模糊近似空间上的粗糙模糊集的公理系统

The Axiomatic Systems of Rough Fuzzy Sets on Fuzzy Approximation Spaces

粗糙集理论是近年来发展起来的一种有效的处理不精确、不确定、含糊信息的理论 ,在机器学习及数据挖掘等领域获得了成功的应用 .粗糙集的公理系统是粗糙集理论与应用的基础 .粗糙模糊集是粗糙集理论的自然的有意义的推广 .作者研究了模糊近似空间上的粗糙模糊集的公理系统 ,用三条简洁的相互独立的公理完全刻划了模糊近似空间上的粗糙模糊集 ,同时还把作者给出的公理系统与粗糙集的公理系统做了对比 ,指出了两者的区别 .

The theory of rough sets can be used to deal with the approximation of an arbitrary subset of a universe by two definable or observable subsets called lower and upper approximation. There are at least two methods for the development of this theory, the constructive and axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. An advantage of the axiomatic approach is that it can focus on algebraic properties of approximation. This paper defines a pair of dual approximation operators of rough fuzzy sets and states an axiomatic system that must be satisfied by the operators. The axiomatic system of rough fuzzy sets on the fuzzy approximation space is studied. An independent axiomatic system that describes the upper approximation of the rough fuzzy sets is given. The upper approximation of the rough fuzzy sets is characterized by the axiomatic system. The axiomatic system of the upper approximation of the rough fuzzy sets also is compared with that of other rough sets.