【作者】 朱峰；

【导师】 张雪峰；

【作者基本信息】 东北大学 ， 运筹学与控制论， 2008， 硕士

【摘要】 粗糙集是由波兰数学家Pawlak首先提出的一种处理不完备和不确定性知识的新型数学工具,已经在机器学习、决策分析、知识获取、模式识别和专家系统等领域取得了一些成功的应用。但是,随着对粗糙集研究地不断深入,粗糙集模型的局限性也逐渐暴露出来。由于利用粗糙集理论处理的分类必须是完全正确或肯定的,而且必须是离散型数据,这样致使大量有用信息在数据提取及其离散化过程中丢失,粗糙集的这一局限性限制了它的应用。于是,近年来许多学者从多方面对粗糙集模型进行推广,出现了实数粗糙集模型、变精度粗糙集模型、概率粗糙集模型、广义粗糙集模型、模糊粗糙集模型等,并且与其它学科相结合,取得了巨大成果。实数粗糙集模型是在标准粗糙集模型中引入误差率,并且基于广义相关度的概念下,去掉了数据离散化这一步骤,大大减少了在数据处理过程中信息减少造成的不良后果,增强了粗糙集模型的抗噪声能力和对新数据的预测能力。本文主要是基于实数粗糙集模型,对连续信息系统的属性约简算法进行研究。第一章绪论部分,主要介绍Pawlak粗糙集理论研究的概况,以及它研究的主要方面和需要解决的问题。第二章在引入知识和知识库的概念之后,介绍Pawlak粗糙集的模型、信息系统、属性约简以及辨识矩阵的方法。第三章主要是引入广义重要度的概念,并在此基础上定义实数粗糙集,基于实数粗糙集的连续属性值决策系统的属性约简的问题,给出实际的算法和算例。第四章主要从区间数决策系统的排序问题以及属性约简的实现,通过算例说明算法的有效性和可行性。第五章是根据以前各章介绍的内容开发一个基于粗糙集的属性约简系统,输入数据后可以自动生成属性约简,以及对区间数进行排序等。第六章根据粗糙集理论提出在多个决策表中提取规则的方法,在不同支持水平下,提取不同的规则：可以分为两个水平,第一水平下其中一个决策表支持而与另一个决策表没有冲突,第二水平下两个决策表都支持的决策规则。对每一水平下,都可根据决策表提取一定的规则。结论部分总结全文,并对以后的研究做出展望。更多还原

【Abstract】 Rough set model (RSM) is a new mathematical approach to uncertain and vague data analysis, which is proposed by mathematician Pawlak. The application of rough set theory for machine learning, knowledge acquisition, decision analysis, expert system and pattern recognition has been proved to be very successful.But with the development of RSM, the limitation of RST is exposed gradually. The classification of object must be correct and positive. This led to some useful information were lost during the process of rule extraction which limits the applications of RSM. In recent years, a lot of scholars extend RST from many aspects, such as VPRS model, probabilistic rough sets model, generalized rough sets model and fuzzy rough sets model and so on.The real rough set (RRS) model was proposed to deal with consecutive attribute decision-making table. It introduces the error rate and gets rid of the step of scattering data based on generalized degree of magnitude. It reduces the kickback from decreasing information in data processing, and boosts up the ability of resisting interference and forecasting new data.In this paper, we mainly studies attribution reduction of the information system based on the RRS model. There are six chapters in this paper. In the first chapter,it mainly introduces the situation of Pawlak rough set theory and it’s mostly aspects of investigation. In the second chapter, the basic conception of Pawlak rough set model, the information system, attribute reduction. In the third chapter, broad sense attribute significance and RRS model and attribute reductions of RRS model are introduced. At the same time the methods of them were given. A practical example is given to explain the validity and feasibility of algorithms.In the forth chapter, interval numbers attributer decision making is introduced, and attribute reductions are introduced in two methods.A practical example is given to explain the validity and feasibility of algorithms. In the fifth chapter, a system of attributes reduction based on RRS is empoldered. The system can automatic give the reduction of attributes and compositor interval numbers when data was imported. In the sixth chapter, we study rule induction from two decision tables as abasis of rough set analysis of more than on decision.We point out that the set of all decision rules from two decision tables can be splited in two levels:a first level decision rule is positively supported by a decision table and does not have any conflict with the other decision table and a second level decision rule is positively supported by decision tables.To each level, we propose rule induction methods based on decision matrices.Through the discussions, we demonstrate that many kinds of rule inductions are conceivable.In the last part, the summarization of this paper and the expectation of scientific research in the futher are given.更多还原