【作者】 付艳玲；

【导师】 秦克云；

【作者基本信息】 西南交通大学 ， 基础数学， 2006， 硕士

【摘要】 粗糙集理论是一种新的处理不确定性知识的数学工具,是由波兰科学家Pawlak在1982年首先提出来的,目前已发展成为人工智能的一个重要研究方向,在数据挖掘(data mining)与知识发现(KDD)中具有非常广泛的应用背景,并已获得许多成功的应用。 Pawlak粗糙集模型是以等价关系为基础建立的。为推广粗糙集理论的应用范围,Pawlak粗糙集模型被推广为多种形式,包括模糊粗糙集模型、概率粗糙集模型、变精度粗糙集模型以及一般二元关系下的粗糙集模型等。本文研究基于模糊粗糙集模型的模糊信息系统知识发现问题,具体作了如下研究工作: 针对模糊信息系统,定义了一种相似度量算子来描述对象关于属性的接近程度,由相似度量算子提出关于对象的模糊不可区分关系(?)_B,这是一类一般的模糊相似关系;以模糊不可区分关系为基础,在广义近似空间(U,(?)_B~α)中定义了上、下近似算子,并讨论了相关的性质。 接着,对王熙照定义的模糊约简和模糊核的实现及有关性质和定理作了适当的改进与扩充,使其更加完备化,且讨论了模糊约简与模糊相对约简的关系。 其次,提出了关于属性的模糊相对约简和模糊相对核的概念,讨论它们的基本性质,对于决策属性只有一个且决策属性值域是离散的模糊决策信息系统,设计了模糊相对区分矩阵和相对区分函数,用以求出模糊相对约简和模糊相对核。 最后,以模糊不可区分关系为基础,讨论了属性间的相互依赖关系,对更多还原

【Abstract】 Rough set theory is a new mathematical tool of dealing with uncertain information, scientist Pawlak put forward this theory at 1982. At present it has developed to be an important research direction of artificial intelligent, it has very extensive latent applying background at the field of Data Mining.Pawlak rough set was established at the base of equivalent relation. For generalizing the application area of rough set theory, Pawlak rough set model is generalized to many models included fuzzy rough set model、 probability rough set model、 alterable precision rough set model and the rough set model under the generic binary relation etc. Fuzzy information system knowledge discovery based on fuzzy rough set model is researched in this thesis. Material work is done as follows:Firstly, in allusion to fuzzy information system, a similarity measure operator is defined to describe adjacence degree of objects on attributes. Fuzzy indiscernibility relation (R|~)_b induced by the similarity measure operator takes place of a series of a kind of more generalized fuzzy similarity relations. Based on the fuzzy indiscernibility relation, upper and lower approximation operators are defined in the generalized approximation space (U,(R|~)_b~α) and some proposition is discussed.Then, some theorems or proposition about some concepts such as fuzzy reduction and fuzzy core defined by Wang Xi-zhao are modifiedand improved for more completion and relations between fuzzy reduction and fuzzy relative reduction are discussed.Secondly, some concepts such as fuzzy relative reduction and fuzzy relative core between attributes are put forward and their basal properties are discussed. For the fuzzy decision information system with a decision attribute and a discrete domain, fuzzy relative discernibility matrix and fuzzy relative discernibility function are designed to obtain fuzzy relative reduction and fuzzy relative core.At last, based on fuzzy indiscernibility relation, dependence relations each other between attributes are discussed. Knowledge is discovered for the fuzzy decision information systems with more than a decision attribute, and a method obtaining rules of fuzzy information system is proposed. An applied effective example is given.更多还原