Interval valued Fuzzy n-normed linear space
DOI:
https://doi.org/10.11113/mjfas.v4n1.37Keywords:
Interval valued fuzzy subspace, Operations, Flags, Interval valued fuzzy n-normed linear space,Abstract
The aim of this paper is to introduce the notion of interval-valued fuzzy subspace with its flags and interval-valued fuzzy n-normed linear space. We define the operations intersection, sum, directsum and tensor product of intervalvalued fuzzy subspaces and obtain their corresponding flags. Further we provide some results on interval-valued fuzzy n-normed linear space. AMS Subject Classification : 46S40, 03E72.References
K.S.Abdukhalikov, M.S.Tulenbaev and U.U.Umirbaev,On fuzzy bases of vector spaces,Fuzzy sets and systems,63(1994),201-206.
K.S.Abdukhalikov,The dual of a fuzzy subspace,Fuzzy sets and systems,82(1996),375-381.
K.S.Abdukhalikov,Fuzzy linear maps,Journal of Math. Analysis and Appl.,220(1998),1-12.
T.Bag and S.K.Samanta,Finite dimensional fuzzy normed linear spaces, The Journal of Fuzzy Mathematics,11(2003),No.3,687-705.
S.C.Chang and J.N.Mordesen, Fuzzy linear operators and fuzzy normed linear spaces, Bull.Cal.Math.Soc.,86(1994),429-436.
C.Felbin,Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems, 48 (1992), 239-248.
C.Felbin, The Completion of fuzzy normed linear space, Journal of Mathematical Analysis and Applications,174(1993),No.2,428-440.
C.Felbin, Finite dimensional fuzzy normed linear spaces II, Journal of Analysis, 7 (1999), 117-131.
S.G¨ahler, Lineare 2-Normierte R¨aume, Math.Nachr.,28 (1965),1-43.
S.G¨ahler,Unter Suchungen ¨U ber Veralla gemeinerte m-metrische R¨aume I,Math.Nachr., (1969),165-189.
Hendra Gunawan and M.Mashadi,on n-Normed spaces, International J. Math. & Math. Sci.,27 (2001), No.10,631-639.
A.K.Katsaras and D.B.Liu,Fuzzy vector and fuzzy topological vector spaces, Journal of Math.Analysis and Appl.,58 (1977), 135-146.
A.K.Katsaras, Fuzzy topological vector spaces II, Fuzzy Sets and Systems,12 (1984), 143-154.
S.S.Kim and Y.J.Cho,Strict convexity in linear n-normed spaces, Demonstratio Math.,29 (1996), No.4,739-744.
S.V.Krishna and K.K.M.Sharma,Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems, 63 (1994), 207-217.
P.Lubczonok,Fuzzy vector spaces, Fuzzy sets and systems,38(1990),329-343.
G.Lubczonok, V.Murali On flags and fuzzy subspaces of vector spaces, Fuzzy sets and systems,125(2002),201-207.
B.B.Makamba,V.Murali,Fuzzy direct sums and free submodules, The Journal of Fuzzy Mathematics,(2001)
R.Malceski,Strong n-convex n-normed spaces, Mat.Bilten, 21 (1997), 81-102.
A.Misiak, n-inner product spaces, Math.Nachr.,140 (1989),299-319.
J.N.Mordeson,Bases of Fuzzy vector spaces,Information Sciences,67(1993)87-92.
AL.Narayanan and S.Vijayabalaji, Fuzzy n-normed linear space, International J. Math.& Math. Sci., (2005) No.24, 3963-3977.
G.S.Rhie,B.M.Choi and S.K.Dong,On the completeness of fuzzy normed linear spaces, Math. Japonica, 45 (1997), No.1, 33-37.
L.A.Zadeh,The concept of a linguistic variable and its application to approximate reasoning I,Information Sciences, 8(1975) 199-249.
