David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
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)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
P. V. Andreev & E. I. Gordon (2001). An Axiomatics for Nonstandard Set Theory, Based on Von Neumann-Bernays-Gödel Theory. Journal of Symbolic Logic 66 (3):1321-1341.
Steve Awodey, Carsten Butz & Alex Simpson (2007). Relating First-Order Set Theories and Elementary Toposes. Bulletin of Symbolic Logic 13 (3):340-358.
Helena Rasiowa (1994). Axiomatization and Completeness of Uncountably Valued Approximation Logic. Studia Logica 53 (1):137 - 160.
Gy Fuhrmann (1991). Note on the Integration of Prototype Theory and Fuzzy-Set Theory. Synthese 86 (1):1 - 27.
John P. Burgess (2004). E Pluribus Unum: Plural Logic and Set Theory. Philosophia Mathematica 12 (3):193-221.
Boris Čulina (2013). Logic of Paradoxes in Classical Set Theories. Synthese 190 (3):525-547.
Gy Fuhrmann (1988). Fuzziness of Concepts and Concepts of Fuzziness. Synthese 75 (3):349 - 372.
Siegfried Gottwald (2006). Universes of Fuzzy Sets and Axiomatizations of Fuzzy Set Theory. Part II: Category Theoretic Approaches. Studia Logica 84 (1):23 - 50.
Added to index2009-01-28
Total downloads13 ( #179,414 of 1,699,818 )
Recent downloads (6 months)6 ( #105,649 of 1,699,818 )
How can I increase my downloads?