序决策系统属性约简的优势粗糙集方法研究

The ordered decision system is a common kind of information systems in real life, where condition and decision attribute values are ordered and there exists a monotonicity constraint between them, that is, the object with better descriptions should not be assigned to a worse decision class. Attribute reduction is one of the key issues in rough set theory and its extensions. Dominance-based rough set approach is considered as an important branch of rough set theory because it takes users' preferences into consideration. The main objective of this project is to research on attribute reduction for ordered decision systems based on dominance- based rough set approach. The contents of this project are as follows. The discernibility matrix is constructed to perform attribute reduction for ordered decision systems within the framework of dominance-based rough set approach, and to reduce the computational complexity, only minimal elements that cannot be absorbed by any other elements are located in the discernibility matrix by the sample pair selection technique. Reducts preserving generalized decisions are proposed in inconsistent set-valued ordered decision systems, and the discernibility matrix and its corresponding Boolean function are presented to enumerate all reducts. Rank mutual information based feature selection is proposed for ordered decision systems with the help of different feature selection criteria such as Max-Dependency, min-Redundancy-Max-Relevance and Max-Relevance-Max- Significance. Two new relations between granular structures, the granular equality relation and granularly finer relation, are introduced through the use of their respective Boolean relation matrices, and a novel axiomatic definition of information granularity is given to satisfy the constraints regarding these two relations. These researches shall enrich and flourish the dominance-based rough set approach, both in theory and in practice, and lay a theoretical foundation for further investigation on ordered decision systems.

序决策系统是现实生活中一类常见的信息系统，其中条件属性值和决策属性值是有序的且满足单调性约束条件。属性约简是粗糙集理论及其扩展模型的核心问题之一。优势粗糙集理论是粗糙集理论的一个重要分支，本项目拟用优势粗糙集方法研究序决策系统的属性约简问题。具体内容包括：构造辨识矩阵来求解序决策系统保持分类质量的约简以及利用样本对选择技术确定极小元素以提高计算约简的效率；在不一致集值序决策系统中提出保持广义决策的约简以及构造辨识矩阵计算系统的此类约简；对序决策系统提出基于序互信息的特征选择方法，其中选择标准包括最大依赖性、最小冗余最大相关性、最大相关最大重要性；根据粒结构的几何特征提出粒相等关系和粒精细关系，由此提出一种新的信息粒度理论、建立粒结构不确定度量的新模型。本项目旨在进一步丰富和推广优势粗糙集理论及其应用，为深入研究序决策系统打下理论基础。

序决策系统是现实生活中一类常见的信息系统，其中条件属性值和决策属性值是有序的且满足单调性约束条件。结合模糊集理论、最优化理论和不确定理论，本项目利用优势粗糙集方法研究序决策系统的属性约简问题。具体研究内容包括：序决策系统属性约简的辨识矩阵方法及其简化、不一致直觉模糊序决策系统的两种新型相对约简、不完备信息系统三种近似算子的序关系、基于粒结构几何特征的信息粒度、基于优化方法的直觉模糊新型运算、q-阶正交模糊集的基本概念与聚合算子、基于可信性测度的两种积分形式。取得的重要结果有：(1)利用样本对选择技术简化辨识矩阵计算序决策系统的所有约简；(2)提出了不一致直觉模糊序决策系统的部分一致约简和可能约简；(3)给出了不完备信息系统点近似、子集近似、概念近似关于集合包含关系的Hasse图；(4)引入了知识结构的粒相等关系和粒精细关系，进而给出了信息粒度的公理化定义；(5)根据最优化理论诱导出了直觉模糊值的减法和除法运算；(6)提出了q-阶正交模糊集的相关系数、幂平均算子以及基于Einstein运算和Dombi运算的聚合算子并给出了在聚类分析和决策分析中的应用；(7)提出了可信性空间上的范积分与Choquet积分。这些研究促进了优势粗糙集理论的深入发展及其与相关理论相结合。项目研究成果已发表SCI收录论文9篇，中文核心期刊论文5篇，并出版专著1部。