In this paper, we extend the notions of statistically convergence of order β and strong Cesàro summability of order β, and introduce the notions f-statistically convergence of order β and strong Cesàro summability of order β for β ∈ (0, 1] with respect to an unbounded modulus function f for sequences of fuzzy numbers and give some inclusion theorems.
AizpuruA., Listan-GarciaM.C. and Rambla-BarrenoF., Density by moduli and statistical convergence, Quaest Math37 (2014), 525–530.
2.
ÇakanÜ and AltinY., Some classes of statistically convergent sequences of fuzzy numbers generated by a modulus function, Iranian Journal of Fuzzy Systems12(3) (2015), 47–55.
3.
AltinY., AltinokH. and ÇolakR., Statistical convergence of order α for difference sequences, Quaestiones Mathematicae38(4) (2015), 505–514.
4.
AltinokH., AltinY. and IşikM., Statistical convergence and strong p-Cesáro summability of order β in sequences of fuzzy numbers, Iranian J of Fuzzy Systems9(2) (2012), 65–75.
5.
AltinokH., Statistical convergence of order β for generalized difference sequences of fuzzy numbers, Journal of Intelligent & Fuzzy Systems26 (2014), 847–856.
6.
AytarS. and PehlivanS., Statistical convergence of sequences of fuzzy numbers and sequences of α-cuts, International Journal of General Systems37(2) (2008), 231–237.
7.
BhardwajV.K. and DhawanS., f–statistical convergence of order α and strong Cesaro summability of order α with respect to a modulus, J Inequal Appl2015 (2015), 332. DOI: 10.1186/s13660-015-0850-x.
8.
ÇakalliH., On statistical convergence in topological groups, Pure Appl Math Sci43 (1996), 27–31.
9.
Çanakİ, Tauberian theorems for Cesaro summability of sequences of fuzzy numbers, J Intell Fuzzy Syst27(2) (2014), 937–942.
10.
CasertaA., MaioG.D. and KočcinacL.D.R., Statistical convergence in function spaces, Abstr Appl Anal (2011), 11. Article ID420419. doi: 10.1155/2011/420419.
11.
ÇolakR., Statistical convergence of order α, Modern Methods in Analysis and Its Applications, New Delhi, India: Anamaya Pub, 2010, pp. 121–129.
12.
ÇolakR. and BektaşC.A., λ statistical convergence of order α, Acta Math Sci31(3) (2011), 953–959.
13.
ConnorJ.S., The statistical and strong pCesaro convergence of sequences, Analysis8 (1988), 47–63.
14.
EtM., Strongly almost summable difference sequences of order m defined by a modulus, Studia Sci Math Hungar40(4) (2003), 463–476.
15.
EtM., Spaces of Cesáro difference sequences of order r defined by a modulus function in a locally convex space, Taiwanese J Math10(4) (2006), 865–879.
16.
EtM., CinarM. and KarakaşM., On λ-statistical convergence of order α of sequences of functions, J Inequal Appl2013 (2013), Article ID 204 DOI: 10.1186/1029-242X-2013-204
17.
FastH., Sur la convergence statistique, Colloq Math2 (1951), 241–244.
18.
FridyJ., On statistical convergence, Analysis5 (1985), 301–313.
19.
HazarikaB., Lacunary difference ideal convergent sequence spaces of fuzzy numbers, Journal of Intelligent & Fuzzy Systems25(1) (2013), 157–166.
20.
MaX., LiuQ. and ZhanJ., A survey of decision making methods based on certain hybrid soft set models, Artificial Intelligence Review47 (2017), 507–530.
21.
MatlokaM., Sequences of fuzzy numbers, Busefal28 (1986), 28–37.
22.
MursaleenM. and MohiuddineS.A., On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, Jour Comput Appl Math233(2) (2009), 142–149.
23.
NakanoH., Concave modulars, J Math Soc Japan5 (1953), 29–49.
24.
NurayF. and SavaşE., Statistical convergence of sequences of fuzzy real numbers, Math Slovaca45(3) (1995), 269–273.
25.
QiuD. and ZhangW., Symmetric fuzzy numbers and additive equivalence of fuzzy numbers, Soft Computing17 (2013), 1471–1477.
26.
QiuD., LuC., ZhangW. and LanY., Algebraic properties and topological properties of the quotient space of fuzzy numbers based on Mareš equivalence relation, Fuzzy Sets and Systems245 (2014), 63–82.
27.
QiuD., ZhangW. and LuC., On fuzzy differential equations in the quotient space of fuzzy numbers, Fuzzy Sets and Systems295 (2016), 72–98.
28.
ŠalátT., On statistically convergent sequences of real numbers, Math Slovaca30 (1980), 139–150.
29.
SarmaB., On a class of sequences of fuzzy numbers defined by modulus function, International Journal of Science & Technology2(1) (2007), 25–28.
30.
SavasE., A note on sequence of fuzzy numbers, Inform Sci124(1-4) (2000), 297–300.
31.
SchoenbergI.J., The integrability of certain functions and related summability methods, Amer Math Monthly66 (1959), 361–375.
32.
TaloÖ. and BaşarF., Certain spaces of sequences of fuzzy numbers defined by a modulus function, Demonstratio Math43(1) (2010), 139–149.
33.
TripathyB.C. and BaruahA., Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math Jour50 (2010), 565–574.
34.
ZhanJ., LiuQ. and HerawanT., A novel soft rough set: Soft rough hemirings and its multicriteria group decision making, Applied Soft Computing54 (2017), 393–402.
35.
ZhanJ. and ZhuK., A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Computing21 (2017), 1923–1936.
36.
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.
