区间值模糊集的粗糙度

Roughness of the interval-valued fuzzy sets

给出了粗糙区间值模糊集的概念,并研究了一些基本性质.通过引进区间值模糊集水平上、下区域的概念,解决了粗糙集理论中普遍存在的两个集合的交的上近似不等于两个集合的上近似的交(两个集合的并的下近似不等于两个集合的下近似的并)的问题.定义了区间值模糊集的粗糙度,由于区间值模糊集水平上、下区域概念的引进,得到了比普通模糊集的粗糙度更好的结果.

In this paper, the definition of the rough interval-valued fuzzy set is given and some properties of which are studied. By introducing the concepts of the level upper （lower） boundary areas of the interval-vahied fuzzy sets, the problems that the intersection of the upper approximations of two sets is unequal to the upper approximation of the intersection of two sets （ the union of the lower approximations of two sets is unequal to the lower approximation of the union of two sets） are solved, which commonly exist in the rough sets theory. At last, this paper defines the roughness of the interval-valued fuzzy sets and gets better result than that of the common fuzzy sets because of introducing the concepts of the level upper （lower） boundary area.