In this paper, we have introduced λ- statistical convergence and condition of being λ- statistical Cauchy of real number sequences in fuzzy normed linear spaces. At the same time, in fuzzy normed spaces, we have introduced the concept of (V, λ) summability and (C, 1) summability, and then, we have studied the relation between these concepts and λ- statistical convergence.
AltinokH., AltinY. and EtM., Lacunary almost statistical convergence of fuzzy numbers, Thai Journal of Mathematics2(2) (2004), 265–274.
2.
BagT. and SamantaS.K., Fixed point theorems in Felbin’s type fuzzy normed linear spaces, J Fuzzy Math16(1) (2008), 243–260.
3.
ConnorJ.S., The statistical and strong– Cesaro convergence of sequences, Analysis8 (1988), 47–63.
4.
ÇolakR., On λ– statistical convergence, Conference on Summability and Applications, Istanbul, Turkey, 2011.
5.
DiamondP., KloedenP., Metric Spaces of Fuzzy Sets-Theory and Applications, World Scientific Publishing, Singapore, 1994.
6.
EtM., ÇinarM. and KarakaşM., On λ– statistical convergence of order α of sequences of function, J Inequal Appl204 (2013), 1–8.
7.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
8.
FelbinC., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems48(2) (1992), 239–248.
9.
FridyJ., On statistical convergence, Analysis5 (1985), 301–313.
10.
KalevaO. and SeikkalaS., On fuzzy metric spaces, Fuzzy Sets and Systems12(3) (1984), 215–229.
11.
MizumotoM., TanakaK., Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and Applications, North-Holland Amsterdam, 1979, pp. 153–164.
12.
MohiuddineS.A., ŞevliH. and CancanM., Statistical convergence of double sequences in fuzzy normed spaces, Filomat26(4) (2012), 673–681.
13.
MursaleenM., λ– statistical convergence, Math Slovaca50(1) (2000), 111–115.
14.
SencimenC. and PehlivanS., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems159(3) (2008), 361–370.
15.
ŠalátT., On statistically convergent sequences of real numbers, Math Slovaca30 (1980), 139–150.
16.
SavasE., On strongly λ– summable sequences of fuzzy numbers, Information Science125(1-4) (2000), 181–186.
17.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
18.
SteinhausH., Sur la convergence ordinaire et la convergence asymptotique, Colloq Math2 (1951), 73–74.
19.
XiaoJ. and ZhuX., On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets and Systems125(2) (2002), 153–161.
20.
ZygmundA., Trigonometric Series, Cambridge University Press, Cambridge UK, 1979.
21.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
22.
GudderS., What is fuzzy probability theory?Foundations of Physics30(10) (2000), 1663–1678.
23.
ZhanJ., YuB. and FoteaV.-E., Characterizations of two kinds of hemirings based on probability spaces, Soft Comput20 (2016), 637–648.
24.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Comput21 (2017), 1923–1936.
25.
LiZ. and XieT., The relationship among soft sets, soft rough sets and topologies, Soft Comput18 (2014), 717–728.
26.
LiZ., WenG. and HanY., Decision making based on intuitionistic fuzzy soft sets and its algorithm, J Comput Anal Appl17(4) (2014), 620–631.
27.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artif Intell Rev47 (2017), 507–530.
28.
ZhanJ., AliM.I. and MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Applied Soft Computing56 (2017), 446–457.
29.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and corresponding multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
