In possibility theory, the information available, relative to the value of parameter x, is represented by a possibility distribution . The reader can refer to [Dubois and Prade, 1987a] for a full presentation of possibility theory or to the paper of [Zadeh, 1978] which defines this new theory. An analysis of this paper can also be found in [Bouchon-Meunier, 1995]. Finally, the basic notions can also be consulted in this document.

A possibility distribution corresponds to an interval (or a set) representing imprecise information. Such a set is generally fuzzy [Zadeh, 1965].

The union and the intersection are both principal ways, from others, to fuse the sets.

Let be the referential. Let us then assume we have two sources of information, noted 1 and 2, which inform us about the value of parameter x as follows:

What can we say about x?

There are several answers to this question, depending on whether sets E₁ and E₂ intersect more or less, or not at all, and whether the sources are reliable or not. In each case, knowledge context of the situation will allow a conclusion to be reached.


There is no method able to fusion these two elements, which is able to deal with all possible cases. But there exist different combinatory modes suiting each case.

•   Information Fusion Methods