Deferred Statistical Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces

Yıl 2019, Cilt: 11, 95 - 104, 30.12.2019

Ömer Kişi Erhan Guler

Öz

In this study, the intuitionistic fuzzy deferred statistical convergence of double sequences in the intuitionistic fuzzy normed space is defined by considering deferred density given in 2016 by K\"{u}\c{c}\"{u}kaslan and M. Y\i lmazt\"{u}rk. Besides the main properties of this new method, it is compared with intuitionistic fuzzy statistical convergence of double sequences and itself under different restrictions on the method. Some special cases of the obtained results coincide with known results in literature.

Anahtar Kelimeler

Intuitionistic fuzzy deferred convergence, intuitionistic fuzzy

Kaynakça

• Agnew, R.P., {\em On deferred Cesaro mean}, Comm. Ann. Math., \textbf{33}(1932), 413--421.
• Atanassov, K., Intuitionistic fuzzy sets, VII ITKR Session, Sofia, 20-23 June 1983, (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, 2016, 20(S1), S1--S6.
• Atanassov, K., {\em Intuitionistic fuzzy sets}, Fuzzy Set Syst., \textbf{20}(1986), 87--96.
• Erceg, M.A., {\em Metric spaces in Fuzzy set theory}, J. Math. Anal. Appl., \textbf{69}(1979), 205--230.
• Fast, H., {\em Sur la convergence statistique}, Colloq. Math., \textbf{2}(1951), 241--244.
• Fradkov, A.L., Evans, R.J., {\em Control of Chaos: Methods and applications in engineering}, Chaos, Solitons Fractals, \textbf{29}(2005), 33--56.
• Fridy, J.A., {\em On statistical convergence}, Analysis, \textbf{5}(1985), 301--313.
• George, A., Veeramani, P., {\em On some results in Fuzzy metric space}, Fuzzy Set Syst., \textbf{64}(1994), 395--399.
• Hong, L., Sun, J.Q., {\em Bifurcations of fuzzy nonlinear dynamical systems}, Commun. Nonlinear Sci. Numer. Simul., \textbf{1}(2006), 1--12. Kaleva, O., Seikkala, S.,{\em On Fuzzy metric spaces}, Fuzzy Set Syst., \textbf{12}(1984), 215--229.
• Karakus, S., Demirci, K., Duman, O., {\em Statistical convergence on intuitionistic fuzzyn normed spaces}, Chaos Solitons Fractals, \textbf{35}(2008), 763--769.
• K\"{u}\c{c}\"{u}kaslan M., Yilmazt\"{u}rk, M., {\em On deferred statistical convergence of sequences}, Kyungpook Math. J., \textbf{56}(2016), 357--366.
• Ko\v{c}inac, Lj.D.R., Rashid, M.H.M., {\em On ideal convergence of double sequences in the topology induced by a fuzzy 2-norm}, TWMS J. Pure Appl. Math., \textbf{8(1)}(2017), 97--111.
• Madore, J., {\em Fuzzy physics}, Ann. Phys., \textbf{219}(1992), 187--198.
• Maio, G. Di, Ko\v{c}inac, Lj.D.R., {\em Statistical convergence in topology}, Topology Appl., \textbf{156(1)}(2008), 28--45.
• Melliani, S., Elomari, M., Chadli, L.S., Ettoussi, R., {\em Intuitionistic fuzzy metric space}, Notes on Intuitionistic Fuzzy Sets, \textbf{21(1)}(2015) 43-53.
• Melliani, S., K\"{u}\c{c}\"{u}kkaslan, M., Sadiki, H., Chadli, L.S., {\em Deferred statistical convergence of sequences in intuitionistic fuzzy normed spaces}, Notes on Intuitionistic Fuzzy Sets, \textbf{24(3)}(2018), 64--78, DOI:n 10.7546/nifs.2018.24.3.64-78.
• Mohiuddine, S.A., Mohiuddine, Q.M., Lahoni, D., {\em On generalized statistical convergence in intuitionistic fuzzy normed spaces}, Chaos, Solitons Fractals, \textbf{42}(2009), 1731--1737.
• Mursaleen, M., Mohiuddine, S.A., {\em On lacunary statistical convergence with respect to the intuitionistic fuzzy normed spaces}, J. Comput. appl. Math., \textbf{233}(2009), 142--149.
• Saadati, R., Park, J. H., {\em On the intuitionistic fuzzy topological spaces}, Chaos Solitons Fractals, \textbf{27}(2006), 331--344.
• Sal\'{a}t, T., {\em On statistically convergent sequences of real numbers}, Math. Slovaka, \textbf{30}(1980), 139--150.
• Schweizer, B., Sklar, A., {\em Statistical metric spaces}, Pac. J. Math., \textbf{10(1)}(1960), 313--334.
• Steinhaus, H., \textit{Sur la convergence ordinaire et la convergence asymptotique}, Colloq. Math., \textbf{2}(1951), 73--74.
• Zadeh, L. A., {\em Fuzzy sets}, Inform Control, \textbf{8}(1965), 338--353.