模糊形式背景下的类近似算子

Similarity Approximation Operators in Fuzzy Formal Context

分别在形式背景和模糊形式背景下定义类下近似算子和类模糊下近似算子,并研究它们的性质。证明这两种算子分别等价于形式背景和模糊形式背景下的*算子和模糊*算子。进一步给出类下近似算子与类模糊下近似算子的公理刻画。最后,对偶地讨论类上近似算子和类模糊上近似算子的定义和性质。

This paper studies rough approximations in formal contexts. A novel concept of similarity lower approximation operator is proposed, and the properties of the approximation operators is discussed. It is proved that the similarity lower approximation operator is equivalent to the ＊ operator in a formal context. The aximatic characterization of this operator is then examined. In a fuzzy formal context, by use of the representation theorem, the similarity fuzzy lower approximation operator is also introduced. Finally, we study by duality the similarity upper approximation operator and similarity fuzzy upper approximation operator respectively.