数据分析的三层与三支属性约简系统研究

The attribute reduction regarding rough sets is a basic data analysis and exists extensive applications. For decision tables, the attribute reduction currently retains at only the decision classification level and applies to only the positive certainty, so it lacks systematic study from both the granular level and divided system. The attribute reduction usually uses a fundamental tool of uncertainty measures, and relevant systematic study has development significance. By virtue of the construction technology of granular computing and the division strategy of three-way decisions, this project systematically investigates three-level and three-way attribute reductions based on uncertainty measures, to clarify the scientific establishment and systematic relationship of three-level and three-way attribute reductions, and to illustrate the quantitative and qualitative application principles of attribute reductions. The main research contents include three aspects. (1) Based on three granular levels of decision tables (the macro top of the decision classification, meso middle of a decision class, and micro bottom of a condition class), the hierarchical construction and cut division of uncertainty measures are implemented. (2) At each granular level, three-way quantitative and qualitative attribute reductions regarding positive, boundary, and negative terms are constructed, and their systematic relationships are analyzed. (3) Based on the three granular levels, hierarchical relationships of three-way quantitative and qualitative attribute reductions are analyzed. According to the related study, this project establishes an in-depth and complete system of attribute reductions; thus, it extends and improves the existing research framework of attribute reductions, and it underlies data applications of quantitative and qualitative analyses regarding decision tables.

粗糙集属性约简是基本的数据分析，存在广泛应用。对于决策表，属性约简目前局限于决策分类层与肯定确定性，在粒化层次与分化体系上还缺乏系统研究。属性约简常使用不确定性度量基础工具，相关的系统研究具有开拓意义。本项目采用粒计算构建技术与三支决策剖分策略，系统研究基于不确定性度量的三层与三支属性约简，明确三层与三支属性约简的科学构建与系统关系，阐明属性约简的定量与定性应用原理。研究内容包括：（1）立足决策表三种粒度层次（决策分类宏观高层、决策类中观中层、条件类微观底层），研究不确定性度量的层次构造与截取剖分；（2）在每种粒度层次上，建立关于正、边界、负的三支定量与三支定性属性约简，研究体系关系；（3）立足三种粒度层次，研究三支定量与三支定性属性约简的层次关系。本项目将建立属性约简的深入完备系统，拓展与改进属性约简现行研究框架，为决策表定量与定性分析的数据应用奠定基础。

数据分析能够有效完成信息获取与知识发现，在多种领域的科学研究与实际应用中发挥着重要作用。在当今大数据时代，大量、多样、复杂等数据特性为数据分析提供了机遇与挑战，从而需求先进技术与体系方法的融入探索。本项目从粗糙集智能理论的属性约简数据分析入手，采用粒计算技术来构建三层属性约简，采用三支决策方法来构建三支属性约简，从而完成三横三纵的网络状属性约简系统研究，解决决策表数据分析的粒化层次单一与分化体系单一两项基本问题。主要研究内容与基本获得结果包括如下四个方面。（1）建立传统决策表、邻域决策表、模糊粗糙决策表、区间值决策表等多种形式决策表的三层粒结构，包括决策分类宏观高层、决策类中观中层、条件类微观底层。（2）立足三层粒结构，采用自底向上集成与自顶向下分解，进行不确定性度量（特别是信息度量与代数度量）的三层构建与三支构建，获得相关的度量语义、精确性、层次性、系统性、等价性、改进性、有界性、粒化单调性、集成算法等结果。（3）依托纵横交错网络及其不确定性度量的完备信息化，构建定性属性约简与定量属性约简，研究粒化单调性、扩张完备性、协调退化、约简核、约简强度、约简平衡、约简同构等性质，得到三层约简层次关系与三支约简体系关系，设计开发度量启发式约简搜索算法与结构派生式约简生成算法。（4）将相关的不确定性度量与属性约简应用于机器学习，得到距离测量、特征选择、分类学习、模式识别、决策制定、离群点检测等方面的具体成果。通过这些研究与结果，本项目揭示了数据决策表的三层三支粒计算形成机制与不确定性度量构建原理，建立了三层属性约简与三支属性约简的深入完备理论体系，改进属性约简的现行研究框架与定性定量应用功效，为数据分析理论及其智能处理应用奠定坚实基础。