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中文摘要：
知识约简是粗糙集理论的重要研究内容之一.传统的知识约简主要针对单值信息系统,但在许多实际问题中,信息系统中的数据往往以区间值的形式存在,因此,区间值信息系统的知识约简研究具有重要意义.现有工作中,论域的分类结果存在冗余度大、误分率高等问题.针对上述问题,在区间值信息系统中引入了α-极大相容类的概念,并提出了新的粗糙上下近似算子,α-极大相容类的采用有效地提高了分类和粗糙近似精度.最后,给出了区间值信息系统知识约简的定义和相应区分函数的计算方法,为区间值信息系统的知识获取提供了一条新的途径.
英文摘要：
Knowledge reduction is an important problem of rough set theory.The notion of a reduction plays an essential role in analyzing an information system.A reduction is a minimum subset of attributes that can provide the same descriptive or classification ability as the full set of available attributes.In other words,attributes in a reduction are jointly sufficient and individually necessary in an information system.Original knowledge reduction in Pawlak＇s rough set theory is mainly based on single-valued information systems.However,there always exist interval numbers in a lot of information systems in reality.Thus,knowledge reduction in interval-valued information systems has been a hot issue in the related area in recent years.Although some research works for knowledge reduction in interval-valued information systems have been done,there are still critical problems,such as redundancy of classification results and low accuracy of rough approximation to be dealt with.Aiming at the existing problems,the authors introduce the α-maximal consistent class into interval-valued information systems to improve the accuracy of knowledge classification and rough approximation.A novel measurement for the similarity degree of different interval numbers is proposed in this paper.Furthermore,to simplify knowledge representation,the authors present the methods for constructing the discernibility matrix and attribute reduction in interval-valued information systems or decision systems.Finally,the latent knowledge can be discovered by knowledge reduction.
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