| W.R.Ashby, one of the founders about the cybernetic once said, 'all things are black boxes in nature ,we have being studied black boxes through our lives.' Indeed, the realizing course of men as realizing subject is from unknown to part known, then to all known. At the same, the course about realizing objects is from black boxes to gray boxes, then to white boxes. However, the changes of the nature and the society, the endless of the realizing course, which lead to the road in which scholars research multi-attributes and multi-levels complex systems of huge scale is not smooth. This paper aims at evaluating complex systems with the non- linear process, and several innovations are obtained, such as theoretical basis and technological methods, which are helpful to understand the evaluation of complex systems more deeply, develop the application fields about it. The outcomes are very important in promoting the continuous development, the improvement and the application effects of the theory.In this paper, system ideas and ways, the classification of complex system, complexity and the characters of complex system are generalized, subjective and objective factors which limit evaluations and the problems in the course of evaluation are analyzed, the macroscopical and microscopical significations of evaluation are formulated.At present, linear solutions are often applied to evaluate complex systems. In chapter three, non-linear characters of evaluations system are analyzed by non-linear of systems, evaluation attributes and evaluation ways, which supply non-linear evaluation with theory basis.The quantification of attributes and the distribution of weight are indispensable in the evaluation of complex systems. Another group of reasonable quantified equation is given by discussing a group of quantified equation. It simply introduces two general weight distribution ways in evaluation, that is layer analysis method and entropy method. And it put forward two methods, which solve weight, that is, the weight solution based on relativity degree and another way based on satisfaction degree.The most elementary character of complex system is multi-level andmulti-attribute, four solutions about multi-level and multi-attribute evaluation of complex system are put forward: relativity degree solution, affiliation degree solution, gross profit solution, and entropy solution. Four ways are all non-linear. These methods have the features of wide-range application and simple calculation. In these methods, relativity degree solution is the method in which an ideal solution is established, the relativity degrees of evaluated solutions and the ideal solution are compared and orders are marshaled at last. Affiliation degree solution is the solution in which ideal solution and ill-ideal solution are established, affiliate degrees between evaluated solutions and ideal solution are resolved by establishing a goal function and then orders of all solutions are marshaled according to measurements of affiliation degrees. Gross profit solution is the solution in which both ideal solution and ill-ideal solution are considered, the differences between evaluated solutions and them are measured according to n-dimension Euclidean distance, and then gross profits are calculated. Entropy is a concept in physics, it is cited to measure weights in the information theories. In this paper, it is cited to evaluate all solution according to the measurement of entropy.Generation is a way in which the grey is changed into the white. The research into the characters of operation series is very important to fix up the structures and understand the action characters of systems. And it can offer middle news for modeling and evaluation. In the Charter five, the characters and mathematical structures of r-IAGO generation space are researched by the mathematical methods, the conception of mapping in grey generating space put forward, and the properties that AGO and IAGO are not only the linear transformation, but also the power transformation.
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