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"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.
An Introduction to Fuzzy Quantification: Origins and Basic Concepts.- A Framework for Fuzzy Quantification.- The Axiomatic Class of Plausible Models.- Semantic Properties of the Models.- Special Subclasses of Models.- Special Semantical Properties and Theoretical Limits.- Models Defined in Terms of Three-Valued Cuts and Fuzzy-Median Aggregation.- Models Defined in Terms of Upper and Lower Bounds on Three-Valued Cuts.- The Full Class of Models Defined in Terms of Three-Valued Cuts.- The Class of Models Based on the Extension Principle.- Implementation of Quantifiers in the Models.- Multiple Variable Binding and Branching Quantification.- Discussion.
Posted June 17, 2013