基于正传递关系的粗糙集扩展
Extension of Rough Set Based on Positive Transitive Relation
摘要：
粗糙集理论在不完备信息系统中的应用是实践中的一个关键问题，因为在知识获取中，由于数据测量的误差、数据汇集的局限性或数据理解的局限性等原因，几乎总是会出现缺失值。现有的基于容差或对称相似关系的粗糙集扩展模型通常会舍弃自反关系、对称关系和传递关系中的一种关系，尤其是传递关系。为了克服现有粗糙集扩展模型的局限性，定义了一种新的正传递关系，并在此基础上提出了一种新的粗糙集扩展模型.新模型保留了现有粗糙集扩展模型的优点，同时避免了它们丢弃传递性或对称性的局限性。与已有的可拓模型相比，该模型在处理不完备信息系统时具有更好的性能，同时大大降低了计算复杂性，考虑了正传递性的容差和相似性关系，并根据不完备信息的直观分类补充了相关理论.综上所述，正传递关系可以改进现有的不完备信息系统的理论分析，新提出的可拓模型更适合处理不完备信息系统，具有广阔的应用前景。
英文摘要：
The application of rough set theory in incomplete information systems is a key problem in practice since missing values almost always occur in knowledge acquisition due to the error of data measuring, the limitation of data collection, or the limitation of data comprehension, etc. An incomplete information system is mainly processed by compressing the indiscernibility relation. The existing rough set extension models based on tolerance or symmetric similarity relations typically discard one relation among the reflexive, symmetric and transitive relations, especially the transitive relation. In order to overcome the limitations of the current rough set extension models, we define a new relation called the positive transitive relation and then propose a novel rough set extension model built upon which. The new model holds the merit of the existing rough set extension models while avoids their limitations of discarding transitivity or symmetry. In comparison to the existing extension models, the proposed model has a better performance in processing the incomplete information systems while substantially reducing the computational complexity, taking into account the relation of tolerance and similarity of positive transitivity, and supplementing the related theories in accordance to the intuitive classification of incomplete information. In summary, the positive transitive relation can improve current theoretical analysis of incomplete information systems and the newly proposed extension model is more suitable for processing incomplete information systems and has a broad application prospect.
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