987a].

For any problem in the real world, we must always face the difficulty of using several information sources coming from human opinion, statistics, and so on [Sandri, 1991]. Belief theory allows information coming from different sources to be combined to produce an inference result that can help in taking a decision with some degree of certainty. So, this theory concerns modeling and quantization of the credibility attributed to events.

• Belief Representation
• Mass of Belief
• Example
• Focal Element and Body of Evidence
• Belief and Plausibility
• Properties
• Note
• Example
• Dempster's Rule of Combination
• Example
• Decision
• Conclusion on Belief Theory