  In this article, we study the inconsistency of a system of $\max-T$ fuzzy
relational equations of the form $A \Box_{T}^{\max} x = b$, where $T$ is a
t-norm among $\min$, the product or Lukasiewicz's t-norm. For an inconsistent
$\max-T$ system, we directly construct a canonical maximal consistent subsystem
(w.r.t the inclusion order). The main tool used to obtain it is the analytical
formula which compute the Chebyshev distance $\Delta = \inf_{c \in \mathcal{C}}
\Vert b - c \Vert$ associated to the inconsistent $\max-T$ system, where
$\mathcal{C}$ is the set of second members of consistent systems defined with
the same matrix $A$. Based on the same analytical formula, we give, for an
inconsistent $\max-\min$ system, an efficient method to obtain all its
consistent subsystems, and we show how to iteratively get all its maximal
consistent subsystems.
