包含度与粗糙集数据分析中的度量

粗糙集理论是一种新的处理模糊和不确定知识的软计算工具。粗糙集数据分析是粗糙集理论中的主要应用技术之一，它主要用来分析数据的性质、粗糙分类、分析属性的依赖性和属性的重要性、抽取决策规则等，在人工智能与认知科学领域有着重要的应用。该文通过将包含度概念引入到粗糙集理论中，建立了包含度与粗糙集数据分析中的度量之间的关系，证家了粗糙集数据分析中的有关度量均可归结为包含度。这些结论有助于人们深刻理解粗糙数据分析的本质，可作为建立粗糙集数据分析中的度量的主要依据。

Inclusion Degree and Measures of Rough Set Data Analysis

Rough set theory is emerging as a powerful tool for reasoning about data. Rough set data analysis is one of the main application techniques arising from rough set theory. It provides a technique for gaining insights into properties of data, dependencies, and significance of individual attributes in databases, and has important applications to artificial intelligence and cognitive science, as a tool for dealing with vagueness and uncertainty of facts, and in classification. In order to analyze data effectively, many measures are defined in rough set data analysis, for example, accuracy of rough set, degree of rough belonging, accuracy of approximation of classification, measure of dependency of attributes, and accuracy of decision rule, etc. Although these measures can be applied to justifying effectiveness of data analysis, it is unclear what is the main foundation behind these measures and whether they have any common characteristics. In this paper, the relationship between inclusion degree and measures of rough set data analysis are set up by introducing a concept of inclusion degree in rough set theory. We show that: (1)Accuracy of rough set and degree of rough belonging can be reduced to inclusion degree; (2)Accuracy of approximation of classification and quality of approximation of classification can be reduced to inclusion degree; (3)Measure of dependency of attributes and measure of importance of attributes can be reduced to inclusion degree; (4)Accuracy of decision rule can be reduced to inclusion degree. These results will be very helpful for people to understand the essence of rough set data analysis, and can be regarded as the main foundation of measures which are defined for rough set data analysis.