In this paper we provide procedures for testing the existence of various types of generalized inverses in involutive residuated semigroups and involutive quantales defined by the Moore-Penrose equations, and for computing the extreme inverses whenever they exist. We also determine certain instances when $a^\dag=a^*$, whenever $a^\dag$ exists. The obtained results can be applied to a wide class of quantales of fuzzy relations and fuzzy matrices, as well as to Gelfand quantales.