A Development of Set Theory in Fuzzy Logic

  • Petr Hájek
  • Zuzana Haniková
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 114)


This paper presents an axiomatic set theory FST (‘Fuzzy Set Theory’), as a first-order theory within the framework of fuzzy logic in the style of [4]. In the classical ZFC, we use a construction similar to that of a Boolean-valued universe—over an algebra of truth values of the logic we use—to show the nontriviality of FST. We give the axioms of FST. Finally we show that FST interprets ZF.


Fuzzy Logic Free Variable Residuated Lattice Schematic Extension Logical Axiom 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Petr Hájek
    • 1
  • Zuzana Haniková
    • 1
  1. 1.Institute of Computer SciencePraha 8Czech Republic

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