ON ρ-STATISTICAL CONVERGENCE OF SEQUENCES OF FUZZY NUMBERS

Abstract

In this study, we present the concepts of ρ-statistically convergence for sequences of fuzzy numbers as well as strong (w_ρ (F)) summability and ρ-Cauchy statistically convergence for sequences of fuzzy numbers. We also provide several results concerning these concepts.

Keywords

• Cesàro summability
• Statistical convergence
• Strongly ρ-Cesàro summability. .

References

1. Fast, H., “Sur la convergence statistique”, Colloquium Math., 2, 241-244, 1951.
2. Schoenberg, I.J., “The Integrability of Certain Functions and Related Summability Methods”, Amer. Math. Monthly, 66, 361-375, 1959.
3. Connor, J., “A topological and functional analytic approach to statistical convergence”, Analysis of Divergence , Birkhauser, Boston, 403-413, 1999.
4. Fridy, J., “On statistical convergence”, Analysis 5, 301-313, 1985.
5. Šalát, T., “On statistically convergent sequences of real numbers”, Math. Slovaca, 30, 139-150, 1980.
6. Ercan, S., Altin, Y., Bektaş, Ç., “On lacunary weak statistical convergence of order α”, Communications in Statistics-Theory and Methods, 49(7), 1653-1664, 2020 https://doi.org/10.1080/03610926.2018.1563185
7. Zadeh, L. A., “Fuzzy sets”, Inform and Control, 8, 338-353, 1965.
8. Matloka, M., “Sequences of fuzzy numbers”, BUSEFAL, 28, 28-37, 1986.

9. Altinok, H., Çolak, R., Altin, Y., “On the class of λ-statistically convergent difference sequences of fuzzy numvers”, Soft Computing, 16(6), 1029-1034, 2012 DOI: 10.1007/s00500-011-0800-6
10. Aytar, S., Pehlivan, S., “Statistical convergence of sequences of fuzzy numbers and sequences of α-cuts”, International Journal of General Systems 37(2),231-237, 2008 DOI: 10.1080/03081070701251075
11. UCakan, U., Altin, Y., “Some clases of statistically convergent sequences of fuzzy numbers generated by modulus function”, Iranian Journal of Fuzzy Systems, 12(3), 47-55 , 2015.
12. Çanak, İ., “On Tauberian theorems for Cesaro summability of sequences fuzzy numbers”, J.Intell. Fuzzy Syst. 30, 2657-2661, 2016 DOI: 10.3233/IFS-131053
13. Sezer, S.A., “Statistical harmonic summability of sequences of fuzzy numbers”, Soft Computing, 27, 1933-1940, 2023 DOI: 10.1007/s00500-020-05151-9
14. Tripathy, B.C., Baruah, A., “Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers”, Kyungpook Math. Jour. 50, 565-574, 2010.
15. Nuray, F., Savaş, E., “Statistical convergence of sequences of fuzzy real numbers”, Math. Slovaca 45(3), 269-273, 1995.
16. Çakallı, H., “A variation on statistical ward continuity”, Bull. Malays. Math. Sci. Soc. 40, 1701-1710, 2017. DOI: 10.1007/s40840-015-0195-0
17. Kandemir, H.Ş., “On ρ-statistical convergence in topological groups”, Maltepe Journal of Mathematics, 4(1), 9-14, 2022. doi:10.47087/mjm.1092559
18. Aral, N.D., Kandemir, H.Ş., Et. M., “On ρ− Statistical convergence of sequences of Sets”, Conference Proceeding Science and Tecnology, 3(1),156-159, 2020.
19. Gumus, H., “Rho-statistical convergence of interval numbers”, International Conference on Mathematics and Its Applications in Science and Engineering. 2022.
20. Aral, N.D., Kandemir, H., & Et, M., "On ρ−statistical convergence of order α of sequences of function", e-Journal of Analysis and Applied Mathematics, 2022(1), 45-55, 2022.
21. Aral, N.D., Kandemir, H., & Et, M., "On ρ-statistical convergence of double sequences of order α in topological groups", The Journal of Analysis, 31, 3069–3078, 2023.
22. Aral, N.D., Kandemir, H., & Et, M., "On ρ-statistical convergence of order α of sequences of sets", Miskolc Mathematical Notes, 24(2), 569–578, 2023.