DFS theory offers an axiomatic approach to fuzzy quantification.
It attempts to characterise
`reasonable' models of fuzzy quantifiers in terms
of formal conditions imposed on a fuzzification mapping.
In this way, a large number of linguistically motivated
can be guaranteed to hold for all models of DFS theory,
the so-called determiner fuzzification schemes or DFSes
The report improves upon existing work on DFS theory
an alternative axiom system of only six basic axioms.
The new axiom set is shown
to be equivalent to the original one.
A subclass of DFSes called MB-DFSes is then introduced
which can be defined in terms of a three-valued cutting mechanism.
Based on an investigation of this mechanism, it
becomes possible to prove
that the new DFS axioms form an independent axiom system.
In addition, a number of novel properties of fuzzification mechanisms are discussed and examples of MB-DFSes are investigated from this perspective. A particularly well-behaved DFS is being presented and its special properties as well as their uniqueness are established. This model can be shown to generalize the Sugeno integral (and hence the FG-count approach to fuzzy quantification) to the case of nonmonotonic and arbitrary multiplace quantifiers.
Note. The report is intended as a technical reference and its purpose is to provide the proofs for a number of results related to DFS theory. The style of presentation is therefore rather technical and presentation order is guided by the natural order of the proofs.
Advances in DFS Theory
Technical Report TR2000-01, University of Bielefeld, Technical Faculty, PO-Box 100131, 33501 Bielefeld, Germany, June 2000.
Portable Document Format PDF, 354 pages, 4.462MB