On Asymptotically Lacunary Statistical Equivalent Double Sequences of Fuzzy Numbers

Chirasak Mongkolkeha, Phatiphat Thounthong, Poom Kumam


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.


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

Full Text:



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.


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905