Spaces with fuzzy partitions and fuzzy sets

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 F in the category SpaceFP is introduced and it is proved that F defines a CSLAT -powerset theory in the sense of Rodabaugh.