Studia Logica 73 (3):413 - 430 (2003)
A structural (as opposed to Zadeh's quantitative) approach to fuzziness is given, based on the operator "very", which is added to the language of set theory together with some elementary axioms about it. Due to the axiom of foundation and to a lifting axiom, the operator is proved trivial on the cumulative hierarchy of ZF. So we have to drop either foundation or lifting. Since fuzziness concerns complemented predicates rather than sets, a class theory is needed for the very operator. And of them the Kelley-Morse (KM) theory is more appropriate for reasons of class existence. Several definable realizations of the very-operator are presented in KM⁻. In the last section we consider the operator "very" without the lifting axiom on classes of urelements. To each structurally fuzzy set X a traditional quantitative fuzzy set X̄ is assigned -- its quantitative representation. This way we are able partly to recover ordinary fuzzy sets from the structurally fuzzy ones
|Keywords||Philosophy Logic Mathematical Logic and Foundations Computational Linguistics|
|Categories||categorize this paper)|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
An Axiomatics for Nonstandard Set Theory, Based on Von Neumann-Bernays-Gödel Theory.P. V. Andreev & E. I. Gordon - 2001 - Journal of Symbolic Logic 66 (3):1321-1341.
Relating First-Order Set Theories and Elementary Toposes.Steve Awodey, Carsten Butz & Alex Simpson - 2007 - Bulletin of Symbolic Logic 13 (3):340-358.
Axiomatization and Completeness of Uncountably Valued Approximation Logic.Helena Rasiowa - 1994 - Studia Logica 53 (1):137 - 160.
Note on the Integration of Prototype Theory and Fuzzy-Set Theory.Gy Fuhrmann - 1991 - Synthese 86 (1):1 - 27.
E Pluribus Unum: Plural Logic and Set Theory.John P. Burgess - 2004 - Philosophia Mathematica 12 (3):193-221.
Added to index2009-01-28
Total downloads28 ( #184,935 of 2,177,988 )
Recent downloads (6 months)1 ( #317,698 of 2,177,988 )
How can I increase my downloads?