区间值信息系统不确定性度量的理论、方法与应用

Information systems are actually databases describing the relationships between objects (samples) and attributes (features) which contain explicit knowledge. Many real-world data are interval-valued because of limitation of observation methods and other reasons. Consequently, studies on interval-valued information systems are becoming more and more important. This project expects to construct the uncertainty measurement theories and methods for interval-valued information systems, which will be used to evaluate attribute importance and construct attribute reduction strategy. The project can be divided into the following four parts. Firstly, this project will construct fuzzy similarity relations based on distance measures defined on interval-valued objects.Secondly, this project will construct extended information entropy, rough entropy, knowledge granulation and granulartiy measure for interval-valued information systems from the entropy viewpoint and the granularity viewpoint. Their theoretical properties will also be studied. Thirdly, this project will extend the defined uncertainty measures based on ordinary similarity relations to fuzzy case by using fuzzy similarity relations directly. Fouthly, this project will construct attribute importance evaluation strategy based on the proposed uncertainty measures. Moreover, attribute reduction method will be constructed based on the attribute importance evaluation strategy. This project is expected to enrich the contents of rough set theory and uncertainty measurement, and expand the applications of rough set theory. On the other hand, this project is expected to supply theoretical support for knowledge discovery from interval-valued data, and will contribute to construct and evaluate knowledge discovery algorithms for interval-valued data.

信息系统实际上是描述对象(样本)与属性(特征)关系的数据库，隐含着相关知识。由于观察手段局限以及数据本身的不确定性等原因，现实应用中的数据越来越多地表现为区间值。项目期望建立区间值信息系统不确定性度量理论与方法，并将其应用于区间值信息系统的属性重要性评价中，从而获得区间值信息系统属性约简策略。项目主要研究内容包括：通过区间值信息系统中对象间的距离函数来定义合适的模糊相似关系；利用熵思想和粒度思想，在区间值信息系统中构建信息熵、粗糙熵、知识粒化和粒度度量等不确定性度量标准；直接利用模糊相似关系，将基于粗糙集边界策略、熵策略和粒度策略构造的不确定度量指标进行模糊化拓展；在所建立的不确定性度量基础上，构造属性重要性评价策略与属性约简方法。项目研究将丰富粗糙集理论与不确定性度量的涵盖内容，具有较重要的理论意义。同时项目有助于构建和评价区间值数据中属性选择算法，具有较重要的实际应用价值。

由于观察手段局限以及数据本身的不确定性等原因，现实应用中的数据很多时候表现为区间值。区间值信息系统是传统单值信息系统的拓展，包含有明显的不确定性，而传统单值信息系统可以看作是区间值信息系统的简单特例，因此区间值信息系统不确定性度量的研究尤为重要。项目主要研究内容包括：通过区间值信息系统中对象间的距离定义了模糊相似关系；利用熵思想和粒度思想，在区间值信息系统中构建了信息熵、条件熵、联合熵、粗糙熵、知识粒化和粒度度量等不确定性度量标准；直接利用模糊相似关系，将基于熵策略和粒度策略构造的不确定度量指标进行模糊化拓展；在所建立的不确定性度量基础上，构造了属性重要性评价策略与属性约简方法。项目建立了区间值信息系统(包含不完备区间值信息系统)不确定性度量理论与方法，并将其应用于区间值信息系统的属性重要性评价中，从而获得区间值信息系统属性约简策略。项目丰富了粗糙集理论与不确定性度量的涵盖内容，具有较重要的理论意义；同时项目有助于构建和评价区间值数据中属性选择算法，具有较重要的实际应用价值。