Involutions on Different Goguen L-fuzzy Sets

J.A. Goguen introduced the L-fuzzy sets (that are extension of Zadeh’s fuzzy sets), in which the image set of the membership function is an ordered set $$(L, \le _L)$$ (base set of the L-fuzzy set). Since then, a lot of papers studying different classes of those sets have been published. One of the main topics in this field has been the involutions in each set L, but these involutions are not totally independent. So the present paper is devoted to relate the involutions on the base sets L of some L-fuzzy sets, being L a certain bounded lattice. In particular, we consider L being the bounded lattices defined by [0, 1] and $$[0,1]^2$$ , as well as by the base sets of the Atanassov’s and interval-valued fuzzy sets.