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Topological Approach to Fuzzy Sets and Fuzzy Logic

  • R. F. Albrecht
Conference paper

Abstract

We show how fuzzy set theory and fuzzy logic can be described by classical topology. The basic concepts are filter and ideal bases and morphisms on these. Logics are introduced as hierarchies of valuated objects and the valuations are uniformly topologized to represent approximations to logical terms. As selected applications we consider contractive mappings, roundings, hierarchical filter bases (“pyramids”), adaptable networks.

Keywords

Fuzzy Logic Complete Lattice Adaptable Network Ideal Base Neighborhood System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer-Verlag Wien 1999

Authors and Affiliations

  • R. F. Albrecht
    • 1
  1. 1.Faculty of Natural ScienceUniversity of InnsbruckInnsbruckAustria

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