Journal
SOFT COMPUTING
Volume 21, Issue 24, Pages 7269-7284Publisher
SPRINGER
DOI: 10.1007/s00500-016-2431-4
Keywords
Space with a fuzzy partition; Category of spaces with fuzzy partitions; Fuzzy objects in sets with fuzzy partitions; Powerset theory
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Funding
- Centre of Excellence Project [LQ1602]
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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 in the category SpaceFP is introduced and it is proved that defines a CSLAT-powerset theory in the sense of Rodabaugh.
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