On Asymptotically Lacunary Statistical Equivalent Double Sequences of Fuzzy Numbers
DOI:
https://doi.org/10.26713/cma.v7i3.435Keywords:
Fuzzy numbers, Asymptotical equivalence, Asymptotical double lacunary statistical equivalence, Double sequencesAbstract
In this paper, we present the asymptotically double lacunary statistical equivalent and strongly asymptotically double lacunary statistical equivalent which is a natural combination of the definition for asymptotically equivalence and lacunary statistical double sequences of fuzzy numbers. In addition, we also give some relations among these new notions.Downloads
References
G.A. Anastassiou, Fuzzy approximation by fuzzy convolution type operators, Comput. Math. Appl. 48 (2004), 1369–1386.
L.C. Barros, R.C. Bassanezi and P.A. Tonelli, Fuzzy modelling in population dynamics, Ecol. Model. 128 (2000), 27–33.
P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets Syst. 35 (1990), 241–249.
R. Giles, A computer program for fuzzy reasoning, Fuzzy Sets Syst. 4 (1980), 22–234.
L. Hong and J.Q. Sun, Bifurcations of fuzzy nonlinear dynamical systems, Commun. Nonlinear Sci. Numer. Simul. 1 (2006), 1–12.
M. Marouf, Asymptotic equivalence and summability, Internat. J. Math. Math. Sci. 16 (4) (1993), 755–762.
M. Matloka, Sequences of fuzzy numbers, Busefal 28 (1986), 28-37.
M. Mursaleen and O.H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003), 223–231.
M. Mursaleen and O.H. Edely, Almost convergence and a core theorem for double sequences, J. Math. Anal. Appl. 293 (2004), 532–540.
M. Mursaleen and S.A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals 41 (2009), 2414–2421.
S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems 33 (1989), 123–126.
F. Nuray, Lacunary statisticall convergence of sequence of fuzzy numbers, Fuzzy Sets Syst. 99 (1998), 353–356.
F. Nuray and E. Savas, Statisticall convergence of sequence of fuzzy numbers, Math. Slovaca 45 (1995), 269–273.
R.F. Patterson, On asymptotically statistically equivalent sequences, Demonstratio Math. 36 (1) (2003), 149–153.
R.F. Patterson and E. Savas, On asymptotically lacunary statistical equivalent sequences, Thai J. Math. 4 (2) (2006), 267–272.
E. Savas, On extension asymptotically lacunary statistical equivalent sequences of fuzzy numbers, JCIS 2007 Joint Conference on Information Science, July 18–24, 2007, USA.
E. Savas, On lacunary statistically convergent double sequences of fuzzy numbers, Appl. Math. Lett. 21 (2008), 134–141.
E. Savas and S.A. Mohiuddine, (lambda)-statistically convergent double sequences in probabilistic normed spaces, Math. Slovaca 62 (1) (2012), 99–108.
E. Savas and M. Mursaleen, On statistically convergent double sequences of fuzzy numbers, Inform. Sci. 162 (2004), 183–192.
E. Savas and R.F. Patterson, Double sequence spaces characterized by lacunary sequences, Appl. Math. Lett. 20 (2007), 964–970.
P. Thounthong, A. Luksanasakul, P. Koseeyaporn and D. Bernard Davat, Intelligent model-based control of a standalone photovoltaic±fuel cell power plant with supercapacitor energy storage, IEEE Transactions on Sustainable Energy 4 (1) (January 2013), 240-249.
P. Thounthonga, L. Piegarib, S. Pierfedericic and B. Davatc, Nonlinear intelligent DC grid stabilization for fuel cell vehicle applications with a supercapacitor storage device, International Journal of Electrical Power & Energy Systems 64 (January 2015), 723–733.
K. Wu, Convergences of fuzzy sets based on decomposition theory and fuzzy polynomial function, Fuzzy Sets Syst. 109 (2000), 173–185. [24] L.A. Zadeh, Fuzzy sets, Inform Control 8 (1965), 338–353.
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.