模糊近似空间中模糊粗糙集的新定义及应用

【作者】 孔平；

【导师】 张振良； 陈世联；

【作者基本信息】 昆明理工大学 ， 系统理论， 2003， 硕士

【摘要】 在很多实际的系统中均不同程度的存在着不确定性，因此，如何处理这些信息显得尤为重要，智能信息处理越来越受到广大学者的关注，成为当前信息科学与应用研究的一个热点。人们要求计算机像人脑一样，能自行识别和处理客观世界中的不确定问题。 模糊集理论是美国控制论专家扎德于1965年提出的一种处理非精确的现象的数学工具，该工具着眼于集合的模糊性，利用隶属度的概念来表示集合的模糊程度。 粗糙集理论是由波兰教授帕拉克于20世纪80年代初提出的一种研究不完备，不确定知识库和数据的表达，学习，归纳的数学工具。该数学工具着眼于集合的粗糙程度，借助于不可分辨思想来刻画集合的粗糙程度。 既然模糊集理论和粗糙集理论都可运用观察，测试数据表达知识，进行推理，因此，自然要寻求这两者的结合，即作为粗糙集描述近似空间中的知识是模糊概念时，就有模糊粗糙集理论的产生。这样我们可以利用粗糙集的概念考虑模糊集合的粗近似问题，以及利用模糊集的理论研究模糊粗糙集的模糊性。 本文在简要回忆一下模糊集和粗糙集的基本概念后，以粗糙集理论为背景，在模糊近似空间中给出了模糊粗糙集的另一种定义，讨论了该定义与文献定义的模糊粗糙集的区别，论证了本文所定义的模糊粗糙集的近似精度大于文献定义的模糊粗糙集的近似精度；利用模糊集的有关理论定义了模糊粗糙变换，讨论了模糊粗糙变换的性质，并在此基础上给出了模糊粗糙集的扩张定理；在模糊粗糙集概念的基础上，从概率论的出发点来研究模糊粗糙集，首次提出了概率模糊料糙集的概念，讨论了概率模糊粗糙近似算子的性质。研究了Bayes决策与概率模糊粗糙近似的关系，给出其在医疗诊断方面的具体应用。更多还原

【Abstract】 To some extent, uncertainty exists in most of real systems. Therefore, it is very important how to deal with these kinds of information, and intelligent information proceeding is getting more and more concerned by scholars and becomes a very hot point in theory and application of information science. People need computer to automatically recognize and manage indefinite phenomena in impersonal world. like human cerebra.Fuzzy set theory, put forward by American cybernetics expert Zadeh, is mathematician tool to conduct the inaccurate phenomena. It focuses on the blurring of sets, and explains the extent of inaccuracy of sets using the concept of membership function.Rough set theory, put forward by professor Pawlak, in the early of 20 century 80’s, is a method to study the expression and leaning of incomplete or uncertain knowledge base. The method focuses on the roughness of sets, uses no-division concept to express the roughness of sets.Naturally a combination of these two theories can be searched since fuzzy set theory and rough set theory can be used to express knowledge through observing and testing datum. That is, the fuzzy rough set theory comes into being. When the knowledge described in approximate unite is fuzzy notion. Under such circumstance we may analyze rough approximation problems by rough set theory, and study roughness of fuzzy rough set by fuzzy set theory.In this article, after recalling the basis concepts of fuzzy set and rough set , anew definition of fuzzy rough set is offered, and the deference between the definition and that of given in document is discussed, the approximate accuracy is larger than that of given in document. Using fuzzy set theory, fuzzy rough conversion is defined and its properties are discussed, and the extension theorem of fuzzy rough set is given. Based on fuzzy rough set theory and probability theory, a kind of probability fuzzy rough set is given first, moreover, it’s properties are given and its application in medical diagnose is discussed.更多还原