In this paper, we introduce the concepts of statistically convergent sequences of order β and statistically Cauchy sequences of order β in fuzzy normed spaces. Furthermore, we give the relations between statistically convergent sequences of order β and statistically Cauchy sequences of order β.
AltinokH., KasapM., f-statistical convergence of order β for sequences of fuzzy numbers, Journal of Intelligent and Fuzzy Systems33(2) (2017), 705–712.
2.
AltinokH., AltinY., IşikM., Statistical convergence and strong p cesàro summability of order β in sequences of fuzzy numbers, Iranian J of Fuzzy Systems9(2) (2012), 63–73.
3.
BagT., SamantaS.K., Fixed point theorems in Felbin’s type fuzzy normed linear spaces, J Fuzzy Math16(1) (2008), 243–260.
4.
ÇinarM.,
KarakaşM. and
EtM., On pointwise and uniform statistical convergence of order α for sequences of functions, Fixed Point Theory Appl2013 (2013) 33, 11.
5.
ÇolakR., Statistical convergence of order α Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010 pp. 121–129.
6.
ConnorJ.S., The statistical and strong p– Cesaro convergence of sequences, Analysis8 (1988), 47–63.
7.
DiamondP., KloedenP., Metric Spaces of Fuzzy Sets-Theory and Applications World Scientific Publishing, Singapore, 1994.
8.
EtM., Generalized Cesàro difference sequence spaces of nonabsolute type involving lacunary sequences, Appl Math Comput219(17) (2013), 9372–9376.
9.
EtM., ŞengülH., Some Cesaro-type summability spaces of order α and lacunary statistical convergence of order α, Filomat28(8) (2014), 1593–1602.
10.
EtM., ÇinarM. and
KarakaşM., On λ-statistical convergence of order α of sequences of function, J Inequal Appl2013 (2013), 204, 8.
11.
EtM., AltinokH., AltinY., On some generalized sequence spaces, Appl Math Comput154(1) (2004), 167–173.
12.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
13.
FelbinC., Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems48(2) (1992), 239–248.
14.
FridyJ., On statistical convergence, Analysis5 (1985), 301–313.
15.
GökhanA., EtM., MursaleenM., Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers, Math Comput Modelling49(3-4) (2009), 548–555.
16.
IşikM., Strongly almost (w, λ, q)– summable sequences, Math Slovaca61(5) (2011), 779–788.
17.
KalevaO., SeikkalaS., On fuzzy metric spaces, Fuzzy Sets and Systems12(3) (1984), 215–229.
18.
LakshmikanthamV., MohapatraR.N., Theory of Fuzzy Differential Equations and Inclusions, Taylor and Francis, New York, 2003.
19.
MaX., ZhanJ., AliM.I., MehmoodN., A survey of decision making methods on two classes of hybrid soft set models, Artificial Intelligence Review49(4) (2018), 511–529.
20.
MizumotoM., TanakaK., Some properties of fuzzy numbers, Advances in Fuzzy Set Theory and Applications, North-Holland, Amsterdam, 1979, pp. 153–164.
21.
MohiuddineS.A., ŞevliH. and CancanM., Statistical convergence of double sequences in fuzzy normed spaces, Filomat26(4) (2012), 673–681.
22.
MóriczF., Tauberian conditions, under which statistical convergence follows from statistical summability (C, 1), J Math Anal Appl275(1) (2002), 277–287.
23.
ŠalátT., On statistically convergent sequences of real numbers, Math Slovaca30 (1980), 139–150.
24.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
25.
SteinhausH., Sur la convergence ordinaire et la convergence asymptotique, Colloq Math2 (1951), 73–74.
26.
ŞençimenC. and PehlivanS., Statistical convergence in fuzzy normed linear spaces, Fuzzy Sets and Systems159(3) (2008), 361–370.
27.
ŞengülH. and EtM., On lacunary statistical convergence of order α, Acta Math Sci Ser B Engl Ed34(2) (2014), 473–482.
28.
TurkmenM.R., CinarM., Lacunary statistical convergence in fuzzy normed linear spaces, Applied and Computational Mathematics6(5) (2017), 4023–4030.
29.
TurkmenM.R., CinarM., λ Statistical convergence in fuzzy normed linear spaces, Journal of Intelligent and Fuzzy Systems34(6) (2018), 4023–4030.
30.
XiaoJ., ZhuX., On linearly topological structure and property of fuzzy normed linear space, Fuzzy Sets and Systems125(2) (2002), 153–161.
31.
ZadehL.A., Fuzzy sets, Information and Control8 (1965), 338–353.
32.
ZhanJ., SunB., AlcantudJ.C.R., Covering based multigranulation (I,T)-fuzzy rough set models applications in multiattribute group decision-making, Information Sciences476 (2019), 290–318.
33.
ZhanJ., XuW., Two types ofcoverings based multigranulation rough fuzzy sets and applications to decision making, Artificial Intelligence Review (2018) https://org/10.1007/s10462-018-9649-8.
34.
ZhangL., ZhanJ., Novel classes of fuzzy soft β- coverings-based fuzzy rough sets with applications to multi criteria fuzzy group decision making, Soft Computing (2018) https://doi.org/10.1007/s00500-018-3470-9.
