论复杂系统研究的等级结构与尺度推绎

复杂系统特别是开放的复杂系统是自然科学、工程技术和社会经济领域共同面临的一个重要研究课题．针对复杂系统研究的理论和方法多种多样，其中，等级结构、尺度和尺度推绎等具有普适性．等级结构(hierarchical structure)理论认为，以中心层或核心层(focal level)为中心和基础的三等级结构原理及方法，对研究多数自然和社会系统的形态、过程通常是必需的和足够的．同时，自然界和社会界都存在看多尺度(multi—scale)现象，在运用等级结构理论时往往需要考虑其尺度特性，并采用尺度推泽(scaling)方法．最后，给出3个论证实例．

Hierarchical Structure and Scaling for Complex System

The research on complex systems, especially open and complex systems have become a brand\|new and important field in natural science, technological engineering, and socio\|economics. There are many different theories and methodologies for the research of complex systems, in which the hierarchical structure, scales and scaling are provided with universal significance and practicality. The principle of triadic hierarchical structure which takes focal level as a central or kernel level is necessary and sufficient for investigations into patterns and processes of natural and social systems in most cases. Also, the problem of multi\|scales must be considered, and the approach of scaling must be applied into researches of complex systems. Finally, three practical cases were given so as to improve to understand them.