The statistical convergence for sequences of fuzzy-number-valued functions

Based on the concept of statistical convergence of sequences of fuzzy numbers, the statistical convergence, uniformly statistical convergence and equi-statistical convergence of sequences of fuzzy-number-valued functions are defined and investigated in this paper. The relationship among statistical convergence, uniformly statistical convergence, equi-statistical convergence of sequences of fuzzy-number-valued functions and their representations of sequences of α-level cuts are discussed. In addition, the Egorov and Lebesgue theorems for the statistical convergence of sequences of fuzzy-number-valued functions are obtained in a finite measure set. Finally, the statistical convergence in measure for sequences of fuzzy-number-valued functions is investigated, and it is proved that the outer and inner statistical convergence in measure are equivalent in a finite measure set for a sequence of fuzzy-number-valued functions.