  In folksonomies, users use to share objects (movies, books, bookmarks, etc.)
by annotating them with a set of tags of their own choice. With the rise of the
Web 2.0 age, users become the core of the system since they are both the
contributors and the creators of the information. Yet, each user has its own
profile and its own ideas making thereby the strength as well as the weakness
of folksonomies. Indeed, it would be helpful to take account of users' profile
when suggesting a list of tags and resources or even a list of friends, in
order to make a personal recommandation, instead of suggesting the more used
tags and resources in the folksonomy. In this paper, we consider users' profile
as a new dimension of a folksonomy classically composed of three dimensions
<users, tags, ressources> and we propose an approach to group users with
equivalent profiles and equivalent interests as quadratic concepts. Then, we
use such structures to propose our personalized recommendation system of users,
tags and resources according to each user's profile. Carried out experiments on
two real-world datasets, i.e., MovieLens and BookCrossing highlight encouraging
results in terms of precision as well as a good social evaluation.
