The FA Quantifier Fuzzification Mechanism: analysis of convergence and
  efficient implementations
  The fuzzy quantification model FA has been identified as one of the best
behaved quantification models in several revisions of the field of fuzzy
quantification. This model is, to our knowledge, the unique one fulfilling the
strict Determiner Fuzzification Scheme axiomatic framework that does not induce
the standard min and max operators. The main contribution of this paper is the
proof of a convergence result that links this quantification model with the
Zadeh's model when the size of the input sets tends to infinite. The
convergence proof is, in any case, more general than the convergence to the
Zadeh's model, being applicable to any quantitative quantifier. In addition,
recent revisions papers have presented some doubts about the existence of
suitable computational implementations to evaluate the FA model in practical
applications. In order to prove that this model is not only a theoretical
approach, we show exact algorithmic solutions for the most common linguistic
quantifiers as well as an approximate implementation by means of Monte Carlo.
Additionally, we will also give a general overview of the main properties
fulfilled by the FA model, as a single compendium integrating the whole set of
properties fulfilled by it has not been previously published.
