Extension Catastrophe Progression Method And Its Application

The catastrophe progression method is a comprehensive evaluation method for ranking and analyzing evaluation targets,and it is based on catastrophe theory and fuzzy mathematics.Because the method is scientific,reasonable,and simple in calculation,it has been widely used in many fields such as medicine,economy,and geology.However,this method uses artificial determination of relative importance,so it is subjective.Moreover,the method requires that the number of control variables cannot exceed 4.These characteristics limit the application of the catastrophe progression method.In this paper,we study the catastrophe progression method.The catastrophe progression method is improved by introducing extenics theory.The improved catastrophe progression method is called the extension catastrophe progression method.The work of this paper is as follows.(1)By introducing information entropy theory,the method of determining the importance of control variables is improved.Using the principle that the smaller the entropy value is,the more important the information is,the control variables are reordered by the entropy value.Thereby the objectivity is increased,and the catastrophe system is more credible.(2)By introducing the extension theory,to resolve the contradiction between the catastrophe progression method and actual problems.We setup extension model,and analysis the characteristic that the control variables cannot exceed 4 in the catastrophe model.The extension transformation method is used to transform the contradiction,and the incompatibility problem is transformed into the compatibility problem.Thus,the catastrophe progression method can be used to solve the problem which has more than 4 control variables.(3)By introducing the extension correlation function to improve the combination function in the catastrophe model.At last,we take China's economic growth as the research example and use the extension catastrophe progression method to evaluate China's economic growth in 2008-2017.The results show,this method is very effective in economic growth evaluation,thus,the correctness and effectiveness of the extension catastrophe progression method is verified.