Ebook: Fuzzy Quantifiers: A Computational Theory
Author: Dr. Ingo Glöckner (auth.)
- Tags: Appl.Mathematics/Computational Methods of Engineering, Artificial Intelligence (incl. Robotics), Computational Linguistics
- Series: Studies in Fuzziness and Soft Computing 193
- Year: 2006
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
"Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier. The material will be of interest to those working at the crossroads of natural language and fuzzy set theory. The fields of application comprise fuzzy information aggregation and data fusion, flexible database querying and fuzzy information retrieval, multi-criteria decision-making and linguistic data summarization.
"Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier. The material will be of interest to those working at the crossroads of natural language and fuzzy set theory. The fields of application comprise fuzzy information aggregation and data fusion, flexible database querying and fuzzy information retrieval, multi-criteria decision-making and linguistic data summarization.
"Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier. The material will be of interest to those working at the crossroads of natural language and fuzzy set theory. The fields of application comprise fuzzy information aggregation and data fusion, flexible database querying and fuzzy information retrieval, multi-criteria decision-making and linguistic data summarization.
Content:
Front Matter....Pages I-XVII
An Introduction to Fuzzy Quantification: Origins and Basic Concepts....Pages 1-53
A Framework for Fuzzy Quantification....Pages 55-83
The Axiomatic Class of Plausible Models....Pages 85-109
Semantic Properties of the Models....Pages 111-148
Special Subclasses of Models....Pages 149-160
Special Semantical Properties and Theoretical Limits....Pages 161-177
Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation....Pages 179-220
Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts....Pages 221-235
The Full Class of Models Defined in Terms of Three-Valued Cuts....Pages 237-258
The Class of Models Based on the Extension Principle....Pages 259-276
Implementation of Quantifiers in the Models....Pages 277-353
Multiple Variable Binding and Branching Quantification....Pages 355-373
Discussion....Pages 375-389
Back Matter....Pages 437-460
"Almost all", "many", "some": fuzzy quantifiers are vital for effective communication in natural language (NL). This monograph pursues an axiomatic method to achieve a reliable interpretation of these quantifiers in technical applications of fuzzy quantification. Unlike existing work in this area, it targets a much broader class of quantificational phenomena which includes all cases usually considered in linguistics. The topics addressed in the monograph run the gamut from the introduction of the theoretical framework for analysing fuzzy quantification, the formalization of semantical requirements on models of fuzzy quantification, the construction and detailed study of prototypical models which conform to the linguistic desiderata, the development of algorithms for implementing the main types of quantifiers in these models, and finally a preview to fuzzy branching quantifications which might be necessary for modelling NL sentences involving more than one quantifier. The material will be of interest to those working at the crossroads of natural language and fuzzy set theory. The fields of application comprise fuzzy information aggregation and data fusion, flexible database querying and fuzzy information retrieval, multi-criteria decision-making and linguistic data summarization.
Content:
Front Matter....Pages I-XVII
An Introduction to Fuzzy Quantification: Origins and Basic Concepts....Pages 1-53
A Framework for Fuzzy Quantification....Pages 55-83
The Axiomatic Class of Plausible Models....Pages 85-109
Semantic Properties of the Models....Pages 111-148
Special Subclasses of Models....Pages 149-160
Special Semantical Properties and Theoretical Limits....Pages 161-177
Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation....Pages 179-220
Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts....Pages 221-235
The Full Class of Models Defined in Terms of Three-Valued Cuts....Pages 237-258
The Class of Models Based on the Extension Principle....Pages 259-276
Implementation of Quantifiers in the Models....Pages 277-353
Multiple Variable Binding and Branching Quantification....Pages 355-373
Discussion....Pages 375-389
Back Matter....Pages 437-460
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