Spaces with fuzzy partitions and fuzzy transform.

A category of spaces with fuzzy partitions is introduced, which could serve as a ground category for F-transform constructions. Axioms of fuzzy transformations systems are defined, and it is proved that the upper F-transform is the only fuzzy transformation satisfying these axioms. Relationships among the category of fuzzy partitions, categories of Kuratowski closure and interior operators and the category of fuzzy preorder relations are investigated. [ABSTRACT FROM AUTHOR]