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Fuzzy Quantifiers

A Computational Theory

  • Book
  • © 2006

Overview

Authors:
  1. Ingo Glöckner

    1. LG Prakt. Inf. VII Informatikzentrum, Fern Universität in Hagen, Hagen, Germany

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  • First monograph on fuzzy quantification
  • Strong emphasis on linguistic justification and formal soundness of interpretations

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 193)

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Table of contents (13 chapters)

  1. Front Matter

    Pages I-XVII
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  2. An Introduction to Fuzzy Quantification: Origins and Basic Concepts

    Pages 1-53

  3. A Framework for Fuzzy Quantification

    Pages 55-83

  4. The Axiomatic Class of Plausible Models

    Pages 85-109

  5. Semantic Properties of the Models

    Pages 111-148

  6. Special Subclasses of Models

    Pages 149-160

  7. Special Semantical Properties and Theoretical Limits

    Pages 161-177

  8. Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation

    Pages 179-220

  9. Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts

    Pages 221-235

  10. The Full Class of Models Defined in Terms of Three-Valued Cuts

    Pages 237-258

  11. The Class of Models Based on the Extension Principle

    Pages 259-276

  12. Implementation of Quantifiers in the Models

    Pages 277-353

  13. Multiple Variable Binding and Branching Quantification

    Pages 355-373

  14. Discussion

    Pages 375-389

  15. Back Matter

    Pages 437-460
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Keywords

About this book

From a linguistic perspective, it is quanti?cation which makes all the di?- ence between “having no dollars” and “having a lot of dollars”. And it is the meaning of the quanti?er “most” which eventually decides if “Most Ame- cans voted Kerry” or “Most Americans voted Bush” (as it stands). Natural language(NL)quanti?erslike“all”,“almostall”,“many”etc. serveanimp- tant purpose because they permit us to speak about properties of collections, as opposed to describing speci?c individuals only; in technical terms, qu- ti?ers are a ‘second-order’ construct. Thus the quantifying statement “Most Americans voted Bush” asserts that the set of voters of George W. Bush c- prisesthemajorityofAmericans,while“Bushsneezes”onlytellsussomething about a speci?c individual. By describing collections rather than individuals, quanti?ers extend the expressive power of natural languages far beyond that of propositional logic and make them a universal communication medium. Hence language heavily depends on quantifying constructions. These often involve fuzzy concepts like “tall”, and they frequently refer to fuzzy quantities in agreement like “about ten”, “almost all”, “many” etc. In order to exploit this expressive power and make fuzzy quanti?cation available to technical applications, a number of proposals have been made how to model fuzzy quanti?ers in the framework of fuzzy set theory. These approaches usually reduce fuzzy quanti?cation to a comparison of scalar or fuzzy cardinalities [197, 132].

Authors and Affiliations

  • LG Prakt. Inf. VII Informatikzentrum, Fern Universität in Hagen, Hagen, Germany

    Ingo Glöckner

About the author

Ingo Glöckner received his M.A. in Computational Linguistics and Artificial Intelligence from University of Osnabrück in 1996. He then became a research assistant at the University of Bielefeld, where he pursued research on fuzzy set theory and its application to information retrieval. In 2003, I. Glöckner received his PhD for his thesis on the semantical interpretation and implementation of fuzzy quantifiers. He then joined the Intelligent Information and Communication Systems Group (Prakt. Informatik VII) of Prof. H. Helbig at the FernUniversität in Hagen. His current research activities are centered on the representation and processing of knowledge expressed in natural language.

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