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Topology in Fuzzy Class Theory: Basic Notions

In the formal and fully graded setting of Fuzzy Class Theory (or higher-order fuzzy logic) we make an initial investigation into basic notions of fuzzy topology. In particular we study graded notions of

BA - Obecná matematika

  • 2007
    • •
  • D
Result

Relations in Fuzzy Class Theory: Initial Steps.

This paper studies fuzzy relations in the graded framework of Fuzzy Class Theory (FCT). This includes (i) rephrasing existing work on graded properties of binary fuzzy relations in the framework of Fuz...

BA - Obecná matematika

  • 2008
    • •
  • Jx
Result

Interior-Based Topology in Fuzzy Class Theory

Fuzzy topology based on interior operators is studied in the fully graded framework of Fuzzy Class Theory. Its relation to graded notions of fuzzy topology given by open sets and neighborhoods is shown....

BA - Obecná matematika

  • 2007
    • •
  • D
Result

Fuzzy Class Theory: Some Advanced Topics

The goal of this paper is to push forward the development of the apparatus of the Fuzzy Class theory. We concentrate on three areas: strengthening the universal quantifier, formalizing the idea that `similar' fuzzy...

BA - Obecná matematika

  • 2007
    • •
  • D
Result

Fuzzy Horn logic II: implicationally defined classes

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present gene...

BD - Teorie informace

  • 2006
    • •
  • Jx
Result

Relation Compositions in Fuzzy Class Theory

We investigate the notions of composition systematically in the formal framework of fuzzy class theory FCT. From a limited number of basic theorems we derive a host of corollaries which describe various laws valid for f...

BA - Obecná matematika

  • 2006
    • •
  • D
Result

Relation Compositions in Fuzzy Class Theory

We investigate the notions of composition systematically in the formal framework of fuzzy class theory FCT. From a limited number of basic theorems we derive a host of corollaries which describe various laws valid for f...

BA - Obecná matematika

  • 2006
    • •
  • A
Result

Fuzzy Class Theory as Foundations for Fuzzy Mathematics

LPi-omega is a deductive first-order theory over fuzzy logic LPi, which axiomatically captures Zadehs notion of fuzzy set and aims at giving a unified formal framework for a large part of fuzzy mathematics. An over...

AB - Dějiny

  • 2005
    • •
  • D
Result

Fuzzy Functions and Their Representations in Fuzzy Class Theory

In this contribution, we will present graded notion of fuzzy function and prove its properties w.r.t. set operations and relation compositions. Moreover, representation using a crisp function will be shown in the form of graded theorems....

BA - Obecná matematika

  • 2011
    • •
  • D
Result

Valverde-Style Representation Results in a Graded Framework

This paper generalizes the well-known representations of fuzzy preorders and similarities according to Valverde to the graded framework of Fuzzy Class Theory (FCT). The results yield a generalized construction of <...

BA - Obecná matematika

  • 2007
    • •
  • D
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