In this report, a broad class of standard models
of fuzzy quantification is introduced, all of
which satisfy the adequacy requirements of
DFS theory, an axiomatic theory of fuzzy
natural language quantification.
The new models arise when the known
construction of
DFSes in terms of three-valued cuts is separated
from the fuzzy median-based aggregation used
in previous work on MB-DFSes.
Some of the new models are beneficial
compared to the known MB-DFSes
when the inputs are
overly fuzzy and one still needs a fine-grained
result ranking.
The report develops the full set of criteria
required to check
whether a given model of fuzzy quantification based
on the new construction conforms to the adequacy
conditions of DFS theory;
whether it propagates fuzziness in quantifiers and/or
arguments and hence complies with the intuitive
expectation that less detailed input
should not result in more specific output;
whether it is robust with
respect to noise in the arguments or alternative
interpretations of a fuzzy quantifier;
and how it compares to other DFSes by specificity.
The present report also helps to better relate
existing work on fuzzy quantification to
the axiomatic framework provided by DFS theory.
Recent findings indicate
that
the Sugeno integral and hence the `basic' FG-count
approach can be embedded into DFS theory:
they can be consistently generalized to
the `hard' cases of fuzzy quantification
involving
multi-place, non-quantitative and/or non-monotonic
quantifiers.
The report proves a
similar result for the Choquet integral
and hence the `basic' OWA approach, by
presenting a DFS FCh with the desired
properties.
It is anticipated that FCh
will see a number of
applications in future software systems
that profit from the use of fuzzy quantifiers.
I. Glöckner
A Broad Class of Standard DFSes
Technical Report TR2000-02, University of Bielefeld, Technical Faculty,
PO-Box 100131, 33501 Bielefeld, Germany, December 2000 (2nd edition).
Portable Document Format PDF, 165 pages, 697K