On Asymptotically Lacunary Statistical Equivalent Double Sequences of Fuzzy Numbers

Authors

  • Chirasak Mongkolkeha Department of Mathematics Statistics and Computer Sciences, Faculty of Liberal Arts and Science, Kasetsart University, Kamphaeng-Saen Campus, Nakhonpathom 73140
  • Phatiphat Thounthong Renewable Energy Research Centre, King Mongkut's University of Technology North Bangkok (KMUTNB), Bangkok, Thailand; Department of Teacher Training in Electrical Engineering, Faculty of Technical Education, King Mongkut's University of Technology North Bangkok (KMUTNB), Bangkok
  • Poom Kumam KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand; KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha Uthit Road, Bang Mod, Thung Khru, Bangkok 10140

DOI:

https://doi.org/10.26713/cma.v7i3.435

Keywords:

Fuzzy numbers, Asymptotical equivalence, Asymptotical double lacunary statistical equivalence, Double sequences

Abstract

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

Download data is not yet available.

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

14-11-2016
CITATION

How to Cite

Mongkolkeha, C., Thounthong, P., & Kumam, P. (2016). On Asymptotically Lacunary Statistical Equivalent Double Sequences of Fuzzy Numbers. Communications in Mathematics and Applications, 7(3), 263–273. https://doi.org/10.26713/cma.v7i3.435

Issue

Section

Research Article