粗糙集理论中的知识获取与约简方法的研究
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摘要
粗糙集理论是一种能够有效分析和处理不精确、不一致、以及不完整信息的数学工具。该理论与概率论、模糊集理论和证据理论等其它处理不确定性问题的方法相比,不需要提供解决问题所需的数据集以外的先验知识。经过近三十年的发展,该理论已经被广泛应用于机器学习、近似推理、专家系统、数据挖掘、决策分析、图像处理、医疗诊断、金融数据分析等诸多领域。
粗糙集研究的领域包括,粗糙集模型拓展的研究、知识获取与约简、知识的不确定性度量等,其中知识获取方法和约简算法是粗糙集理论研究中的关键问题。因此,本文主要以拓展粗糙集模型为研究方法,深入研究粗糙集理论中的知识获取方法和约简算法,其主要研究工作和创新内容有如下几点：
(1)针对差异关系粗糙集模型只能解决具有遗漏型未知属性值的不完备决策信息系统中的否定决策规则的获取和简化,不能处理具有丢失型未知属性值的不完备决策信息系统；而概率粗糙集模型虽然可以获得否定决策规则,但是难于约简的缺陷,提出了基于描述子的否定支持集的粗糙集模型,研究了具有丢失型未知属性值的不完备决策信息系统中的否定决策规则获取的问题,提出了一种保持条件描述子否定支持集的下、上近似分布不变的分辨矩阵约简算法。采用上述方法在学生成绩评价信息系统上进行了实例分析,结果表明了其有效性。
(2)针对现有的粗糙集模型不能从不完备和有噪声的决策信息系统中同时获取肯定和否定决策规则并进行约简的缺陷,提出了一种基于变精度描述子的粗糙集模型,研究了不完备和有噪声的决策信息系统中的肯定和否定决策规则的获取问题。为了获取简化的肯定和否定决策规则,提出了基于条件描述子支持集不变的知识约简方法,可以同时简化肯定和否定决策规则。但是,该方法不能得到极优的肯定决策规则和极优的否定决策规则,因此进一步提出了一种保持肯定决策类(或否定决策类)正域分布一致的启发式约简算法,用于获取极优的肯定决策规则(或极优的否定决策规则)。上述方法应用于学生成绩评价系统的实例分析中,结果表明了其有效性。
(3)针对乐观多粒度粗糙集的下近似决策过于宽松,而悲观多粒度粗糙集的下近似决策又过于严格的缺点,提出了一种可变多粒度粗糙集模型,通过引入参数β来控制满足条件的粒度空间的数目,使其克服乐观多粒度和悲观多粒度粗糙集的上述缺陷。研究了可变多粒度粗糙集的性质,证明了可变多粒度粗糙集是乐观多粒度和悲观多粒度粗糙集的泛化,乐观多粒度和悲观多粒度粗糙集是可变多粒度粗糙集的特例。讨论了可变多粒度粗糙集中的度量因子,证明了可变多粒度粗糙集的几种度量都介于乐观多粒度和悲观多粒度粗糙集的度量之间。进一步讨论了可变多粒度粗糙集中的决策规则的获取方法,提出了获取确定性决策规则和可信性决策规则的判定定理,给出了可变多粒度粗糙集中基于属性依赖度的下、上近似分布约简的启发式算法。该理论进一步发展和完善了多粒度粗糙集的决策支持理论。
Rough sets theory (RST) is a mathematical tool, which can effectively analysis and process inaccurate, inconsistency, incomplete information. Compared with some other theories such that probability theory, fuzzy set and evidence theory, RST does not need any prior knowledge except data sets. With over30years development, rough set has been widely applied to many areas, such as machine learning, approximate reasoning, expert system, data mining, decision analysis, image processing, medical diagnosis, financial data analysis and so on.
Rough set research areas include rough set model development research, knowledge acquisition and reduction, measurement of knowledge uncertainty, etc, the method of knowledge acquisition and reduction are keies in the RST. Therefore, this dissertation aims to study of the RST based on the decision rules acquisition and reduction algorithm, the main work and contributions are summarized as following:
(1) Through the analysis of differences relation based rough set and probabilistic rough set, the former is only suitable for acquisition and reduction of negative decision rules in missing type Incomplete Decision Information System(IDIS), however, it is not suitable for handling the lossing type IDIS; the later can obtian negative decision rules, but has no reduction. In this dissertation, rough set model based on descriptors's negative support set is proposed to acquire negative decision rules in lossing type IDIS. The lower/upper approximate distribution reduct based on discernibility matrix is presented, which can preserve the lower/upper approximation distribution about the descriptors's negative support set. Some numureical examples of student global evaluation are employed to substantiate the conceptual arguments.
(2) Existing rough set model can not be used to acquire positive and negative decision rules in incomplete and noised decision information systems. In this dissertation, the variable precision rough set (VPRS) based on descriptors is proposed to investigate the positive and negative decision rules in incomplete and noised decision information systems. The descriptors reduction is presented, which can simplify the positive and negative decision rules at the same time. However, this method can not obtain the optimal positive and negative decision rules. Therefore, a heuristic reduction algorithm is presented, which can preserve the positive region distribution consistent about positive decision class (negative decision class). And the results of examples about student global evaluation show its effectiveness.
(3) To overcome the limitations of the optimistic multigranulation rough set (OMRS) be too relaxed and the pessimistic multigranulation rough set (PMRS) be too strict, the variable multigranulation rough set (VMRS) is presented, in our VMRS, the threshold β, is used to control the number of granulations. It is proven that VMRS is ageneralization of OMRS and PMRS, OMRS and PMRS is the special case of VMRS. Furthermore, several important measurements are introduced into VMRS; it is shown that the measurements of VGRS are between the measurements of OMRS and PMRS. Some methods of acquisition of decision rules in VMRS are deeply discussed and its judgment theorem is also presented. The reductions of VMRS are investigated and the heuristic reduction algorithms based on attribute dependency are proposed, which can preserve lower/upper approximate distribution consistent. These results are meaningful both in the theory and applications for multigranulation rough set.
粗糙集研究的领域包括,粗糙集模型拓展的研究、知识获取与约简、知识的不确定性度量等,其中知识获取方法和约简算法是粗糙集理论研究中的关键问题。因此,本文主要以拓展粗糙集模型为研究方法,深入研究粗糙集理论中的知识获取方法和约简算法,其主要研究工作和创新内容有如下几点：
(1)针对差异关系粗糙集模型只能解决具有遗漏型未知属性值的不完备决策信息系统中的否定决策规则的获取和简化,不能处理具有丢失型未知属性值的不完备决策信息系统；而概率粗糙集模型虽然可以获得否定决策规则,但是难于约简的缺陷,提出了基于描述子的否定支持集的粗糙集模型,研究了具有丢失型未知属性值的不完备决策信息系统中的否定决策规则获取的问题,提出了一种保持条件描述子否定支持集的下、上近似分布不变的分辨矩阵约简算法。采用上述方法在学生成绩评价信息系统上进行了实例分析,结果表明了其有效性。
(2)针对现有的粗糙集模型不能从不完备和有噪声的决策信息系统中同时获取肯定和否定决策规则并进行约简的缺陷,提出了一种基于变精度描述子的粗糙集模型,研究了不完备和有噪声的决策信息系统中的肯定和否定决策规则的获取问题。为了获取简化的肯定和否定决策规则,提出了基于条件描述子支持集不变的知识约简方法,可以同时简化肯定和否定决策规则。但是,该方法不能得到极优的肯定决策规则和极优的否定决策规则,因此进一步提出了一种保持肯定决策类(或否定决策类)正域分布一致的启发式约简算法,用于获取极优的肯定决策规则(或极优的否定决策规则)。上述方法应用于学生成绩评价系统的实例分析中,结果表明了其有效性。
(3)针对乐观多粒度粗糙集的下近似决策过于宽松,而悲观多粒度粗糙集的下近似决策又过于严格的缺点,提出了一种可变多粒度粗糙集模型,通过引入参数β来控制满足条件的粒度空间的数目,使其克服乐观多粒度和悲观多粒度粗糙集的上述缺陷。研究了可变多粒度粗糙集的性质,证明了可变多粒度粗糙集是乐观多粒度和悲观多粒度粗糙集的泛化,乐观多粒度和悲观多粒度粗糙集是可变多粒度粗糙集的特例。讨论了可变多粒度粗糙集中的度量因子,证明了可变多粒度粗糙集的几种度量都介于乐观多粒度和悲观多粒度粗糙集的度量之间。进一步讨论了可变多粒度粗糙集中的决策规则的获取方法,提出了获取确定性决策规则和可信性决策规则的判定定理,给出了可变多粒度粗糙集中基于属性依赖度的下、上近似分布约简的启发式算法。该理论进一步发展和完善了多粒度粗糙集的决策支持理论。
Rough sets theory (RST) is a mathematical tool, which can effectively analysis and process inaccurate, inconsistency, incomplete information. Compared with some other theories such that probability theory, fuzzy set and evidence theory, RST does not need any prior knowledge except data sets. With over30years development, rough set has been widely applied to many areas, such as machine learning, approximate reasoning, expert system, data mining, decision analysis, image processing, medical diagnosis, financial data analysis and so on.
Rough set research areas include rough set model development research, knowledge acquisition and reduction, measurement of knowledge uncertainty, etc, the method of knowledge acquisition and reduction are keies in the RST. Therefore, this dissertation aims to study of the RST based on the decision rules acquisition and reduction algorithm, the main work and contributions are summarized as following:
(1) Through the analysis of differences relation based rough set and probabilistic rough set, the former is only suitable for acquisition and reduction of negative decision rules in missing type Incomplete Decision Information System(IDIS), however, it is not suitable for handling the lossing type IDIS; the later can obtian negative decision rules, but has no reduction. In this dissertation, rough set model based on descriptors's negative support set is proposed to acquire negative decision rules in lossing type IDIS. The lower/upper approximate distribution reduct based on discernibility matrix is presented, which can preserve the lower/upper approximation distribution about the descriptors's negative support set. Some numureical examples of student global evaluation are employed to substantiate the conceptual arguments.
(2) Existing rough set model can not be used to acquire positive and negative decision rules in incomplete and noised decision information systems. In this dissertation, the variable precision rough set (VPRS) based on descriptors is proposed to investigate the positive and negative decision rules in incomplete and noised decision information systems. The descriptors reduction is presented, which can simplify the positive and negative decision rules at the same time. However, this method can not obtain the optimal positive and negative decision rules. Therefore, a heuristic reduction algorithm is presented, which can preserve the positive region distribution consistent about positive decision class (negative decision class). And the results of examples about student global evaluation show its effectiveness.
(3) To overcome the limitations of the optimistic multigranulation rough set (OMRS) be too relaxed and the pessimistic multigranulation rough set (PMRS) be too strict, the variable multigranulation rough set (VMRS) is presented, in our VMRS, the threshold β, is used to control the number of granulations. It is proven that VMRS is ageneralization of OMRS and PMRS, OMRS and PMRS is the special case of VMRS. Furthermore, several important measurements are introduced into VMRS; it is shown that the measurements of VGRS are between the measurements of OMRS and PMRS. Some methods of acquisition of decision rules in VMRS are deeply discussed and its judgment theorem is also presented. The reductions of VMRS are investigated and the heuristic reduction algorithms based on attribute dependency are proposed, which can preserve lower/upper approximate distribution consistent. These results are meaningful both in the theory and applications for multigranulation rough set.
引文
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