Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function

Document Type: Research Paper


1 Department of Mathematics, Nevsehir Hac Bektas Veli University, Nevsehir- Turkey

2 Department of Mathematics, Firat University, Elazig-Turkey


The purpose of this paper is to generalize the concepts of statistical
convergence of sequences of fuzzy numbers defined by a modulus function
using difference operator $Delta$ and give some inclusion relations.


[1] H. Altnok, R. C olak and M. Et, -di erence sequence spaces of fuzzy numbers, Fuzzy Sets
and Systems, 160(21) (2009), 3128{3139.
[2] H. Altnok and R. C olak, Almost lacunary statistical and strongly almost lacunary conver-
gence of generalized di erence sequences of fuzzy numbers, J. Fuzzy Math., 17(4) (2009),
[3] H. Altnok and M. Mursaleen, -Statistical boundedness for sequences of fuzzy numbers,
Taiwanese Journal of Mathematics, 15(5) (2011), 2081-2093.
[4] M. Basarr and M. Mursaleen, Some sequence spaces of fuzzy numbers generated by in nite
matrices, J. Fuzzy Math., 11(3) (2003), 757-764.
[5] J. Connor, A topological and functional analytic approach to statistical convergence, Analysis
of divergence (Orono, ME, 1997), 403{413, Appl. Numer. Harmon. Anal., Birkhauser Boston,
Boston, MA, 1999.
[6] P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems, 35 (1990),
[7] M. Et and R. C olak, On some generalized di erence sequence spaces, Soochow J. Math.,
21(4) (1995), 377-386.
[8] M. Et, H. Altnok and R. C olak, On -ô€€€statistical convergence of di erence sequences of
fuzzy numbers, Inform. Sci., 176(15) (2006), 2268{2278.
[9] H. Fast, Sur la convergence statistique, Colloq. Math., (1951), 241-244.
[10] J. A. Fridy, On statistical convergence, Analysis., 5 (1985), 301-313.
[11] H. Kzmaz, On certain sequence spaces, Canadian Math. Bull., 24 (1981), 169-176.
[12] J. S. Kwon, On statistical and p-Cesaro convergence of fuzzy numbers, Korean J. Comput.
Appl. Math., 7(1) (2000), 195-203.
[13] M. Matloka, Sequences of fuzzy numbers, BUSEFAL, 28 (1986), 28-37.

[14] M. Mursaleen and M. Basarr, On some new sequence spaces of fuzzy numbers, Indian J.
Pure and Appl. Math., 34(9) (2003), 1351{1357.
[15] S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33 (1989), 123-126.
[16] H. Nakano, Concave modulars, J. Math. Soc. Japan, 5 (1953), 29{49.
[17] F. Nuray and E. Savas, Statistical convergence of fuzzy numbers, Math. Slovaca, 45(3) (1995),
[18] T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30 (1980),
[19] B. Sarma, On a class of sequences of fuzzy numbers de ned by modulus function, International
Journal of Science & Technology, 2(1) (2007), 25-28.
[20] I. J. Schoenberg, The integrability of certain functions and related summability methods,
Amer. Math. Monthly, 66 (1959), 361-375.
[21]  O. Talo and F. Basar, Certain spaces of sequences of fuzzy numbers de ned by a modulus
function, Demonstratio Math., 43(1) (2010), 139{149.
[22] B. C. Tripathy and A. J. Dutta, Bounded variation double sequence space of fuzzy real
numbers, Comput. Math. Appl., 59(2) (2010), 1031{1037.
[23] L. A. Zadeh, Fuzzy sets, Inform and Control, 8 (1965), 338-353.