BEST APPROXIMATION SETS IN -n-NORMED SPACE CORRESPONDING TO INTUITIONISTIC FUZZY n-NORMED LINEAR SPACE

Document Type : Research Paper

Authors

1 Department of Mathematics, Anna University, Tiruchirappallli, Panruti Campus, Tamilnadu, India

2 Department of Mathematics, Annamalai university, Annamalainagar- 608002, Tamilnadu, India

Abstract

The aim of this paper is to present the new and interesting notion
of ascending family of  $alpha $ −n-norms corresponding to an intuitionistic fuzzy nnormed
linear space. The notion of best aproximation sets in an  $alpha $ −n-normed
space corresponding to an intuitionistic fuzzy n-normed linear space is also
defined and several related results are obtained.

Keywords


[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
[2] K. T. Atanassov, Intuitionistic fuzzy sets, Physica-Verlag Heidelberg, Newyork, 1999.
[3] T. Bag and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, The Journal of
Fuzzy Mathematics, 11(3) (2003), 687-705.
[4] S. C. Chang and J. N. Mordesen, Fuzzy linear operators and fuzzy normed linear spaces,
Bull. Cal. Math. Soc., 86 (1994), 429-436.
[5] C. Felbin, The completion of fuzzy normed linear space, Journal of Mathematical Analysis
and Applications, 174(2) (1993), 428-440.
[6] C. Felbin, Finite dimensional fuzzy normed linear spaces II, Journal of Analysis, 7 (1999),
117-131.
[7] S. G¨ahler, Lineare 2-normierte R¨aume, Math. Nachr., 28 (1965), 1-43.
[8] S. G¨ahler, Unter Suchungen ¨U ber Veralla gemeinerte m-metrische R¨aume I, Math. Nachr.,
1969, 165-189.
[9] H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. Math. Sci., 27(10) (2001),
631-639.
[10] S. S. Kim and Y. J. Cho, Strict convexity in linear n-normed spaces, Demonstratio Math.,
29(4) (1996), 739-744.
[11] S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and
Systems, 63 (1994), 207-217.
[12] R. Malceski, Strong n-convex n-normed spaces, Mat. Bilten, 21 (1997), 81-102.
[13] A. Misiak, n-inner product spaces, Math. Nachr., 140 (1989), 299-319.
[14] A. Narayanan and S. Vijayabalaji, Fuzzy n-normed linear space, Int. J. Math. Math. Sci.,
24 (2005), 3963-3977.
[15] A. Narayanan, S. Vijayabalaji and N. Thillaigovindan, Intuitionistic fuzzy bounded linear
operators, Iranian Journal of Fuzzy Systems, 4(1) (2007), 89-101.