  The problem of minimizing finite fuzzy interpretations in fuzzy description
logics (FDLs) is worth studying. For example, the structure of a fuzzy/weighted
social network can be treated as a fuzzy interpretation in FDLs, where actors
are individuals and actions are roles. Minimizing the structure of a
fuzzy/weighted social network makes it more compact, thus making network
analysis tasks more efficient. In this work, we study the problem of minimizing
a finite fuzzy interpretation in a FDL by using the largest crisp
auto-bisimulation. The considered FDLs use the Baaz projection operator and
their semantics is specified using an abstract algebra of fuzzy truth values,
which can be any linear and complete residuated lattice. We provide an
efficient algorithm with a complexity of $O((m \log{l} + n) \log{n})$ for
minimizing a given finite fuzzy interpretation $\mathcal{I}$, where $n$ is the
size of the domain of $\mathcal{I}$, $m$ is number of nonzero instances of
atomic roles of $\mathcal{I}$ and $l$ is the number of different fuzzy values
used for instances of atomic roles of $\mathcal{I}$. We prove that the fuzzy
interpretation returned by the algorithm is minimal among the ones that
preserve fuzzy TBoxes and ABoxes under certain conditions.
