Statistical convergence of order β in sequences of fuzzy numbers

This study consists of the five main chapters. In the first chapter, we give some informations about the historical development of statistical convergence and fuzzy numbers. In the second chapter, we give some fundamental definitions and theorems which are necessary in this study and then touch on notions of difference sequence spaces and statistical convergence, strongly Cesàro summability and lacunary statistical convergence of a sequence of real or complex. In the third chapter, we give the concepts of fuzzy set, fuzzy number and sequence of fuzzy numbers and mention convergence, boundedness, statistical convergence and strongly p-Cesàro summability of the sequences of fuzzy numbers. In the fourth chapter, we define the spaces N_{θ}^{β}(p,F,Δ^{m}), S_{θ}^{β}(F,Δ^{m}) and w_{p}^{β}(F,Δ^{m}) for sequences of fuzzy numbers using generalized difference operator Δ^{m} and a lacunary sequence θ and give some relations between them, where β∈(0,1] and p>0. Furthermore, some inclusion theorems are presented related to the spaces S_{θ}^{β}(F,Δ^{m}) and w_{p}^{β}(θ,f,F,Δ^{m}) according to modulus function f. In the next section, we introduce the concept of strongly N_{θ}^{β}(p,F,Δ^{m},M)-summable with respect to the Orlicz function M and obtain the relation between the classes of N_{θ}^{β}(p,F,Δ^{m},M) and S_{θ}^{β}(F,Δ^{m}). Moreover, we examine these classes for different two lacunary sequences like θ=(k_{r}) and θ′=(s_{r}). In the fifth and last chapter, we give the results obtained from the thesis.