Öz
In this paper, we introduce the concepts of rough ideal convergence, rough ideal limit set and rough ideal Cauchy sequence for double sequences of fuzzy numbers. We establish some properties of this convergence and obtain relation between rough ideal limit set and extreme ideal limit points of such sequences. Next, we explore the relation between ideal convergence and its rough analogue. Finally, we examine the connections between the set of cluster points and rough ideal limit set within double sequences of fuzzy numbers.
Anahtar Kelimeler
Double sequence Fuzzy numbers Ideal convergence Rough convergence
Kaynakça
- F. G. Akcay and S. Aytar, “Rough Convergence of a Sequence of Fuzzy Numbers,” Bull. Math. Anal. Appl., vol. 7, no. 4, pp. 17-23, 2015.
- F. Babaarslan and A. N. Tuncer, “Rough Convergence of Double Sequences of Fuzzy Numbers,” J. Appl. Anal. Comput., vol. 10, no. 4, pp. 1335-1342, 2020, doi: 10.11948/20190195.
- P. Das, P. Kostyrko, W. Wilczyński, and P. Malik, “I and I*-Convergence of Double Sequences,” Math. Slovaca, vol. 58, no. 5, pp. 605-620, Aug. 2008.
- K. Demirci, “I-Limit Superior and Limit Inferior,” Math. Commun., vol. 6, no. 2, pp. 165-172, 2001.
- E. Dündar, “On Rough I_2-Convergence of Double Sequences,” Numer. Funct. Anal. Optim., vol. 37, no. 4, pp. 480-491, 2016.
- E. Dündar and Ö. Talo, “I_2-Convergence of Double Sequences of Fuzzy Numbers,” Iran. J. Fuzzy Syst., vol. 10, no. 3, pp. 37-50, 2013.
- H. Fast, “Sur La Convergence Statistique,” Colloq. Math., vol. 2, no. 3-4, pp. 241-244, 1951.
- P. Kostyrko, T. Salát, and W. Wilczyński, “I-Convergence,” Real Anal. Exch., vol. 26, no. 2, pp. 669-686, 2000.
- V. Kumar and K. Kumar, “On the Ideal Convergence of Sequences of Fuzzy Numbers,” Inf. Sci., vol.178, no. 24, pp. 4670-4678, Dec. 2008.
- C. Kuratowski, Topologie I., Warszawa, 1958.
- M. Matloka, “Sequences of Fuzzy Numbers,” Busefal, vol. 28, pp. 28-37, 1986.
- E. Savaş and M. Mursaleen, “On Statistically Convergent Double Sequences of Fuzzy Numbers,” Inf. Sci., vol. 162, no. 3-4, pp. 183-192, 2004.
- J. Nagata, Modern General Topology. John Wiley, 1974.
- F. Nuray, “I-Convergence of Sequences of Fuzzy Numbers,” New Math. Nat. Comput., vol. 4, no. 2, pp. 231-236, 2008, doi: 10.1142/S1793005708001045.
- H. X. Phu, “Rough Convergence in Normed Linear Spaces,” Numer. Funct. Anal. Optim., vol. 22, no. 1-2, pp. 201-204, 2001.
- T. Šalát, B. C. Tripathy, and M. Ziman, “On Some Properties of I-Convergence,” Tatra Mt. Math. Publ., vol. 28, no. 2, 274-286, 2004.
- E. Savaş, “A Note on Double Sequences of Fuzzy Numbers,” Turk. J. Math., vol. 20, no. 2, pp. 175–178, 1996.
Öz
Kaynakça
- F. G. Akcay and S. Aytar, “Rough Convergence of a Sequence of Fuzzy Numbers,” Bull. Math. Anal. Appl., vol. 7, no. 4, pp. 17-23, 2015.
- F. Babaarslan and A. N. Tuncer, “Rough Convergence of Double Sequences of Fuzzy Numbers,” J. Appl. Anal. Comput., vol. 10, no. 4, pp. 1335-1342, 2020, doi: 10.11948/20190195.
- P. Das, P. Kostyrko, W. Wilczyński, and P. Malik, “I and I*-Convergence of Double Sequences,” Math. Slovaca, vol. 58, no. 5, pp. 605-620, Aug. 2008.
- K. Demirci, “I-Limit Superior and Limit Inferior,” Math. Commun., vol. 6, no. 2, pp. 165-172, 2001.
- E. Dündar, “On Rough I_2-Convergence of Double Sequences,” Numer. Funct. Anal. Optim., vol. 37, no. 4, pp. 480-491, 2016.
- E. Dündar and Ö. Talo, “I_2-Convergence of Double Sequences of Fuzzy Numbers,” Iran. J. Fuzzy Syst., vol. 10, no. 3, pp. 37-50, 2013.
- H. Fast, “Sur La Convergence Statistique,” Colloq. Math., vol. 2, no. 3-4, pp. 241-244, 1951.
- P. Kostyrko, T. Salát, and W. Wilczyński, “I-Convergence,” Real Anal. Exch., vol. 26, no. 2, pp. 669-686, 2000.
- V. Kumar and K. Kumar, “On the Ideal Convergence of Sequences of Fuzzy Numbers,” Inf. Sci., vol.178, no. 24, pp. 4670-4678, Dec. 2008.
- C. Kuratowski, Topologie I., Warszawa, 1958.
- M. Matloka, “Sequences of Fuzzy Numbers,” Busefal, vol. 28, pp. 28-37, 1986.
- E. Savaş and M. Mursaleen, “On Statistically Convergent Double Sequences of Fuzzy Numbers,” Inf. Sci., vol. 162, no. 3-4, pp. 183-192, 2004.
- J. Nagata, Modern General Topology. John Wiley, 1974.
- F. Nuray, “I-Convergence of Sequences of Fuzzy Numbers,” New Math. Nat. Comput., vol. 4, no. 2, pp. 231-236, 2008, doi: 10.1142/S1793005708001045.
- H. X. Phu, “Rough Convergence in Normed Linear Spaces,” Numer. Funct. Anal. Optim., vol. 22, no. 1-2, pp. 201-204, 2001.
- T. Šalát, B. C. Tripathy, and M. Ziman, “On Some Properties of I-Convergence,” Tatra Mt. Math. Publ., vol. 28, no. 2, 274-286, 2004.
- E. Savaş, “A Note on Double Sequences of Fuzzy Numbers,” Turk. J. Math., vol. 20, no. 2, pp. 175–178, 1996.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Temel Matematik (Diğer) |
| Bölüm | Research Articles |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Mayıs 2024 |
| Gönderilme Tarihi | 2 Mayıs 2024 |
| Kabul Tarihi | 30 Mayıs 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 2 Sayı: 1 |
