Difference sequences of order m of fuzzy numbers and statistical convergence

ABSTRACT Ph D. Thesis DIFFERENCE SEQUENCES OF ORDER m OF FUZZY NUMBERS AND STATISTICAL CONVERGENCE Yavuz ALTIN Fırat University- Graduate School of Natural and Applied Sciences Department of Mathematics 2005, Sayfa: 53+VIII This thesis consists of three chapters. In the first chapter, some fundamental definitions and theorems which will be used in the later chapters are given. In the second chapter the concept of fuzzy sets, sequences of fuzzy numbers and sta tistical convergence of fuzzy numbers are given. In the three chapter, using the difference operator and the lacunary sequence the con cepts of lacunary statistical convergence and strongly lacunary convergence of sequences of fuzzy numbers are introduced and several relations related to these concepts are given. It is shown that lacunary Am- statistical convergence and lacunary strongly AT- convergence are equivalent for Am- bounded sequences of fuzzy numbers. Furthermore, some topo logical properties of the fuzzy sequences space m (