The problem of minimizing fuzzy interpretations in fuzzy description logics (FDLs) is important both theoretically and practically. For instance, fuzzy or weighted social networks can be modeled as fuzzy interpretations, where individuals represent actors and roles capture interactions. Minimizing such interpretations yields more compact representations, which can significantly improve the efficiency of reasoning and analysis tasks in knowledge-based systems. We present the first algorithm that minimizes a finite fuzzy interpretation while preserving fuzzy concept assertions in FDLs without the Baaz projection operator and the universal role, under the Gödel semantics. The considered class of FDLs ranges from the sublogic of $f\!\mathcal{ALC}$ without the union operator and universal restriction to the FDL that extends $f\!\mathcal{ALC}_{reg}$ with inverse roles and nominals. Our algorithm is given in an extended form that supports approximate preservation: it minimizes a finite fuzzy interpretation $\mathcal{I}$ while preserving fuzzy concept assertions up to a degree $γ\in (0,1]$. Its time complexity is $O((m\log{l} + n)\log{n})$, where $n$ is the size of the domain of $\mathcal{I}$, $m$ is the number of nonzero instances of atomic roles in $\mathcal{I}$, and $l$ is the number of distinct fuzzy values used in such instances plus 2. Methodologically, our approach fundamentally differs from existing ones, as it avoids quotient constructions traditionally employed for minimizing fuzzy interpretations and fuzzy automata.

翻译：模糊描述逻辑（FDLs）中模糊解释的最小化问题在理论和实践层面均具有重要意义。例如，模糊或加权社交网络可建模为模糊解释，其中个体代表参与者，角色捕捉交互关系。最小化此类解释能产生更紧凑的表示形式，从而显著提升基于知识的系统中推理与分析任务的效率。本文提出了首个在Gödel语义下最小化有限模糊解释的算法，该算法能在不含Baaz投影算子与全称角色的FDLs中保持模糊概念断言。所考虑的FDLs类别涵盖从无并集算子与全称限制的$f\!\mathcal{ALC}$子逻辑，到扩展了逆角色与命名个体的$f\!\mathcal{ALC}_{reg}$。我们以扩展形式给出该算法，支持近似保持：在最小化有限模糊解释$\mathcal{I}$的同时，将模糊概念断言保持至$γ\in (0,1]$的程度。其时间复杂度为$O((m\log{l} + n)\log{n})$，其中$n$为$\mathcal{I}$论域大小，$m$为$\mathcal{I}$中原子角色非零实例的数量，$l$为此类实例中使用的不同模糊值数量加2。在方法论层面，我们的方法与现有方法存在根本差异，其避免了传统用于最小化模糊解释与模糊自动机的商构造。