中文摘要：

函数单向S-粗集对偶（dual of function one direction singular rough set）,具有单向动态特性和规律特性;它是函数S-粗集（function singular rough set）的基本形式之一。函数S-粗集是在改进S-粗集的基础上提出的。利用函数单向S-粗集对偶的动态特性和规律特性,给出^-f-规律,^-f-规律的属性特征,属性距离,^-f-冗余规律概念。利用这些概念,提出规律与它的^-f-属性控制,并给出^-f-属性控制定理,^-f-属性控制判定定理,^-f-属性控制识别准则与应用。

英文摘要：

Dual of function one direction singular rough sets has one direction dynamic characteristics and taw characteristics, and it＇s one of the basic form of the function singular rough set. The function singular rough set is put forward by reforming S-rough sets. With the aid of the dynamic characteristics and law characteristics of dual of the function one direction singular rough set, this paper puts forward the concepts of ^-f-law, the attribute characteristic of ^-f-law, attribute distance and the ^-f-redundance law. Utilizing these concepts, this paper presents the law and its ^-f-attribute control and proposes, the theorem of ^-f-attribute control, the decision theorem of ^-f-attribute control and the recognisition rule and application of f attribute control.