NORM AND INNER PRODUCT ON FUZZY LINEAR SPACES OVER FUZZY FIELDS

Document Type: Research Paper

Authors

Department of Mathematical Sciences, Kannur University, Man- gattuparamba, Kannur, Kerala, 670 567, India.

Abstract

In this paper, we introduce the concepts of norm and inner prod-
uct on fuzzy linear spaces over fuzzy elds and discuss some fundamental
properties.

Keywords


[1] T. Bang and S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math.,
11(3) (2003), 687-705.
[2] R. Biswas, Fuzzy inner product spaces and fuzzy norm functions, Information Sciences, 53
(1991), 185-190.
[3] S. C. Cheng and J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces,
Bull. Calcutta Math. Soc., 86(5) (1994), 429-436.
[4] A. M. El-Abyad and H. M. El-Hamouly, Fuzzy inner product spaces, Fuzzy Sets and Systems,
44(2) (1991), 309-326.
[5] C. Felbin, Finite dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48(2)
(1992), 239-248.
[6] C. Felbin, Finite dimensional fuzzy normed linear space. II, Journal of Analysis, 7 (1999),
117-131.
[7] M. Goudarzi and S. M. Vaezpour, On the de nition of fuzzy Hilbert spaces and its application,
J. Nonlinear Sci. Appl., 2(1) (2009), 46-59.
[8] A. K. Katsaras, Fuzzy topological vector spaces. II, Fuzzy Sets and Systems, 12(2) (1984),
143-154.
[9] G. J. Klir and B. Yuan, Fuzzy sets and fuzzy logic: theory and applications, Prentice-Hall of
India, New Delhi, 2002.
[10] J. K. Kohli and R. Kumar, On fuzzy inner product spaces and fuzzy co-inner product spaces,
Fuzzy Sets and Systems, 53(2) (1993), 227-232.
[11] S. V. Krishna and K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and
Systems, 63(2) (1994), 207-217.
[12] R. Saadati and S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. and
Computing, 17 (2005), 475-484.
[13] S. M. Vaezpour and F. Karimi, t-best approximation in fuzzy normed spaces, Iranian Journal
of Fuzzy Systems, 5(2) (2008), 93-99.
[14] G. Wenxiang and L. Tu, Fuzzy linear spaces, Fuzzy Sets and Systems, 49 (1992), 377-380.
[15] C. Wu and J. Fang, Fuzzy generalization of Kolmogoro s theorem, J. Harbin Inst. Technol.,
1 (1984), 1-7.
[16] J. Xiao and X. Zhu, On linearly topological structure and property of fuzzy normed linear
space, Fuzzy Sets and Systems, 125(2) (2002), 153-161.
[17] H. J. Zimmermann, Fuzzy set theory and its applications (second revised edition), Allied
Publishers Limited, New Delhi, 1996.