Fuzzy objects in spaces with fuzzy partitions

Fuzzy objects in spaces with fuzzy partitions

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 s...

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Veröffentlicht in:Soft computing (Berlin, Germany) Germany), 2017-12, Vol.21 (24), p.7269-7284
Hauptverfasser: Močkoř, Jiří, Holčapek, Michal
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Artificial Intelligence
Computational Intelligence
Control
Engineering
Equality
Foundations
Fuzzy sets
Mathematical Logic and Foundations
Mechatronics
Partial differential equations
Robotics
Set theory
Similarity
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Beschreibung
Zusammenfassung: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 F in the category SpaceFP is introduced and it is proved that F defines a CSLAT -powerset theory in the sense of Rodabaugh.
ISSN:1432-7643
1433-7479
DOI:10.1007/s00500-016-2431-4