## 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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