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一个粗糙集代数是由集合代数加上一对对偶近似算子构成的。首先研究了两种类型的基于覆盖的粗糙集代数的相关性质,可以得到在经典覆盖的情形下,粗糙集代数没有很好的性质。为此,引入了单调的覆盖的概念,进而讨论了在单调覆盖的情形下粗糙集代数的相关性质,得到了许多很好的结果。
A rough set algebra is composed of set algebra plus a pair of dual approximation operators. First of all, we study the correlation properties of two types of cover-based rough set algebra. It can be seen that rough set algebra does not have good properties under classical coverage. To this end, the concept of monotone coverage is introduced, and then the relative properties of rough set algebra under monotone coverage are discussed. Many good results are obtained.