Fundamental Possibilistic Concepts

Uncertainty sources are diverse: incomplete domain knowledge, noisy and conflicting data, incomplete information, linguistic imprecise and ambiguous knowledge, etc. One of the theories dealing with uncertainties is possibility theory that was introduced to allow reasoning to be carried out in the framework of a vague knowledge about the uncertainties. In fact, possibility theory can be described as a collection of techniques centered on the concept of a possibility distribution used for the representation and manipulation of the ambiguous or vague knowledge about the encountered uncertainty. In this chapter, the fundamental concept of possibility distributions is detailed in terms of its definition, its informative facets, and its different distribution models. An important issue detailed within this chapter is related to subnormal possibility distributions where the available ambiguous knowledge is inconsistent.