中文摘要：

模糊粗集是粗集的模糊化。现有模糊粗集大多建立在t-范数、模糊（t-）相似关系以及对偶原理基础之上。本文将模糊知识（模糊数据）的属性值集[0，1]拓广到一般完备格，基于一般二元模糊关系、模糊合取算子以及模糊合取和模糊蕴涵间的“伴随”关系研究一类模糊粗近似算子。本文对一般模糊粗集的代数结构做了详尽的探讨，并研究了新的模糊粗集与经典粗集和模糊粗集之间的联系。结论表明：粗集的这种模糊化方法保持了Pawlak粗集的代数性质；所提出的模糊粗集是现有典型模糊粗集的一般化；而且，模糊粗近似的贴近度得以提高。

英文摘要：

Fuzzy rough set is a fuzzification of rough set with fuzzy logic. Existing typical fuzzy rough sets were defined on the basis of t-norms, fuzzy （t-）similarity relations, as well as the duality principle. This paper studies a class of fuzzy rough approximation operators based on a general binary fuzzy relation, a fuzzy conjunction operator, as well as the adjunction between the conjunction and a fuzzy implication operator by extending the value set [-0,1-] of attributes of fuzzy knowledge to a complete lattice. The algebraic structure of the generalized fuzzy rough sets and the relationship of the fuzzy rough sets with existing rough sets and with existing typical fuzzy rough sets are explored. Conclusions show that the fuzzification of rough sets preserves the algebraic properties of Pawlak rough sets. The proposed fuzzy rough sets can be regarded as the generalization of existing typical fuzzy rough sets. Moreover, the close degree of the generalized fuzzy rough approximations is enhanced.