Statistical convergence of sequences has been studied in neutrosophic normed spaces (NNS) by Kirişci and Şimşek [39]. Ideal convergence is more general than statistical convergence for sequences. This has motivated us to study the ideal convergence in NNS. In this paper, we study the concept of ideal convergence and ideal Cauchy for sequences in NNS.
AtanassovK.T., PasiG. and YagerR., Intuitionistic fuzzyinterpretations of multi-person multicriteria decision making, Proceedings of First International IEEE Symposium IntelligentSystems1 (2002), 115–119.
4.
KramosilI. and MichalekJ., Fuzzy metric and statistical metricspaces, Kybernetika11 (1975), 336–344.
5.
KalevaO. and SeikkalaS., On fuzzy metric spaces, Fuzzy Setsand Systems12 (1984), 215–229.
6.
GeorgeA. and VeeramaniP., On some results in fuzzy metric spaces, Fuzzy Sets and Systems64 (1994), 395–399.
7.
GeorgeA. and VeeramaniP., On some results of analysis for fuzzymetric spaces, Fuzzy Sets and Systems90 (1997), 365–368.
SaadatiR. and ParkJ.H., On the intuitionistic fuzzy topologicalspaces, Chaos, Solitons and Fractals27 (2006), 331–344.
10.
TurksenI., Interval valued fuzzy sets based on normal forms, Fuzzy Sets and Systems20 (1996), 191–210.
11.
AtanassovK.T. and GargovG., Interval valued intuitionistic fuzzysets, Fuzzy Sets and Systems31(3) (1989), 343–349.
12.
SmarandacheF., A unifying field in logics: Neutrosophic logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics, Phoenix: Xiquan (2003).
13.
YagerR.R., Pythagorean fuzzy subsets, In Proceedings of joint IFSAWorld Congress and NAFIPS annual meeting, Edmonton, Canada (2013), 57–61.
14.
SmarandacheF., Neutrosophic set, a generalisation of theintuitionistic fuzzy sets, Int J Pure Appl Math24(2005), 287–297.
15.
SmarandacheF., Neutrosophy. Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, Ann Arbor, Michigan, USA (1998).
16.
MolodtsovD., Soft set theory-First results, Computer andMathematics with Applications Solitons and Fractals41(2009), 2414–2421.
17.
ChengS.C. and MordesonJ.N., Fuzzy linear operators and fuzzynormed linear spaces, Bull Cal Math Soc86 (1994), 429–436.
DebnathP., Lacunary ideal convergence in intuitionistic fuzzynormed linear spaces, Comput Math Appl63 (2012), 708–715.
31.
KarakayaV., ŞimsekN., ErtürkM. and GursoyF., λ–Statistical convergence of sequences of functionsin intuitionistic fuzzy normed spaces, J Funct Space Appl2012(2012), 1–14. Article ID 926193, doi:10.1155/2012/926193.
KumarV. and MursaleenM., On (λ; μ)-statisticalconvergence of double sequences on intuitionistic fuzzy normedspaces, Filomat25 (2011), 109–120.
34.
MohiuddineS.A. and Danish LohaniQ.M., On generalized statisticalconvergence in intuitionistic fuzzy normed space, Chaos,Solitons and Fractals42 (2009), 1731–1737.
35.
MursaleenM. and MohiuddineS.A., On lacunary statisticalconvergence with respect to the intuitionistic fuzzy normed space, J Comput Appl Math233(2) (2009), 142–149.
36.
MursaleenM. and MohiuddineS.A., Statistical convergence of doublesequences in intuitionistic fuzzy normed spaces, Chaos,Solitons and Fractals41 (2009), 2414–2421.
37.
MursaleenM., MohiuddineS.A. and EdelyO.H.H., On the idealconvergence of double sequences in intuitionistic fuzzy normedspaces, Comput Math Appl59 (2010), 603–611.
38.
KirisciM. and ŞimşekN., Neutrosophic metric spaces, Mathematical Sciences, Math Sci14 (2020), 241–248.
39.
KirisciM. and ŞimşekN., Neutrosophic normed spaces and statistical convergence, The Journal of Analysis, doi: 10.1007/s41478-020-00234-0.
40.
ŞimşekN. and KirişciM., Fixed point theorems inneutrosophic metric spaces, Sigma J Eng Nat Sci10(2) (2019), 221–230.
41.
KirisciM., ŞimşekN. and AkyiğitM., Fixed point results for a new metric space, Math Meth Appl Sci (2020), 1–7. doi: 10.1002/mma.6189.
YeJ., A multicriteria decision-making method using aggregationoperators for simplifed neutrosophic sets, J Intell FuzzySystems26 (2014), 2459–2466.
44.
SmarandacheF. and VlădăreanuL., Applications of neutrosophic logic to robotics: An introduction, IEEE International Conference on Granular Computing, 2011, Kaohsiung, Taiwan.
45.
MajumdarP., Neutrosophic sets and its applications to decisionmaking, Comput Intell Big Data Analysis19 (2015), 97–115.
46.
DasS, DasR and TripathyB.C., Multi-criteria group decision makingmodel using single-valued neutrosophic set, Log Forum16(3) (2020), 421–429.
47.
DasR. and TripathyB.C., Neutrosophic multiset topological space, Neutrosophic Sets and Systems35 (2020), 142–152.
48.
DasS. and TripathyB.C., Pairwise neutrosophic-b-open set inneutrosophic bitopological spaces, Neutrosophic Sets andSystems38 (2020), 135–144.
49.
KostyrkoP., Š SalátT. and WilczynsskiW., I-convergence, Real Anal Exchange26(2) (2000), 669–686.
50.
KostyrkoP., MacajM., Š SalátT. and SleziakM., I-convergence and extremal I-limit points, Math Slovaca55 (2005), 443–464.
