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Special issue on Hybrid Intelligence using rough sets

机译：使用粗糙集的混合智能特刊

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摘要

The problem of imperfect knowledge under uncertain environments has been tackled for a long time by philosophers, logicians and mathematicians. Rough set theory proposed by Zdzislaw Pawlak has attracted attention of many researchers and practitioners all over the world, and has a fast growing group of researchers interested in this methodology. Fuzzy set theory proposed by Lotfi Zadeh helps to understand and manipulate imperfect knowledge. Fuzzy sets are defined by partial membership, in contrast to crisp membership used in classical definition of a set. Rough set theory, expresses vagueness, not by means of membership, but employing a boundary region of a set. The back bone of rough set theory is the approximation space and lower and upper approximations of a set. The approximation space is a classification of the domain of interest into disjoint categories. The lower approximation is a description of the domain objects which are known with certainty to belong to the subset of interest, whereas the upper approximation is a description of the objects which possibly belong to the subset. Any subset defined through its lower and upper approximations is called a rough set. The main advantage of rough set theory is that it does not need any preliminary or additional information about data - like probability in statistics, grade of membership in fuzzy set and so on. Readers may consult the International Rough Set Society Web page for more online resources, publications etc.
机译：哲学家，逻辑学家和数学家们长期以来一直在解决不确定环境下知识不完善的问题。 Zdzislaw Pawlak提出的粗糙集理论引起了全世界许多研究人员和从业者的关注，并且快速增长的研究人员对这种方法感兴趣。 Lotfi Zadeh提出的模糊集理论有助于理解和操纵不完美的知识。与集合的经典定义中使用的明晰隶属度相反，模糊集由部分隶属度定义。粗糙集理论不是通过隶属度而是使用集合的边界区域来表达模糊性。粗糙集理论的后盾是集合的近似空间以及上下近似。近似空间是将感兴趣域划分为不相交的类别。较低的近似是确定地知道属于感兴趣子集的域对象的描述，而较高的近似是可能属于该子集的对象的描述。通过其上下近似定义的任何子集都称为粗糙集。粗糙集理论的主要优点是它不需要任何有关数据的初步或附加信息，例如统计中的概率，模糊集的隶属度等。读者可以查阅国际粗糙集协会网页以获得更多在线资源，出版物等。

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