In this paper we study approximation properties (APs) and bounded approximation properties (BAPs) in the setting of intuitionistic fuzzy n-Banach spaces (IFnBSs). Further, we define strong intuitionistic fuzzy n-continuous and strong intuitionistic fuzzy n-bounded operators and using them we prove the existence of an IFnBS with AP. In addition, we provide examples which show that there exist IFnBSs with the AP which fail to have the BAP.
T.Bag and S.K.Samanta, Finite dimensional fuzzy normed linear spaces, J Fuzzy Math11 (2003), 687–705.
3.
S.C.Cheng and J.N.Mordeson, Fuzzy linear operator and fuzzy normed linear space, Bull Cal Math Soc86 (1994), 429–436.
4.
P.Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput Math Appl63 (2012), 708–715.
5.
P.Debnath, Results on lacunary difference ideal convergence in intuitionistic fuzzy normed linear spaces, J Intell Fuzzy Syst28 (2015), 1299–1306.
6.
P.Debnath, A generalized statistical convergence in intu-itionistic fuzzy n-normed linear spaces, Ann Fuzzy Math Inform12(4) (2016), 559–572.
7.
P.Debnath and M.Sen, 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.
8.
P.Debnath and M.Sen, Some results of calculus for functions having values in an intuitionistic fuzzy n-normed linear space, J Intell Fuzzy Syst26(2) (2014), 2983–2991.
J.Lindenstrauss, On Jame's paper "separable conjugate spaces", Isr J Math9 (1971), 279–284.
19.
X.Ma, J.Zhan, M.I.Ali, and N.Mehmood, A survey of decision making methods based on two classes of hybrid soft set models, Artif Intell Rev49(4) (2018), 511–529.
20.
M.Mursaleen, S.A.Mohiuddine and H.H.Edely, On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces, Comput Math Appl59 (2010), 603–611.
21.
R.Saadati and J.H.Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons & Fractals27 (2006), 331–344.
22.
M.Sen and P.Debnath, Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, Math Comput Modelling54 (2011), 2978–2985.
23.
M.Sen, S.Nath and B.C.Tripathy, Best approximation in quotient probabilistic normed space, J Appl Anal23(1) (2017), 53–57.
24.
B.C.Tripathy, M.Sen and S.Nath, I-convergence in probabilistic n-normed space, Soft Comput16 (2012), 1021–1027.
25.
B.S.Tripathy and S.Borgohain, On a class of n-normed sequences related to the lp-space, Bol Soc Parana Mat (3)31(1) (2013), 167–173.
26.
S.Vijayabalaji, N.Thillaigovindan and Y.B.Jun, Intuitionistic fuzzy n-normed linear space, Bull Korean Math Soc44 (2007), 291–308.
27.
Y.Yilmaz, On some basic properties of differentiation in intuitionistic fuzzy normed spaces, Math Comput Modelling52 (2010), 448–458.
28.
Y.Yilmaz, Schauder bases and approximation property in fuzzy normed spaces, Comput Math Appl59 (2010), 1957–1964.
J.Zhan and J.C.R.Alcantud, A novel type of soft rough covering and its application to multicriteria group decision making, Artif Intell Rev, 2018. 10.1007/s10642-018-9617-3
31.
J.Zhan and Q.Wang, Certain types of soft converings base-drough sets with applications, Int J Mach Learn Cybern, 2018.10.1007/s13042-018-0785-x
32.
J.Zhan and W.Xu, Two types of covering based multigranulation rough fuzzy sets and applications to decision making, Artif Intell Rev, 2018. 10.1007/s10462-018-9649-8
33.
L.Zhang and J.Zhan, Fuzzy soft ß-covering based fuzzy rough sets and corresponding decision-making applications, Int J Mach Learn Cybern, 2018, 10.1007/s13042-018-0828-3
34.
L.Zhang and J.Zhan, Novel classes of fuzzy soft ß-coverings based fuzzy rough sets with applications to multi-criteria fuzzy group decision making, Soft Comput, 2018.10.1007/s00500-018-3470-9