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Soft Computing

, Volume 21, Issue 24, pp 7269–7284 | Cite as

Fuzzy objects in spaces with fuzzy partitions

  • Jiří Močkoř
  • Michal Holčapek
Foundations

Abstract

A theory of fuzzy objects is derived in the category SpaceFP of spaces with fuzzy partitions, which generalize classical fuzzy sets and extensional maps in sets with similarity relations. It is proved that fuzzy objects in SpaceFP can be characterized by some morphisms in the category of sets with similarity relations. A powerset object functor \({\mathcal {F}}\) in the category SpaceFP is introduced and it is proved that \({\mathcal {F}}\) defines a CSLAT-powerset theory in the sense of Rodabaugh.

Keywords

Space with a fuzzy partition Category of spaces with fuzzy partitions Fuzzy objects in sets with fuzzy partitions Powerset theory 

Notes

Acknowledgements

This study was funded by the Centre of Excellence Project LQ1602.

Compliance with ethical standards

Conflict of interest

Author declares that he has no conflict of interest.

Human and animal rights

This article does not contain any studies with human participants or animals performed by the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic

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