There are several notions of convergence of fuzzy number sequences in the literature. The aim of this paper is to introduce and study a new concept of the rough fuzzy ideal convergent triple sequences defined by Orlicz function. Also, some topological properties of the resulting sequence spaces of rough fuzzy numbers were examined.
M.Arslan and E.Dündar, Rough convergence in 2-normed spaces, Bull Math Anal Appl10(3) (2018), 1–9.
2.
S.Aytar, Rough statistical convergence, Numer Funct Anal Optim29(3-4) (2008), 291–303.
3.
S.Aytar, The rough limit set and the core of a real sequence, Numer Funct Anal Optim29(3-4) (2008), 283–290.
4.
A.Esi, On some triple almost lacunary sequence spaces defined by Orlicz functions, Research and Reviews: Discrete Mathematical Structures1(2) (2014), 16–25.
5.
A.Esi, S.Araci and M.Acikgoz, Statistical convergence of Bernstein operators, Appl Math Inf Sci10(6) (2016), 2083–2086.
6.
A.Esi and M.Necdet Çatalbaş, Almost convergence of triple sequences, Global Journal of Mathematical Analysis2(1) (2014), 6–10.
7.
A.Esi and E.Savas, On lacunary statistically convergent triple sequences in probabilistic normed space, Appl Math Inf Sci9(5) (2015), 2529–2534.
8.
S.Debnath, B.Sarma and B.C.Das, Some generalized triple sequence spaces of real numbers, J Nonlinear Anal Optim6(1) (2015), 71–79.
9.
E.Dündar, On rough I2-convergence of double sequences, Numer Funct Anal Optim37(4) (2016), 480–491.
10.
E.Dündar and B.Altay, Multipliers for bounded ℓ-2--convergence of double sequences, Math Comput Modelling55(3-4) (2012), 1193–1198.
11.
E.Dündar and C.Çakan, Rough I-convergence, Demonstr Math47(3) (2014), 638–651.
12.
E.Dündar and C.Çakan, Rough convergence of double sequences, Gulf Journal of Mathematics2(1) (2014), 45–51.
13.
E.Dündar and Ö.Talo, I2-convergence of double sequences of fuzzy numbers, Iran J Fuzzy Syst10(3) (2013), 37–50.
14.
A.J.Dutta, A.Esi and B.C.Tripathy, Statistically convergent triple sequence spaces defined by Orlicz function, J Math Anal4(2) (2013), 16–22.
15.
P.K.Kamthan and M.Gupta, Sequence spaces and series, Lecture Notes in Pure and Applied Mathematics, 65. Marcel Dekker, Inc, New York, 1981.
16.
Ö.Kişi and E.Dündar, Rough I2-lacunary statistical convergence of double sequences, J Inequal Appl2018(230) (2018), 1–16.
17.
P.Kostyrko, T.Salat and W.Wilczynski, I-convergence, Real Anal Exchange26(2) (2000), 669–686.
18.
J.Lindenstrauss and L.Tzafriri, On Orlicz sequence spaces, Israel J Math10 (1971), 379–390.
19.
J.Musielak, Orlicz spaces and modular spaces, Lecture Notes in Mathematics, 1034. Springer-Verlag, Berlin, 1983.
20.
F.Nuray, G.Gök and U.Ulusu, Iσ-convergence, Math Commun16(2) (2011), 531–538.
21.
H.X.Phu, Rough convergence in normed linear spaces, Numer Funct Anal Optim22(1-2) (2001), 199–222.
22.
H.X.Phu, Rough continuity of linear operators, Numer Funct Anal Optim23(1-2) (2002), 139–146.
23.
H.X.Phu, Rough convergence in infinite-dimensional normed spaces, Numer Funct Anal Optim24(3-4) (2003), 285–301.
24.
R.Potucek, The sum of the series of reciprocals of the quadratic polynomials with one negative and one positive integer root, In: Proceedings of the 16th Conference on Applied Mathematics APLIMAT 2017 Faculty of Mechanical Engineering, Slovak University of Technology in Bratislava, 2017, pp. 1252–1253. ISBN 978-80-227-4650-2.
25.
A.Şahiner, M.Gürdal and F.K.Düden, Triple sequences and their statistical convergence, Selçuk J Appl Math8(2) (2007), 49–55.
26.
A.Şahiner and B.C.Tripathy, Some I-related properties of triple sequences, Selçuk J Appl Math9(2) (2008), 9–18.
27.
N.Subramanian and A.Esi, The generalized tripled difference of χ3 sequence spaces, Global Journal of Mathematical Analysis3(2) (2015), 54–60.
U.Ulusu, E.Dündar and F.Nuray, Lacunary I2-invariant convergence and some properties, International Journal of Analysis and Applications16(3) (2018), 317–327.
