Fuzzy linguistic quantifiers --
operators
intended to model vague quantifying expressions in natural language
like `almost all' or `few' -- have gained importance
as operators for
information aggregation and the fusion of gradual evaluations.
They
are particularly
appealing because of their ease-of-use: people are familiar with
these operators, and can apply them
for technical aggregation purposes
in the same way as in
everyday language.
Because of the
irregular and
rather intangible phenomena
it tries
to model -- viz, those of imprecision and uncertainty
-- fuzzy
logic should be particularly
specific about its
foundations.
However, work
on mathematical foundations and linguistic
justification of fuzzy linguistic quantifiers is scarce.
In the paper, we propose
a framework for
evaluating approaches
to fuzzy quantification which relates these to the logico-linguistic
theory of generalized quantifiers (TGQ).
By
reformulating these approaches as fuzzification mechanisms,
we can investigate
properties of
the fuzzification mappings which express important
aspects of the meaning of natural language quantifiers.
I. Glöckner
A Framework for Evaluating Approaches to Fuzzy Quantification
Technical Report TR99-03, Technische Fakultät, Universität Bielefeld,
July 1999. 33 pages
Parts of this report have been published in conference proceedings: KES'99 (manuscript, discussion of OWA approach) and MFI'99 (manuscript, discussion of Sigma-Count approach).