The Laws Of Large Numbers For Uncorrelated Set-valued And Fuzzy Set-valued Random Variables

The laws of large numbers of single-valued random variables have got perfect conclusions.But some events are uncertain In life,there are limitations to describe event with singlevalued random variable.Set-valued and fuzzy set-valued random variables are generalizations of single-valued random variables.Set-valued stochastic theory has also become an important branch of probability theory.This paper is mainly studied two parts based on the laws of large numbers of uncorrelated single-valued random variable sequences.The laws of large numbers for uncorrelated set-valued random variables and the laws of large numbers for uncorrelated fuzzy set-valued random variables.The first part proves the weak laws of large numbers and the strong laws of large numbers for uncorrelated set-valued random variables.The convergence is in the sense of the Hausdorff distance.Firstly,similar to the definition of uncorrelated single-valued random variables,we define uncorrelated set-valued random variables.And discuss the properties of uncorrelated setvalued random variables.After that,we prove the laws of large numbers of set-valued random variables with triangle inequality,and control convergence theorem.These conclusions are generalizations of the laws of large numbers for existing uncorrelated single-valued random variables.The second part proves the weak laws of large numbers for uncorrelated fuzzy set-valued random variables.The convergence is in the sense of extended Hausdorff distance.Firstly,we define uncorrelated fuzzy set-valued random variables.And discuss the properties of uncorrelated fuzzy set-valued random variables.Finally,the conclusions of the set-valued random variables in Chapter 3 are extended to the field of fuzzy set-valued fields.The weak laws of large numbers for uncorrelated fuzzy set-valued random variables is proved by the method of sandwich.