基于双量化近似空间的粗糙集模型相关研究

Quantification in approximate space is an important element for expansion and application of rough set model. At present, the relative quantification is a research focus, while the absolute quantification makes low progress; meanwhile, double-quantification formed by the relative and absolute quantification just starts. By using mathemaical method and granular computing method, this project mainly makes related study on rough set model in approximate space on the double-quantification; it aims to illustrate formation mechanism and application function of uncertainty, quantitative semantics, optimal computing and rough set model according to the double-quantification, and provide thoughts for description and application of the double-quantification in approximate space. The main study contents are as follows: (1) quantitative mapping and mathematical structure in approximate space are both constructed, uncertainty analyses of knowledge, concepts and rules are made; (2) a principle of parameter description on the double-quantification is provided, and basic semantics granules and basic data granules are both studied; (3) a system of region granules is explored in rough set model on the double-quantification, and the whole hierarchy structure is studied to explore both quantitative semantics extraction and optimal computing of the model; (4) expansion theory on quantitative rough set models is studied, and a system of concrete rough set models on the double-quantification and the corresponding expansion structure are both explored, and benign rough set models on the double-quantification are extracted. Based on the study, this project has provided bases for relationship analysis of granular computing and uncertainty in approximate space, and has promoted development of knowledge discovery on quantification in approximate space.

近似空间中的量化是粗糙集模型进行扩张与应用的重要元素。目前，相对量化是研究热点，绝对量化进展缓慢，两者结合形成的双量化才刚起步。本项目主要在双量化近似空间中，采用数学方法与粒计算方法，进行粗糙集模型相关研究，阐明基于双量化的不确定性、量化语义、优化计算、粗糙集模型等的形成机理与应用功效，为近似空间中的双量化描述与应用提供思路。研究内容主要包括：（1）建立量化映射，构建近似空间的数学结构，进行知识、概念、规则的不确定性分析；（2）建立双量化的参数描述原则，研究基本语义粒与基本数据粒；（3）研究双量化粗糙集模型的区域粒体系，构建整体粒层次结构，探讨模型的量化语义提取与优化计算；（4）研究量化粗糙集模型的扩张理论，构建具体双量化模型系统并研究其扩张结构，挖掘良性双量化模型实例。通过这些研究，本项目为近似空间中的粒计算与不确定性的关系分析奠定基础，并推进近似空间中关于量化的知识发现发展。

粗糙集模型存在于近似空间，基于近似空间量化的粗糙集模型相关研究具有关联于量化扩张与约简应用的基础性。目前，近似空间量化主要聚焦相对性，进而粗糙集模型采用相对量化。事实上，近似空间量化还存在绝对性，相对量化与绝对量化集成形成的双量化蕴含着粗糙集模型刻画与应用的系统性、完备性、准确性，但罕有相关的深入系统报道。本项目立足双量化基础理念，采用数学方法与粒计算技术，构建双量化近似空间，进而在其中进行粗糙集模型相关研究。主要研究内容与基本获取结果包括如下五个方面。（1）挖掘相对度量与绝对度量，构建量化映射并获得数学性质；探讨近似空间的数学结构并获得几何形态，证明了近似空间的二维特性；进行不确定性度量挖掘，建立了知识、概念、规则的不确定性刻画。（2）独立分析与并行集成精度与程度的量化阈值描述，确立了双量化的参数描述原则；研究语义粒与数据粒，得到相应的数学形态、基本结构、语义描述、优化计算。（3）构建双量化粗糙集模型，得到基本区域粒系统；搭建多层粒体系并获取整体粒层次结构，得到构建模型在不同粒层次上的语义提取与优化计算并开发了相应算法。（4）分析定量粗糙集模型对定性粗糙集模型的扩张特性，建立量化粗糙集模型的扩张理论；构建具体双量化粗糙集模型系统并研究扩张结构，选取良性双量化粗糙集模型并获得基于双量化近似空间的具体粒计算结果。（5）针对双量化粗糙集模型，利用语义度量、概率测度、信息熵等不确定性度量进行属性约简的应用研究，获得属性约简的层次体系。通过这些研究与结果，本项目构建了双量化近似空间与双量化粗糙集模型，阐明了相对与绝对双量化的数学形态、不确定性、粒计算、量化扩张、属性约简等的形成机理、相互关系、应用功效，奠定了基于粒计算的不确定性度量集成构建与基于粒计算的量化属性约简层次应用的坚实基础。