【作者】 操海燕；

【导师】 吕跃进；

【作者基本信息】 广西大学 ， 管理科学与工程， 2008， 硕士

【摘要】 粗糙集理论是处理模糊和不确定性问题的一个重要的数学工具,它的特点是不需要任何先验信息,已经在决策分析、知识获取、模式识别、医疗诊断、金融分析等领域取得了成功的应用。属性约简的研究是粗糙集理论是核心内容之一,寻找信息系统的最优约简或全部约简已被证明是一个NP-HARD问题。本文在变精度粗糙集的属性约简及应用方面做了如下主要研究:研究了变精度粗糙集的属性约简算法。本文从分类质量和等价类这两个层次上各提出了一个属性约简算法。基于分类质量层次提出了信息度和重要度加权的变精度粗糙集的约简算法,这个算法综合考虑了属性所包含的信息量和属性区分对象多少这两个因素,进一步提高了约简的质量。另外提出了基于等价类层次的变精度的粗糙集的属性约简算法,这个算法确保得到真正的约简。实例表明,算法是有效的。论文还研究了变精度粗糙集属性约简在沪深A股分析中的应用。作者选出了在2008年1月8日前15个交易日内,涨幅在50%以上的37只股票为研究对象,以收益、资产收益率等8个指标为属性,建立了一个应用模型。经过数据预处理,利用信息度和重要度加权的约简算法进行了约简,得出了约简。在约简的基础上,用SAS统计分析软件进行了非线性回归分析,结论是显著的,在约简的基础上大大简化了分析复杂度。此应用进一步拓展了变精度粗糙集在金融分析领域的应用,具有一定的创新性与实用性。更多还原

【Abstract】 Rough set theory is an important mathematical approach to uncertain and vague problem analysis. The main advantage of rough set theory is that it does not need any additional information. Rough set theory has been applied successfully for the field of decision analysis, knowledge acquisition, pattern recognition, medical diagnosis, financial analysis and soon.A study of attribute reduction is a very important aspect of rough set. It was proved that find optimal or all reduction is a Np-hard problem. This text does the following research for attribute reduction and application on the rough set of variable precision.Study attribute reduction algorithm of variable precision rough set. This article proposes two attribute reduction algorithms from the classification quality level and equivalent level. Based on the level of classification quality proposes weight of information quantity and important degree reduction algorithm, the algorithm considers two factors: the attributes of the information quantity and the attributes can distinguish the number of objects, improve the quality of the reduction. In addition, reduction algorithm based on equivalent level insures the reduction is a true reduction. And demonstrate algorithms by examples. The examples show that the algorithm is effective.Research the application of attribute reduction of variable precision rough set in the Shanghai and Shenzhen A-share analysis. The author elected 37 stocks which raise more than 50 percent in the 15 trading days before January 8, 2008, earnings per share, net assets yield etc. 8 stocks’ indicators are attributes, establishment of a model application. After data preprocessing, use the reduction algorithm of weighted of information quantity and importance degree, get the reduction, on the basis of Reduction, use SAS Statistical analysis software has a non-linear regression analysis to the reduction model, the conclusion is signification, greatly simplifying the analysis of complexity. Further expand the application of the variable precision rough set in the financial analysis, have some innovative and practical.更多还原