On the analysis of set-based fuzzy quantified reasoning using classical
  syllogistics
  Syllogism is a type of deductive reasoning involving quantified statements.
The syllogistic reasoning scheme in the classical Aristotelian framework
involves three crisp term sets and four linguistic quantifiers, for which the
main support is the linguistic properties of the quantifiers. A number of fuzzy
approaches for defining an approximate syllogism have been proposed for which
the main support is cardinality calculus. In this paper we analyze fuzzy
syllogistic models previously described by Zadeh and Dubois et al. and compare
their behavior with that of the classical Aristotelian framework to check which
of the 24 classical valid syllogistic reasoning patterns or moods are
particular crisp cases of these fuzzy approaches. This allows us to assess to
what extent these approaches can be considered as either plausible extensions
of the classical crisp syllogism or a basis for a general approach to the
problem of approximate syllogism.
