双论域决策系统的属性约简理论与算法研究

Attribute reduction of decision systems is an important topic in rough set theory. This project will make the following researches on decision systems over dual-universes. 1.We will study measures of uncertainty of decision systems over dual-universes. Concretely, we will define significance of attributes, information entropies, discernibity matrices and discernibility functions for decision systems over dual-universes and will discuss their applications in knowledge representation. 2.We will investigate the theory and algorithms of atttribute reduction of decision systems over dual-universes. We first define the attribute reduction of decision systems over dual-universes and then design reduction algorithms based on significance of attributes, information entropies, discernibity matrices and discernibility functions respectively. Numerical experiments will be carried out to test, improve and implement the algorithms. 3.We will also study properties of homomorphisms between approximation spaces over dual-universe as well as those between decision systems over dual-universes and discuss their applications in attribute reduction. The theory and methods of this project will further enrich rough set theory and thus will have theoretical significance and application value on intelligent computing, machine learning, data mining and knowledge discovery and related fields.

决策系统的属性约简是粗糙集理论的一个重要研究课题。本项目拟对双论域决策系统展开如下研究：1、研究双论域决策系统的不确定性度量。定义双论域决策系统的属性重要度、信息熵、辨识矩阵及辨识函数等对象，研究其性质及其在知识表示中的应用；2、研究双论域决策系统的属性约简理论和算法。定义双论域决策系统的属性约简，分别设计基于属性重要度、信息熵、辨识矩阵及辨识函数的约简算法，并通过数据实验进行算法测试、算法改进和算法实现；3、研究双论域近似空间同态、双论域决策系统同态的性质及其在属性约简中的应用。本课题的理论和方法将进一步丰富粗糙集理论，对智能计算、机器学习、数据挖掘与知识发现等相关领域的研究有着理论意义和应用价值。

粗糙集与形式概念分析是数据挖掘与数据处理的两个有效工具，在研究方法上，二者之间也有着很多联系，尤其是双论域粗糙集模型，它与形式背景有着极其相似的结构。因此，我们借鉴形式概念分析中的属性约简方法来研究双论域决策系统的属性约简。在对形式概念分析和计算推理中的包含度、真值度、协调集、可辨识集等不确定性度量概念进行研究的基础上，研究了双论域决策系统的相关的不确定性度量；研究了双论域决策系统属性约简的理论；研究了domain理论中的一些特殊domain范畴的性质。项目研究一方面扩充了不确定性推理的研究内容，刻划了认知逐步深化的过程，另一方面也为双论域决策系统的相关研究提供了新思路，并且从更深层次上揭示了知识的本质, 对已有的知识约简理论进行了拓广。项目研究成果有望应用于知识获取。