In classical functional analysis, continuous mappings are essential for the study of many important theorems such as open mapping theorem, closed graph theorem and uniform boundedness theorem. These results are yet to be established in the general setting of an intuitionistic fuzzy n-normed linear space (IFnNLS). This motivates us to introduce the notion of continuous linear operators in this generalized setting. Furthermore, we establish the uniform continuity theorem and Banach’s contraction principle in an IFnNLS.
BagT. and SamantaS.K., Finite dimensional fuzzy normed linear spaces, J Fuzzy Math11 (2003), 687–705.
3.
ChengS.C. and MordesonJ.N., Fuzzy linear operator and fuzzy normed linear space, Bull Cal Math Soc86 (1994), 429–436.
4.
DebnathP.Lacunary difference ideal convergence in intuitionistic fuzzy normed linear spaces, J Intell Fuzzy Syst28 (2015), 1299–1306.
5.
DebnathP.A generalized statistical convergence in intuitionistic fuzzy n-normed linear spaces, Ann Fuzzy Math Inform12(4) (2016), 559–572.
6.
DebnathP. and SenM., Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy n-normed linear spaces, J Intell Fuzzy Syst26(6) (2014), 975–982.
7.
DebnathP. and SenM., Some results of calculus for functions having values in an intuitionistic fuzzy n-normed linear space, J Intell Fuzzy Syst26(2) (2014), 2983–2991.
8.
EsiA. and HazarikaB., λ-ideal convergence in intuitionistic fuzzy 2-normed linear space, J Intell Fuzzy Syst24 (2013), 725–732.
KormosilI. and MichalekJ., Fuzzy metric and statistical metric spaces, Kybernetica11 (1975), 326–334.
14.
MaX., LiuQ. and ZhanJ., A survey of decision making method based on certain hybrid soft set models, Artif Intell Rev47 (2017), 507–530.
15.
MursaleenM., MohiuddineS.A. and EdelyH.H., On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comp Math Apl59 (2010), 603–611.
16.
NadabanS. and DzitacI., Atomic decompositions of fuzzy normed linear spaces for wavelet applications, Informatica25(4) (2014), 643–662.
17.
SaadatiR. and ParkJ.H., On the intuitionistic fuzzy topological spaces, Chaos Solitons & Fractals27 (2006), 331–344.
18.
SenM. and DebnathP., Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, Math Comput Model54 (2011), 2978–2985.
19.
TangY., WenL.L. and WeiG.W., Approaches to multiple attribute group decision making based on the generalized dice similarity measures with intuitionistic fuzzy information, International Journal of Knowledge-based and Intelligent Engineering Systems21(2) (2017), 85–95.
20.
TripathyB.C., SenM. and NathS., I-convergence in probabilistic n-normed space, Soft Comput16 (2012), 1021–1027.
21.
TripathyB.S. and BorgogainS., On a class of n-normed sequences related to the ℓp-space, Bol Soc Parana Mat (3)31(1) (2013), 167–173.
22.
VijayabalajiS. and NarayananA., Fuzzy n-normed linear space, J Math Math Sci24 (2005), 3963–3977.
23.
VijayabalajiS., ThillaigovindanN. and JunY.B., Intuitionistic fuzzy n-normed linear space, Bull Korean Math Soc44 (2007), 291–308.
24.
WeiG.W., WangH.J. and LinR., Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision making with incomplete weight information, Knowl Inf Syst26(2) (2011), 337–349.
25.
WeiG.W., WangH.J., LinR. and ZhaoX.F., Grey relational analysis method for intuitionistic fuzzy multiple attribute decision making with preference information on alternatives, Int J Comput Int Syst4(2) (2011), 164–173.
ZhanJ., AliM.I. and MehmoodN., On a novel uncertain soft set model: Z-soft fuzzy rough set model and corresponding decision making methods, Appl Soft Comput56 (2017), 446–457.
28.
ZhanJ., LiuQ. and HerawanT., A novel sof rough set: Soft rough hemirings and its multicriteria group decision making, Appl Soft Comput54 (2017), 393–402.
29.
ZhanJ. and ZhuK., A novel of soft rough fuzzy set: Z-soft rough fuzzy ideals of hemirings and corresponding decision making, Soft Comput21 (2017), 1923–1936.
