Whereas probability theory uses a single number, the probability, to describe how likely an event is to occur, possibility theory uses two concepts, the possibility and the necessity of the event. For any set, the necessity measure is defined by
In the above formula, denotes the complement of, that is the elements of that do not belong to . It is straightforward to show that:
- for any
and that:
Note that contrary to probability theory, possibility is not self-dual. That is, for any event, we only have the inequality:
However, the following duality rule holds:
- For any event, either, or
Accordingly, beliefs about an event can be represented by a number and a bit.
Read more about this topic: Possibility Theory
Famous quotes containing the word necessity:
“Teach thy necessity to reason thus:
There is no virtue like necessity.”
—William Shakespeare (1564–1616)
“To expect to increase prices and then to maintain them at a higher level by means of a plan which must of necessity increase production while decreasing consumption is to fly in the face of an economic law as well established as any law of nature.”
—Calvin Coolidge (1872–1933)
“Heredity is a strong factor, even in architecture. Necessity first mothered invention. Now invention has little ones of her own, and they look just like grandma.”
—E.B. (Elwyn Brooks)