For a completely distributive De Morgan algebra L, we develop a general framework of L-fuzzy rough sets. Said precisely, we introduce a pair of L-fuzzy approximation operators, called upper and lower L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. It is shown that the proposed approximation operators are a common extension of the L-fuzzifying approximation operators derived from L-fuzzy relations (INS 2019) and the approximation operators derived from general neighborhood systems (KBS 2014). Furthermore, we investigate the unary, serial, reflexive, transitive and symmetric conditions in general L-fuzzifying neighborhood systems, and then study the associated approximation operators from both a constructive method and an axiomatic method. Particularly, for transitivity (resp., symmetry), we give two interpretations, one is an appropriate generalization of transitivity (resp., symmetry) for L-fuzzy relations, and the other is a suitable extension of transitivity (resp., symmetry) for general neighborhood systems. In addition, for some special L-fuzzifying approximation operators, we use single axiom to characterize them, respectively. At last, the proposed approximation operators are applied in the research of incomplete information system, and a three-way decision model based on them is established. To exhibit the effectiveness of the model, a practical example is presented.

对于完全分布的De Morgan代数L，我们开发了L模糊粗糙集的一般框架。精确地说，我们引入一对大号-Fuzzy近似算，上部称为和下部大号从一般衍生-fuzzifying近似算大号-fuzzifying附近的系统。结果表明，拟议的近似算子是从L-模糊关系（INS 2019）和一般邻域系统（KBS 2014）衍生的L-模糊化近似算子的共同扩展。此外，我们研究了一般L中的一元，连续，自反，及物和对称条件-模糊化邻域系统，然后从构造方法和公理方法中研究关联的近似算子。特别是，对于传递性（resp。，对称），我们给出两种解释，一种是对L-模糊关系的传递性（resp。，对称）的适当概括，另一种是传递性（resp。，对称）的适当扩展。用于一般的邻里系统。另外，对于一些特殊的L-模糊化近似算子，我们分别使用单个公理来表征它们。最后，将提出的近似算子应用于不完备信息系统的研究中，建立了基于它们的三向决策模型。为了展示该模型的有效性，给出了一个实际的例子。