Social structural transition and social hierarchization exist objectively in modern china 摘要在当代中国，社会结构的变迁和社会分层客观存在。
2.
There is a significant difference between various hierarchies in sports population , sports activities performed and playgrounds for performing sports activities , which is called " sports hierarchization " 各阶层在体育人口的数量、参与体育活动的内容以及参与体育活动的场所等方面都存在着显著性的差异，称之为“体育分层” 。
3.
The hierarchization of peasant communicative objects , diversification of relations between communicative subjects , and " the pattern of difference sequence " reflected in trust relation all reflected this kind of logic : the communicative behavior choice of peasant is a kind of rational choice on the basis of the the traditional " pattern of difference sequence " and the traditional " pattern of difference sequence " is heading for rationalization 农民交往对象的等级化、交往主体间关系的多元化、信任关系的“差序格局”都反映出这样一种逻辑：农民的交往行为选择是在传统“差序格局”基础上的一种理性选择，传统的“差序格局”正在走向理性化。
4.
In consideration of social hierarchization and sports relation participation , this phenomenon is conducive not only to locating the root causes for unequal sports hierarchization and reducing the difference between various hierarchies in sports activities performed , but also to the growth of sports population , the boost of sports popularization , and the development of the sports industry 对社会分层与参与体育关系的思考，不仅有助于挖掘不平等体育分层现象的根源、缩小各阶层在参与体育活动方面的差距，而且有利于体育人口的增长、体育大众化的推进以及体育产业的发展。
5.
Based on the information theory , it is proved that the entropy of information system and the mutual information of decision system are constant in the hierarchization of attributes . so the rst hierarchical reduction approaches have strict mathematic basis . the application in acquiring the control decision of a cement kiln shows the validity of the hierarchical reduction approach 本文从信息理论的角度分别证明属性分层递阶不改变信息系统的信息熵和决策系统的互信息，从而使分层递阶约简算法体系具有严格的数学基础；分层递阶约简算法在某水泥窑炉控制决策获取中的应用证实其有效性。
