FUZZY HYPERVECTOR SPACES OVER VALUED FIELDS

Document Type: Research Paper

Author

Department of Mathematics, University of Mazandaran, Babolsar, Iran

Abstract

In this note we first redefine the notion of a fuzzy hypervector
space (see [1]) and then introduce some further concepts of fuzzy hypervector
spaces, such as fuzzy convex and balance fuzzy subsets in fuzzy hypervector
spaces over valued fields. Finally, we briefly discuss on the convex (balanced)
hull of a given fuzzy set of a hypervector space.

Keywords


[1] R. Ameri, Fuzzy (Co-)Norm Hypervector Spaces, Proceedings of the 8th International Congress
in Algebraic Hyperstructures and Applications, Samotraki, Greece, September 1-9
(2002)71-79.
[2] R. Ameri and M. M. Zahedi, Hypergroup and Join Spaces induced by a fuzzy subset, PU.M.A
8 (1997) 155-168.
[3] R. Ameri and M. M. Zahedi, Fuzzy Subhypermodules over fuzzy hyperrings, Sixth International
Congress on AHA, Democritus Univ. (1996) 1–14.
[4] R. Ameri, Fuzzy (Transposition) Hypergroups, Italian Journal of Pure and applied mathematics
(to appear).
[5] R. Ameri and M. M. Zahedi, Hyperalgebraic System, Italian Journal of Pure and Applied
Mathematics, 6 (1999) 21–32.
[6] R. Ameri, On Fuzzy Inner Product of Hyperspaces, Proceedings of the Thired Seminar on
fuzzy sets and Applications, Jun, 19-20, (2002) 9-13.
[7] D. S. Comer, Polygroups Derived from Cogroups, Journal of Algebra, 89 (1984) 397-405.
[8] P. Corsini, Prolegomena of Hypergroup Theory, Aviani Editore 1979.

[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] P.S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981) 264-269.
[15] A. K. Katsaras and D.B. Liu,Fuzzy Vector Spaces and Fuzzy Topological Spaces, J. Math.
Anal. Appl. 58 (1977) 135-146.
[16] Ath. Kehagias, L-fuzzy Join and Meet Hyperoperations and the Associated L-fuzzy Hyperalgebras,
Rend. Circ. Mat., Palermo, 51 (2002) 503-526.
[17] Ath. Kehagias, An Example of L-fuzzy Join Space, Rend. Circ. Mat., Palermo, 52 (2003)
322-350.
[18] V. Leoreanu, Direct Limit and inverse limit of Join Spaces Associated with Fuzzy Sets, Pure
Math. Appl. 11 (2000) 509-512.
[19] R. Lowen, Convex Fuzzy Sets, FSS, 3 (1980) 291-310.
[20] F. Marty, Sur une generalization de la notion de groupe, 8iem congres des Mathematiciens
Scandinaves, Stockholm (1934) 45-49.
[21] S. Nanda, Fuzzy Linear Spaces Over valued Fields, FSS, 42 (1991) 351-354.
[22] S. Nanda, Fuzzy Fields and Fuzzy Linear Spaces, Fuzzy Sets and Systems, 19 (1986) 89-94.
[23] A. Rosenfeld, Fuzzy groups,J. Math. Anal. Appl. 35 (1971) 512-517.
[24] K. Serafimindis and Ath. Kehagias, The L-fuzzy Corsini Join Hyperoperation, Italian Journal
of Pure and applied mathematics, 12 (2002) 83-90.
[25] M. S. Tallini, Hypervector Spaces, Proceedings of Fourth Int. Congress in Algebraic Hyperstructures
and Applications, Xanthi, Greece, world scientific (1990) 167-174.
[26] M. S. Tallini, Hypervector Spaces and Norm in such Spaces, Algebraic Hyperstructures and
Applications, Hardonic Press (1994) 199-206.
[27] Lu Tu and Wen-Xiang Gu,Fuzzy algebraic system (I): Direct products, Fuzzy Sets and Systems,
61 (1994) 313-327.
[28] T. Vougiuklis, Hyperstructures and their representations, Hardonic Press, Inc. 1994.
[29] H. S. Wall, Hypergroups, Amer.J Math. (1937) 77-98.
[30] Gu Wenxiang, Lu Tu, Fuzzy Linear Spaces, Fuzzy Sets and Systems, 94 (1992) 377-380.
[31] L. A. Zadeh, Fuzzy Sets, Inform. and Control, 8 (1965) 338-353.
[32] M. M. Zahedi, M. Bolurian and A. Hasankhani, On polygroups and Fuzzy subpolygroups,
Journal of Fuzzy Mathematics, 3 (1995) 1-15.