A Framework for Evaluating Approaches to Fuzzy Quantification


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


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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).

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