What does UML say?
The difference between primary and secondary actors is not UML. The UML specification (see UML 2.5.1 page 638) does not even define the semantics when several actors are associated with the same use-case:
Each UseCase specifies some behavior that a subject can perform in collaboration with one or more Actors. (...)
The manner in which multiple Actors participate in the UseCase depends on the specific situation on hand and is not defined in this specification. For instance, a particular UseCase might require simultaneous action by two separate Actors or it might require complementary and successive actions by the Actors. (...)
An Actor models a type of role played by an entity that interacts with the subjects of its associated UseCases.
In UML, actors are classifiers, and classifiers may be specializations of other classifiers of the same kind. So, yes, from an UML perspective, an actor can be a generalization of another actor regardless of primary or secondary.
By the way, the notation of a generalization is a big non-filled triangle shape. The small arrow head whether open or plain is not correct; it's even misleading.
Is it about roles or is it about users?
According to your narrative:
Admin
is a secondary actor because he will react according members actions. On the other hand, (...) he can do everything a Member
can.
The main question here, is to know if you speak of the users (i.e. the persons who interact with the system) or if you speak about the user's role. To help you determining that, let's reason with an extreme case: suppose you'd have an intelligent bot or an external system that would replace the Admin
(e.g. using some kind of interface); would this automated Admin
still have to be a Member
?
- If yes, the role of
Admin
seems to automatically imply the role of Member
. Generalization is ok.
- If no, the role of
Admin
in reality independent of the role of Member
and it just occurs that human users that have the admin role also have the Member
role. In this case you should not use the generalization.
Use-case value and primary vs. secondary actors
UML is neutral about that, but use-cases should in principle be of value to a user, and help the user to achieve his/her goals. Without this principle of value, there is no primary and no secondary users. Here for example Spence & Bittner's definitions:
Primary actors: (...) The primary actors are those for whom the system is built; they are those to whom the system provides sufficient economic value to warrant its construction.
Secondary actors: These are the actors that support the use cases provided by the system and those that support the system itself.
I suspect that if an Admin
generates quotes ("devis" in French in your diagram) and invoices ("Facture" in French), there are chances that it's not a secondary actor, but a primary actor.
Last but not the least, verify your usage of include
and extend
. This seems to correspond to a navigation flow or a functional decomposition (or both) of your system and not really use-cases. But I'll not develop more: for that you'd need to translate your use-cases.