Fuzzy Sets in Approximate Reasoning: A Personal View

Fuzzy set-based methods contribute to the formalization of different types of approximate reasoning, mainly in two ways. First, when modeling classes and properties, fuzzy sets naturally encode gradual properties, such as, e.g., 'large', whose satisfaction is a matter of degree and may be only partial for particular instances. Due to this ability, fuzzy sets are naturally entitled to capture intermediary situations and to be instrumental in the formalization of interpolative reasoning. More generally, similarity-based approximate reasoning can greatly benefit from fuzzy set approaches since similarity is usually a matter of degree. Second, fuzzy sets can also represent incomplete information pervaded with uncertainty. They are then viewed as possibility distributions and give birth to possibility and necessity measures to assess the degrees to which a statement is possible or is certain taking into account the available (incomplete) information. Fuzzy rules whose conclusion part are uncertain can then be modelled in this framework and used for deduction purposes. Moreover, possibility theory can handle default reasoning where plausible conclusions are drawn in a given state of information but may be later defeated when they are inconsistent with a new piece of information which becomes available. The possibilistic modelling of uncertainty is also shown to be useful in abductive reasoning for diagnosis problems. The paper provides an overview of the way fuzzy sets can serve for different types of reasoning purposes and gives the background necessary to the understanding of the basic methodological issues.