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$\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS

Yıl 2016, Cilt: 4 Sayı: 2, 183 - 192, 01.10.2016

Ozer Talo Erdinc Dundar

Öz

The statistical limit inferior and limit superior for sequences of fuzzy numbers have been introduced by Aytar, Pehlivan and Mammadov [Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems, 157(7) (2006) 976--985]. In this paper, we extend concepts of statistical limit superior and inferior to $\mathcal{I}$-limit superior and $\mathcal{I}$-inferior for a sequence of fuzzy numbers. Also, we prove some basic properties.

Anahtar Kelimeler

Fuzzy numbers sequences of fuzzy numbers Ideal convergence Ideal limit superior and inferior

Kaynakça

  • [1] H. Altinok, R. Colak and Y. AltIn, On the class of-statistically convergent di erence sequences of fuzzy numbers, Soft Computing 16(6)(2012),1029{1034.
  • [2] Y. Altn , M. Mursaleen, H. Altnok, Statistical summability (C; 1)-for sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent and Fuzzy Systems 21(2010), 379{384.
  • [3] S. Aytar, S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Information Sciences, 177(16) (2007) 3290{3296.
  • [4] S. Aytar, S. Pehlivan, M. Mammadov, The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159 (24) (2008) 3369{3379.
  • [5] S. Aytar, M. Mammadov, S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems, 157(7) (2006) 976{985.
  • [6] S. Aytar, S. Pehlivan, On I-convergent sequences of real numbers. Ital. J. Pure Appl. Math. 21 (2007), 191{196.
  • [7] H. Altinok, M. Mursaleen, -Statistical Boundedness for Sequences of fuzzy numbers, Taiwanese Journal of Mathematics 15(5) (2011), 2081{2093
  • [8] F.Bas.ar, Summability Theory and its Applications, in: Monographs, Bentham Science Publishers, (2011), e-books.
  • [9] I. Canak, On the Riesz mean of sequences of fuzzy real numbers, Journal of Intelligent and Fuzzy Systems 26 (6) 2014, 2685{2688
  • [10] K. Demirci, I- limit superior and limit inferior, Mathematical Communications, 6 (2001), 165{172
  • [11] E. Dundar,  O. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems Vol. 10, No. 3, (2013) pp. 37-50
  • [12] J. A. R. Freedman, J. J. Sember, Densities and summability, Paci c Journal of Mathematics, 95 (1981), 293{305.
  • [13] B. Hazarika, Lacunary difference ideal convergent sequence spaces of fuzzy numbers, Journal of Intelligent & Fuzzy Systems 25 (2013), 157{166
  • [14] B. Hazarika, On -uniform density and ideal convergent sequences of fuzzy real numbers, Journal of Intelligent & Fuzzy Systems, 26 (2014), 793{799.
  • [15] D. H. Hong, E. L. Moon, J. D. Kim, A note on the core of fuzzy numbers, Applied Mathematics Letters, 23(5) (2010), 651{655. [16] P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Analysis Exchange, 26(2) (2000), 669{686.
  • [17] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak,I-convergence and extremal I-limit points, Mathematica Slovaca, 55 (2005), 443{464.
  • [18] V. Kumar, K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Information Sciences, 178(2008), 4670{4678.
  • [19] V. Kumar, A. Sharma, K. Kumar, N. Singh, On I-Limit Points and I-Cluster Points of Sequences of Fuzzy Numbers, International Mathematical Forum, 57(2) (2007), 2815{2822.
  • [20] H. Li, C.Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Sets and Systems, 158 (2007), 2317{2338.
  • [21] M. Matloka, Sequences of fuzzy numbers, BUSEFAL, 28(1986), 28{37.
  • [22] S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33 (1989), 123{126.
  • [23] F. Nuray and E. Savas, Statistical convergence of fuzzy numbers, Mathematica Slovaca 45(3) (1995), 269{273.
  • [24] T. Salt, B.C. Tripathy, M. Ziman, On I-convergence eld, Italian Journal of Pure and Applied Mathematics 17 (2005), 45{54.
  • [25] E. Savas, Some double lacunary I-convergent sequence spaces of fuzzy numbers de ned by Orlicz function, Journal of Intelligent & Fuzzy Systems 23 (2012), 249{257.
  • [26] E. Savas,A note on double lacunary statistical I-convergence of fuzzy numbers, Soft Computing (2012), 16 591{595.
  • [27] E. Savas, On convergent double sequence spaces of fuzzy numbers de ned by ideal and Orlicz function, Journal of Intelligent & Fuzzy Systems 26 (2014), 1869{1877
  • [28] C. -x. Wu, C.Wu, The supremum and in mum of the set of fuzzy numbers and its application, Journal of Mathematical Analysis and Applications, 210 (1997), 499-511.
  • [29]  O. Talo, Talo, C. Cakan, The extension of the Knopp core theorem to the sequences of fuzzy numbers, Information Sciences 276 (2014), 10{20.
  • [30]  O. Talo, Some properties of limit inferior and limit superior for sequences of fuzzy real numbers, Information Sciences, 279(2014), 560{568
  • [31]  O. Talo, F. Basar, On the Slowly Decreasing Sequences of Fuzzy Numbers, Abstract and Applied Analysis Article ID 891986 doi:10.1155/2013/891986 (2013), 1-7.
  • [32] B.C. Tripathy, A.J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, Journal of Intelligent and Fuzzy Systems 24(1)(2013), 185{189.
  • [33] B.C. Tripathy, M. Sen, On fuzzy I-convergent di erence sequence space, Journal of Intelligent & Fuzzy Systems 25(3) (2013), 643{647.

Yıl 2016, Cilt: 4 Sayı: 2, 183 - 192, 01.10.2016

Ozer Talo Erdinc Dundar

Öz

Kaynakça

  • [1] H. Altinok, R. Colak and Y. AltIn, On the class of-statistically convergent di erence sequences of fuzzy numbers, Soft Computing 16(6)(2012),1029{1034.
  • [2] Y. Altn , M. Mursaleen, H. Altnok, Statistical summability (C; 1)-for sequences of fuzzy real numbers and a Tauberian theorem, Journal of Intelligent and Fuzzy Systems 21(2010), 379{384.
  • [3] S. Aytar, S. Pehlivan, Statistical cluster and extreme limit points of sequences of fuzzy numbers, Information Sciences, 177(16) (2007) 3290{3296.
  • [4] S. Aytar, S. Pehlivan, M. Mammadov, The core of a sequence of fuzzy numbers, Fuzzy Sets and Systems, 159 (24) (2008) 3369{3379.
  • [5] S. Aytar, M. Mammadov, S. Pehlivan, Statistical limit inferior and limit superior for sequences of fuzzy numbers, Fuzzy Sets and Systems, 157(7) (2006) 976{985.
  • [6] S. Aytar, S. Pehlivan, On I-convergent sequences of real numbers. Ital. J. Pure Appl. Math. 21 (2007), 191{196.
  • [7] H. Altinok, M. Mursaleen, -Statistical Boundedness for Sequences of fuzzy numbers, Taiwanese Journal of Mathematics 15(5) (2011), 2081{2093
  • [8] F.Bas.ar, Summability Theory and its Applications, in: Monographs, Bentham Science Publishers, (2011), e-books.
  • [9] I. Canak, On the Riesz mean of sequences of fuzzy real numbers, Journal of Intelligent and Fuzzy Systems 26 (6) 2014, 2685{2688
  • [10] K. Demirci, I- limit superior and limit inferior, Mathematical Communications, 6 (2001), 165{172
  • [11] E. Dundar,  O. Talo, I2-convergence of double sequences of fuzzy numbers, Iranian Journal of Fuzzy Systems Vol. 10, No. 3, (2013) pp. 37-50
  • [12] J. A. R. Freedman, J. J. Sember, Densities and summability, Paci c Journal of Mathematics, 95 (1981), 293{305.
  • [13] B. Hazarika, Lacunary difference ideal convergent sequence spaces of fuzzy numbers, Journal of Intelligent & Fuzzy Systems 25 (2013), 157{166
  • [14] B. Hazarika, On -uniform density and ideal convergent sequences of fuzzy real numbers, Journal of Intelligent & Fuzzy Systems, 26 (2014), 793{799.
  • [15] D. H. Hong, E. L. Moon, J. D. Kim, A note on the core of fuzzy numbers, Applied Mathematics Letters, 23(5) (2010), 651{655. [16] P. Kostyrko, T. Salat and W. Wilczynski, I-convergence, Real Analysis Exchange, 26(2) (2000), 669{686.
  • [17] P. Kostyrko, M. Macaj, T. Salat, M. Sleziak,I-convergence and extremal I-limit points, Mathematica Slovaca, 55 (2005), 443{464.
  • [18] V. Kumar, K. Kumar, On the ideal convergence of sequences of fuzzy numbers, Information Sciences, 178(2008), 4670{4678.
  • [19] V. Kumar, A. Sharma, K. Kumar, N. Singh, On I-Limit Points and I-Cluster Points of Sequences of Fuzzy Numbers, International Mathematical Forum, 57(2) (2007), 2815{2822.
  • [20] H. Li, C.Wu, The integral of a fuzzy mapping over a directed line, Fuzzy Sets and Systems, 158 (2007), 2317{2338.
  • [21] M. Matloka, Sequences of fuzzy numbers, BUSEFAL, 28(1986), 28{37.
  • [22] S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33 (1989), 123{126.
  • [23] F. Nuray and E. Savas, Statistical convergence of fuzzy numbers, Mathematica Slovaca 45(3) (1995), 269{273.
  • [24] T. Salt, B.C. Tripathy, M. Ziman, On I-convergence eld, Italian Journal of Pure and Applied Mathematics 17 (2005), 45{54.
  • [25] E. Savas, Some double lacunary I-convergent sequence spaces of fuzzy numbers de ned by Orlicz function, Journal of Intelligent & Fuzzy Systems 23 (2012), 249{257.
  • [26] E. Savas,A note on double lacunary statistical I-convergence of fuzzy numbers, Soft Computing (2012), 16 591{595.
  • [27] E. Savas, On convergent double sequence spaces of fuzzy numbers de ned by ideal and Orlicz function, Journal of Intelligent & Fuzzy Systems 26 (2014), 1869{1877
  • [28] C. -x. Wu, C.Wu, The supremum and in mum of the set of fuzzy numbers and its application, Journal of Mathematical Analysis and Applications, 210 (1997), 499-511.
  • [29]  O. Talo, Talo, C. Cakan, The extension of the Knopp core theorem to the sequences of fuzzy numbers, Information Sciences 276 (2014), 10{20.
  • [30]  O. Talo, Some properties of limit inferior and limit superior for sequences of fuzzy real numbers, Information Sciences, 279(2014), 560{568
  • [31]  O. Talo, F. Basar, On the Slowly Decreasing Sequences of Fuzzy Numbers, Abstract and Applied Analysis Article ID 891986 doi:10.1155/2013/891986 (2013), 1-7.
  • [32] B.C. Tripathy, A.J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, Journal of Intelligent and Fuzzy Systems 24(1)(2013), 185{189.
  • [33] B.C. Tripathy, M. Sen, On fuzzy I-convergent di erence sequence space, Journal of Intelligent & Fuzzy Systems 25(3) (2013), 643{647.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Articles
Yazarlar

Ozer Talo Bu kişi benim

Erdinc Dundar

Yayımlanma Tarihi 1 Ekim 2016
Gönderilme Tarihi 3 Haziran 2014
Yayımlandığı Sayı Yıl 2016 Cilt: 4 Sayı: 2

Kaynak Göster

APA Talo, O., & Dundar, E. (2016). $\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS. Konuralp Journal of Mathematics, 4(2), 183-192.
AMA Talo O, Dundar E. $\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS. Konuralp J. Math. Ekim 2016;4(2):183-192.
Chicago Talo, Ozer, ve Erdinc Dundar. “$\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS”. Konuralp Journal of Mathematics 4, sy. 2 (Ekim 2016): 183-92.
EndNote Talo O, Dundar E (01 Ekim 2016) $\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS. Konuralp Journal of Mathematics 4 2 183–192.
IEEE O. Talo ve E. Dundar, “$\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS”, Konuralp J. Math., c. 4, sy. 2, ss. 183–192, 2016.
ISNAD Talo, Ozer - Dundar, Erdinc. “$\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS”. Konuralp Journal of Mathematics 4/2 (Ekim 2016), 183-192.
JAMA Talo O, Dundar E. $\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS. Konuralp J. Math. 2016;4:183–192.
MLA Talo, Ozer ve Erdinc Dundar. “$\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS”. Konuralp Journal of Mathematics, c. 4, sy. 2, 2016, ss. 183-92.
Vancouver Talo O, Dundar E. $\mathcal{I}$-LIMIT SUPERIOR AND $\mathcal{I}$-LIMIT INFERIOR FOR SEQUENCES OF FUZZY NUMBERS. Konuralp J. Math. 2016;4(2):183-92.
 Kapak Resmi İndir
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