An approach to general quantification using representation by levels

Authors:
Daniel Sánchez;Miguel Delgado;María-Amparo Vila
Affiliations:
European Centre for Soft Computing, Edificio Científico-Tecnológico, Mieres, Asturias, Spain and Dept. Computer Science and A.I., University of Granada E.T.S.I.I.T., Granada, Spain;Dept. Computer Science and A.I., University of Granada E.T.S.I.I.T., Granada, Spain;Dept. Computer Science and A.I., University of Granada E.T.S.I.I.T., Granada, Spain
Venue:
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Year:
2011

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Abstract

In this paper we propose an extension of generalized quantification to the fuzzy case using a recently proposed level representation of fuzziness. The level representation allows the extension of crisp quantification to the fuzzy case in a simple way, keeping all its properties. The expressive power of this extension to the theory of generalized quantifiers goes far beyond the usual fuzzy quantification framework based on absolute and relative fuzzy quantifiers. The proposal offer many potentially interesting possibilities for developing applications inspired in the Computing with Words and Perceptions paradigm, remarkably linguistic summarization of data.