On fuzzy syllogisms
Didier Dubois, Henri M. Prade · Computational Intelligence · 1988
This paper provides a systematic treatment of possibly imprecisely or vaguely specified numerical quantifiers in default syllogisms, following an approach initiated by Zadeh. The obtained propagation rules are derived from simple properties of relative cardinality or, equivalently, conditional probability. Uncertainty in the description of numerical quantifiers is handled using possibility theory and, particularly, fuzzy arithmetic. The advantages of this default reasoning method are its ability to model any kind of quantifier and to build new defaults by chaining existing ones, in a rigorous manner. This approach also emphasizes the difference between two types of uncertain pieces of knowledge, i.e., conjectures versus general rules.