Some properties of fuzzy number sequences

The first chapter of this thesis that consist of five chapters, we mention a short history of the fuzzy numbers and in order to understanding the topic we give some examples from daily life. In the second chapter, we give some fundamental definitions and theorems which will be used in the next chapters. In the third chapter, we will explain a statement that has density of order β and by using this concept statistical convergence of order β will be defined and relations between strongly p- Cesàro summability of order β will be given. In addition, the concept of λ- statistically convergent of order β that generalized case of statistically convergent is given. In the fourth chapter, we analyse the fuzzy set and some algebraic properties between the fuzzy numbers and metric defined on L(R) fuzzy number set which generated by these numbers. We define the concepts of fuzzy number, fuzzy set and sequence of fuzzy numbers and moreever we give some properties of the sequences fuzzy numbers: Convergence, boundedness, statistical convergence and strongly p-Cesàro summability of in the sequences fuzzy numbers and moreover, by a nondecreasing positive λ=(λ_{n}) sequence that λ_{n+1}≤λ_{n}+1,λ₁=1 and goes to ∞, short information and examples about λ- statistically convergent and λ- summability of the sequences fuzzy numbers is given. In the fifth chapter, by using generalized difference sequence for Λ a sequence that λ=(λ_{n})∈Λ and 0<β≤1 the sequences of fuzzy numbers of S_{λ}^{β}(Δ_{F}^{m}) the space of λ- statistical convergence of order β and the w_{λ}^{β}(Δ_{F}^{m}) space of λ- summable sequence of order β are defined and some theorems about these spaces are given. Also for belong to Λ class λ=(λ_{n}) and μ=(μ_{n}) sequences inclusion relations between S_{λ}^{γ}(Δ_{F}^{m}),S_{μ}^{β}(Δ_{F}^{m}),w_{μ}^{β}(Δ_{F}^{m},p), and w_{λ}^{γ}(Δ_{F}^{m},p) spaces are examined. Also, by using a modulus function f some inclusion relations between strongly λp- Cesàro summable sequence of order β and Δ_{λ}^{m}- statistical convergence sequence of order β are given. Keywords: Sequence of fuzzy numbers, Statistical convergence, Cesàro summability, Modulus function, Difference sequences