F-tramsform, power set theory, monads, monadic relation

Classical F-transform for lattice-valued fuzzy sets can be defined using the Zadeh’s power set monad and a special monadic relation. In this paper we use the fact that power set structures of hesitant fuzzy sets, fuzzy soft sets or intuitionistic fuzzy sets also define power set monads and we show how by selecting appropriate monadic relations the F-transforms for these fuzzy type structures can be defined.