A Broad Class of Standard DFSes

Abstract

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.

Reference

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).

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Ingo Glöckner, Ingo.Gloeckner@FernUni-Hagen.DE (Homepage)