模糊近似空间中下近似算子的新定义

首先对β算子进行了研究，得到了2个结果，并将β算子扩展为2个矩阵之间的β运算。然后依据β算子及所得结果，给出了模糊近似空间中模糊集下近似的一种解析式定义，并刻画了新定义下的粗糙模糊集的基本性质。最后与刘责龙的定义进行对比分析，举例说明刘的文章中关于截集的一个结果是错误的，并说明新的下近似算子具有一定的优越性。

A New Lower Approximation Operator in Fuzzy Approximation Spaces

In this paper two propositions of β operator are acquired and β operator is extended to matrixes＇ operation. Then a new lower approximation operator is given based on β operator and its properties. Elementary properties of the new lower approximation are established. This new lower approximation operator is superior to the definition by Liu Guilong. Finally, this paper proves that a property of lower approximation in Liu Guilong＇s paper is wrong by using an example.