Abstract We present a general method that can be used to unify the theoretical results for several new MV-valued fuzzy sets, such as intuitionistic fuzzy sets, neutrosophic fuzzy sets, fuzzy soft sets, or multivalued fuzzy sets and their mutual combinations. The results created in this way have properties identical to analogous results for classic MV-valued fuzzy sets, and it is not necessary to prove these results separately for each new type of fuzzy sets. To illustrate this general method, we will show how two related fuzzy Chang topologies can be derived in these new types of fuzzy sets from general approximation spaces.

A category of fuzzy type automata in monads (in clone form) is introduced. A monad of extensional fuzzy sets in sets with similarity relations and a monad of fuzzy objects in spaces with fuzzy partitions are introduced and relationships between fuzzy automata in sets with similarity relation or in spaces with fuzzy partitions, on one hand, and fuzzy type automata in corresponding monads, on the other, are investigated.

Functors with objects functions representing fuzzy objects in some categories of sets with similarity relations are defined and relationships between these functors are investigated. For fuzzy objects some closure operators are introduced and continuity of functors of fuzzy objects with respect to these closure operators is investigated.