Fuzzy quantification is a linguistic granulation technique capable of expressing the global characteristics of a collection of individuals, or a relation between individuals, through meaningful linguistic summaries. However, existing approaches to fuzzy quantification fail to provide convincing results in the important case of two-place quantification (e.g. ``many blondes are tall''). We develop an axiomatic framework for fuzzy quantification which complies with a large number of linguistically motivated adequacy criteria. In particular, we present the first models of fuzzy quantification which provide an adequate account of the ``hard'' cases of multiplace quantifiers, non-monotonic quantifiers, and non-quantitative quantifiers, and we show how the resulting operators can be efficiently implemented based on histogram computations.
I. Glöckner and A. Knoll
A Formal Theory of Fuzzy Natural Language
Quantification and its Role in Granular Computing.
In:
W. Pedrycz (Ed.) Granular Computing: An Emerging Paradigm.
Studies in Fuzziness and Soft Computing, Vol. 70,
Physica-Verlag, April 2001.