Fuzzy set theory has at least two advantages;

• It allows imprecise knowledge to be modelled, such that an approximation of a numerical value (``about 3.80 meters''), or a vague information expressed, for instance in natural language (``high''). Very few methodologies allow this sort of modeling.
• It is the only way to deal, within the same framework, with knowledge numerically provided by measuring devices, and knowledge symbolically expressed by a human observer for instance.

However, fuzzy set theory does not allow imprecision and uncertainty to be handled with the same formalism. But these two types of imperfection in knowledge are closely linked, if only because, in many cases, the more accuracy is required for the terms of an assertion, the less certain becomes the assertion.

The following example of conversation illustrates this concept:

- ``How old is he?''    - ``About twenty''    - ``Are you sure?''    - ``Absolutely!''    - ``This is really imprecise!''    - ``Well, in fact, I think he is 31, but I am not sure.''

Moreover, a reasoning based on imprecise knowledge often generates uncertainties on the final decision that must be taken. The following reasoning illustrates this problem:

1. Being over 18, makes one eligible to vote.   2. We know that Peter is about 18, is he allowed to vote?      3. It is quite possible, but not certain.

 Possibility theory was introduced in 1978 by L.A. Zadeh [Zadeh, 1978], in connection with the fuzzy set theory, to allow a reasoning to be carried out on imprecise or vague knowledge, making it possible to deal with uncertainties on this knowledge.

The developments of this introduction constitute a method of formalizing non-probabilistic uncertainties on events. I.e. a means of assessing to what extent the occurrence of an event is possible and to what extent we are certain of its occurrence, without, however, knowing the evaluation of the probability of this occurrence. This can happen, for instance, when there is no similar event to be referred to.

• Example
• Evaluation of Possibility
• Evaluation of Necessity
• Relations between Possibility Measures and Necessity Measures
• Comparison between Possibility and Probability
• Histogram and Possibility Distribution