Analysis And Regression Of Set-valued And Fuzzy Sets

In many economic systems and stochastic control systems,we often need to use the random inclusion problem.Set valued stochastic process can solve this problem.Set valued stochastic process comes from people's research on economic distribution problem,which reflects the objectivity of things description.Set valued stochastic process has important theoretical value and application prospects.Since the level cut set of fuzzy numbers is set-valued,fuzzy set-valued stochastic processes and set-valued stochastic processes are widely used in artificial intelligence and other fields.This paper is mainly divided into two parts: set-valued integral and fuzzy set-valued regression.Firstly,the research status at home and abroad is described,and the related notation used in this paper is given.Then,according to the improved integral property of fuzzy set-valued stochastic process,the proof of Lebesgue integral property theorem suitable for set-valued stochastic process is given,and the related inference of Lebesgue integral is obtained,and Aumann representation theorem is proved.The traditional linear regression model has been well applied and developed in our life.In the past,most of the data used in the research is real value single point data.With the progress of science and technology,the classical regression model is no longer suitable for complex data.If we only consider the single point data,the fluctuation information of the research object will be lost.This paper introduces the interval value regression model,taking interval value data as the research object,which can better reflect the volatility of things.Considering the missing data,incomplete data and fuzzy data,according to the properties of fuzzy random variables and set-valued random process,the cut set ?-CM regression model and CRM regression model of fuzzy set-valued random process are obtained.The fuzzy set-valued regression model is discussed,and the model of fuzzy set-valued stochastic process is given.