In this article, we study the inconsistency of systems of $\min-\rightarrow$
fuzzy relational equations. We give analytical formulas for computing the
Chebyshev distances $\nabla = \inf_{d \in \mathcal{D}} \Vert \beta - d \Vert$
associated to systems of $\min-\rightarrow$ fuzzy relational equations of the
form $\Gamma \Box_{\rightarrow}^{\min} x = \beta$, where $\rightarrow$ is a
residual implicator among the G\"odel implication $\rightarrow_G$, the Goguen
implication $\rightarrow_{GG}$ or Lukasiewicz's implication $\rightarrow_L$ and
$\mathcal{D}$ is the set of second members of consistent systems defined with
the same matrix $\Gamma$. The main preliminary result that allows us to obtain
these formulas is that the Chebyshev distance $\nabla$ is the lower bound of
the solutions of a vector inequality, whatever the residual implicator used.
Finally, we show that, in the case of the $\min-\rightarrow_{G}$ system, the
Chebyshev distance $\nabla$ may be an infimum, while it is always a minimum for
$\min-\rightarrow_{GG}$ and $\min-\rightarrow_{L}$ systems.

研究模糊关系方程组的不一致性，提出计算 Chebyshev 距离的分析公式，阐述了 Chebyshev 距离作为解向量不等式的下界，在 G"odel，Goguen 和 Lukasiewicz 的蕴涵关系中的特殊情况下，Chebyshev 距离可能是下确界或最小值。