Suppose that we ask the following question:

To answer this question, it is difficult to know if we must take into account:

• what Mr. Bean did every previous Monday, or
• what he does the first Monday of the month, or
• the first Monday of the year, or
• what he uses to do on January, and so on.

The uncertainty of an event is described in possibility theory at the same time :

• by the degree of possibility of this event and
• by the degree of possibility of the opposite event

These two degrees are only slightly related.

Possibility allows the representation of both the inaccuracy (as fuzzy subsets) and the quantification of uncertainty (as a pair of numbers possibility-necessity).