A formal theory of fuzzy natural language quantification and its role in granular computing

  • Authors:

  • Ingo Glöckner;Alois Knoll

  • Affiliations:

  • University of Bielefeld, Faculty of Technology, 33501 Bielefeld, Germany;University of Bielefeld, Faculty of Technology, 33501 Bielefeld, Germany

  • Venue:
  • Granular computing
  • Year:
  • 2001

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Abstract

Fuzzy quantification is a linguistic granulation technique capable of expressing the global characteristics of a collection of individuals, or a relation between individuals, through meaningful linguistic summaries. However, existing approaches to fuzzy quantification fail to provide convincing results in the important case of two-place quantification (e.g. "many blondes are tall"). We develop an axiomatic framework for fuzzy quantification which complies with a large number of linguistically motivated adequacy criteria. In particular, we present the first models of fuzzy quantification which provide an adequate account of the "hard" cases of multiplace quantifiers, non-monotonic quantifiers, and non-quantitative quantifiers, and we show how the resuiting operators can be efficiently implemented based on histogram computations.