Sequences of Fuzzy numbers

ABSTRACTPhd ThesisSEQUENCES OF FUZZY NUMBERSHıfsı ALTINOKFırat UniversityGraduate School of Science and TechnologyDepartment of Mathematics2007, Page: 55In the first chapter of this thesis that consists of three chapters, we give some fun-damental definitions and theorems which will be used in the later chapters and examinedifference sequences and N −functions in the special class of convex functions and someproperties of Orlicz functions.In the second chapter, we give the concepts of fuzzy set, fuzzy number and the se-quences of fuzzy number which forms base of this study and show statistical convergenceand boundedness of them by giving some examples.In the first section of third chapter, we define the fuzzy sequence spacesc (∆m , F, M, p) , c0 (∆m , F, M, p) , m S (∆m , F, M, p)∞ (∆ , F, M, p) , andS0 (∆m , F, M, p) using an Orlicz function M and ∆m −generalized difference operator andexamine some topological properties of these spaces. In the second section we defineλ−fuzzy difference sequence classes and give some relations that belong to these classes,where λ = (λn ) is a non-decreasing sequence of positive real numbers. In the last sec-tion, we examine strongly uniform convergence of sequences of fuzzy numbers by using alacunary sequence θ = (kr ) .Key Words: Fuzzy set, Fuzzy number, Sequence of fuzzy numbers, Orlicz function,Statistical convergence, Lacunary sequence.