FUZZY BASIS OF FUZZY HYPERVECTOR SPACES

Document Type: Research Paper

Authors

1 School of Mathematics, Statistics and Computer Science, College of Sciences, University of Tehran, Tehran, Iran

2 Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran

Abstract

The aim of this paper is the study of fuzzy basis and dimension
of fuzzy hypervector spaces. In this regard, first the notions of fuzzy linear
independence and fuzzy basis are introduced and then some related results are
obtained. In particular, it is shown that for a large class of fuzzy hypervector
space the fuzzy basis exist. Finally, dimension of a fuzzy hypervector space is
defined and the basic properties of that are investigated.

Keywords


[1] R. Ameri, Fuzzy hypervector spaces over valued fields, Iranian Journal of Fuzzy Systems, 2
(2005), 37-47.
[2] R. Ameri, H. Hedayati and A. Molaee, On fuzzy hyperideals of 􀀀-hyperrings, Iranian Journal
of Fuzzy Systems, to appear.
[3] R. Ameri, Fuzzy (co-)norm hypervector spaces, Proceeding of the 8th International Congress
in Algebraic Hyperstructures and Applications, Samotraki, Greece, September 1-9 (2002),
71-79.
[4] R. Ameri and O. R. Dehghan, On dimension of hypervector spaces, European Journal of
Pure and Applied Mathematics, 1(2) (2008), 32-50.
[5] R. Ameri and O. R. Dehghan, Fuzzy hypervector spaces, Advances in Fuzzy Systems, Article
ID 295649, 2008.
[6] R. Ameri and M. M. Zahedi, Hypergroup and join spaces induced by a fuzzy subset, PU.M.A
8 (1997), 155-168.
[7] R. Ameri and M. M. Zahedi, Fuzzy subhypermodules over fuzzy hyperrings, 6th International
Congress in Algebraic Hyperstructures and Applications, Democritus University, (1996), 1-14.
[8] P. Corsini, Prolegomena of hypergroup theory, Second edition, Aviani editor, (1993).

[9] P. Corsini and V. Leoreanu, Applications of hyperstructure theory, Kluwer Academic Publications,
2003.
[10] P. Corsini and V. Leoreanu, Fuzzy sets and join spaces associated with rough sets, Rend.
Circ. Mat., Palermo, 51 (2002), 527-536.
[11] P. Corsini and I. Tofan, On fuzzy hypergroups, PU. M. A, 8 (1997), 29-37.
[12] B. Davvaz, Fuzzy HV -submodules, Fuzzy Sets and Systems, 117 (2001), 477-484.
[13] B. Davvaz, Fuzzy HV -groups, Fuzzy Sets and Systems, 101 (1999), 191-195.
[14] A. De Luca and S. Termini, A definition of non-probabilistic entropy in the setting of fuzzy
sets theory, Information and control, 20 (1970), 301-312.
[15] A. K. Katsaras and D. B. Liu, Fuzzy vector spaces and fuzzy topological vector spaces, Journal
of Mathematical Analysis and Applications, 58 (1977), 135-146.
[16] P. Lubczonok, Fuzzy vector spaces, Fuzzy Sets and Systems, 38 (1990) 329-343.
[17] F. Marty, Sur une generalization de la notion de groupe, 8th Congress Des Mathematiciens
Scandinaves, Stockholm, (1934), 45-49.
[18] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scientific Pub. Co. Inc.,
1998.
[19] S. Nanda, Fuzzy linear spaces over valued fields, Fuzzy Sets and Systems, 42 (1991), 351-354.
[20] S. Nanda, Fuzzy fields and fuzzy linear spaces, Fuzzy Sets and Systems, 19 (1986), 8994.
[21] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[22] M. S. Tallini, Hypervector spaces, Fourth Int. Congress on AHA, (1990), 167-174.
[23] M. S. Tallini, Weak hypervector spaces and norms in such spaces, Algebraic Hyperstructures
and Applications, Hardonic Press, (1994), 199-206.
[24] T. Vougiouklis, Hyperstructures and their representations, Hardonic, Press, Inc., 1994.
[25] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.