On Sequence Spaces Of Fuzzy Numbers Based On General Statistical Convergence

Statistical convergence was introduced and investigated in connection with prob-lems of series summation, measure theory, approximation theory, the matrix sum-mation, trigonometric series theory, Fourier analysis, Banach space theory and many other branches of mathematics. Considering the uncertainty of data information in the mathematical modeling, this uncertainty is often shown as a fuzzy number, the problem of statistical convergence for a sequence of fuzzy numbers have already discussed. However, in the more general sense, the problem of statistical conver-gence for sequence spaces of fuzzy numbers (such as based on Orlicz functions and strongly lacunary convergence, weighted statistical convergence and αβ-statistical convergence), haven’t seen a comprehensive study. In this paper, based on gen-eral statistical convergence, we research some properties of sequence spaces of fuzzy numbers, and discuss the relationships of these spaces.Firstly, the concepts of strongly lacunary convergence and lacunary statistical convergence are defined which are based on Orlicz functions, and it shows that the spaces are linear spaces. In addition, the relationships of these spaces are in-vestigated by means of the discussion of strongly lacunary convergence, lacunary statistical convergence and strong convergence for the sequence of fuzzy numbers.Then, the concepts of the weighted convergence and weighted statistical con-vergence for a sequence of fuzzy numbers are defined, and their properties are also investigated. Besides, the relationship among weighted convergence, weighted sta-tistical convergence and statistical convergence are discussed for a sequence of fuzzy numbers.The last, we introduce the concepts of αβ-statistically convergent of order γ and strongly αβ-convergent of order γ,and their properties are also investigated. At the same time, some connections between αβ-statistically convergent of order γ and strongly αβ-convergent of order γ for a sequence of fuzzy numbers are established.