Research On Convergence Theory Of Fuzzy N-cube Number Space

Fuzzy number spaces play a key role in fuzzy analysis.Fuzzy n-cell numbers are a kind of special n dimensional fuzzy numbers,whose level sets of cuts are all hyperrectangles.They have widely used in the fields of engineering technology and operational research.This thesis is a further study of the convergence theory of fuzzy n-cell number spaces.The main results are stated as follows:Firstly,we improve the supremum and infimum of order bounded sets of fuzzy n-cell numbers established by Wang,and we prove that.Then we give the definition of levelwise convergent sequences of fuzzy n-cell numbers.Futhermore,we give the necessary and sufficient condition for a fuzzy n-cell number sequence {um} to be levelwise convergent in L(En).Moreover,we study the levelwise convergence properties of fuzzy n-cell number sequences.Also,we study the relationship between levelwise Cauchy sequences and levelwise convergent sequences of fuzzy n-cell numbers.Secondly,we introduce the concepts of statistical convergence,statistical Cauchy and levelwise statistical convergence of sequences in fuzzy n-cell number spaces.Meanwhile we study the properties and establish the relationships between the three and the corresponding function sequences in L(En).