The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ, μ)-ideal statistical convergence and strongly weighted (λ, μ)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.
References
[1]
Zadeh, L.A. (1965) Fuzzy Sets. Information and Control, 8, 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
[2]
Buck, R.C. (1953) Generalized Asymptote Density. American Journal of Mathematics, 75, 335-346. https://doi.org/10.2307/2372456
[3]
Savaş, E. (2001) On Statistically Convergent Sequences of Fuzzy Numbers. Information Sciences, 137, 277-282. https://doi.org/10.1016/S0020-0255(01)00110-4
[4]
Matloka, H. (1986) Sequences of Fuzzy Numbers. Busefal, 28, 28-37.
[5]
Nanda, S. (1989) On Sequences of Fuzzy Numbers. Fuzzy Sets and Systems, 33, 123-126. https://doi.org/10.1016/0165-0114(89)90222-4
[6]
Nuray, F. and Savas, E. (1995) Statistical Convergence of Sequences of Fuzzy Numbers. Mathematica Slovaka, 45, 269-273.
[7]
Talo, O. and Basar, F. (2009) Determination of the Duals of Classical Sets of Sequences of Fuzzy Numbers and Related Matrix Transformations. Computers & Mathematics with Applications, 58, 717-733. https://doi.org/10.1016/j.camwa.2009.05.002
[8]
Belen, C. and Mohiuddine, S.A. (2013) Generalized Weighted Statistical Convergence and Application. Applied Mathematics and Computation, 219, 9821-982. https://doi.org/10.1016/j.amc.2013.03.115 6.
[9]
Muhammed, C. and Mikail, E. (2016) Generalized Weighted Statistical Convergence of Double Sequences and Applications. Filomat, 30, 753-762. https://doi.org/10.2298/FIL1603753C
[10]
Dutta, H. and Gogoi, J. (2019) Weighted -Statistical Convergence Connecting a Statistical Summability of Sequences of Fuzzy Numbers and Korovkin-Type Approximation Theorems. Soft Computing, 23, 12883-12895. https://doi.org/10.1007/s00500-019-03846-2
[11]
Goetschel, R. and Voxman, W. (1986) Elementary Fuzzy Calculus. Fuzzy Sets and Systems, 18, 31-43. https://doi.org/10.1016/0165-0114(86)90026-6
[12]
Gong, Z.T. and Feng, X. (2016) αβ-Statistical Convergence and Strong αβ-Convergence of Order for a Sequence of Fuzzy Numbers. Journal of Computational Analysis and Applications, 21, 228-236.
[13]
Mursaleen, M. and Mohiuddine, SA. (2009) On Lacunary Statistical Convergence with Respect to the Intuitionistic Fuzzy Normed Space. Journal of Computational and Applied Mathematics, 233, 142-149. https://doi.org/10.1016/j.cam.2009.07.005
[14]
Das, P., Kostyrko, P., Wilczyski, W. and Malik, P. (2008) I and -Convergence of Double Sequences. Mathematica Slovaca, 58, 605-620. https://doi.org/10.2478/s12175-008-0096-x
[15]
Hazarika, B. (2013) Lacunary Difference Ideal Convergent Sequence Spaces of Fuzzy Numbers. Journal of Intelligent and Fuzzy Systems, 25, 157-166. https://doi.org/10.3233/IFS-2012-0622
[16]
Kumar, V. and Kumar, K. (2008) On the Ideal Convergence of Sequences of Fuzzy Numbers. Information Sciences, 178, 4670-4678. https://doi.org/10.1016/j.ins.2008.08.013
[17]
Damla, B. (2020) Statistical Convergence of Order for Double Sequences of Fuzzy Numbers. Journal of Intelligent and Fuzzy Systems, 39, 6949-6954. https://doi.org/10.3233/JIFS-200039
[18]
Savaş, E. (1996) A Note on Double Sequences of Fuzzy Numbers. Turkish Journal of Mathematics, 20, 175-178.
[19]
Saini, K., Raj, K. and Mursaleen, M. (2021) Deferred Cesro and Deferred Euler Equi-Statistical Convergence and Its Applications to Korovkin-Type Approximation Theorem. International Journal of General Systems, 50, 567-579. https://doi.org/10.1080/03081079.2021.1942867
[20]
Savaş, E. and Mursaleen (2004) On Statistically Convergent Double Sequences of Fuzzy Numbers. Information Sciences, 162, 183-192. https://doi.org/10.1016/j.ins.2003.09.005
[21]
Parashar, S.D. and Choudhary, B. (1994) Sequence Spaces Defined by Orlicz Functions. Indian Journal of Pure and Applied Mathematics, 25, 419-428.
