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FUZZY BASIS OF FUZZY HYPERVECTOR SPACES | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 8، دوره 7، شماره 3، زمستان 2010، صفحه 97-113 اصل مقاله (232.1 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2010.193 | ||
نویسندگان | ||
Reza Ameri ![]() | ||
1School of Mathematics, Statistics and Computer Science, College of Sciences, University of Tehran, Tehran, Iran | ||
2Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran | ||
چکیده | ||
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. | ||
کلیدواژهها | ||
Fuzzy hypervector space؛ Fuzzy linear independence؛ Fuzzy basis؛ Dimension | ||
مراجع | ||
[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. | ||
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