Representing Reliability and Hesitation in Possibility Theory: A General Framework

Abstract

Possibility theory, introduced by Zadeh in [5], is a formalism that tries to capture in mathematical terms imprecise (typically, linguistic) information about the more or less plausible values that a variable may assume. For instance, a statement like “decent houses in Gent do not come cheap” flexibly restricts plausible buying prices by pointing out that a low budget will not get very you far in this town. Compare this to “I found a nice place in Gent for about 100.000 EUR”, which gives you a guarantee (by explicit example) that properties in a given price range can be found. The examples we quoted are instances of what is called negative or constraint-based and positive or observation-based information respectively in the literature [3, 4]: the first kind rules out certain values for the buying price X, while the second kind only designates certain observed values as “definitely possible” while saying nothing about the rest.