Soft pseudo-topological (Tallini) hypervector spaces
الموضوعات :
1 - Department of Computer Engineering and Information Technology, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
الکلمات المفتاحية: Soft set, soft hypervector space, pseudo-topological hypervector space, soft pseudo-topological hypervector space,
ملخص المقالة :
In this paper, we study the pseudo-topological (Tallini) hypervector spaces over the topological field and introduce the notions of soft hypervector spaces, soft pseudo-topological hypervector spaces, and soft pseudo-topological subhyperspaces. Also, we show that the product of two soft pseudo-topological hypervector spaces is a soft pseudo-topological hypervector space.
[1] R. Ameri, Topological (transposition) hypergroups, Ital. J. Pure Appl. Math. (2003), 171-176.
[2] R. Ameri, O. R. Dehghan, On dimension of hypervector spaces, European J. Pure. Appl. Math. 1 (2) (2008), 32-50.
[3] R. Ameri, M. Hamidi, A. Samadifam, Topological vector space derived from (Tallini) topological space, J. Linear. Topological. Algebra. 13 (2) (2024), 71-80.
[4] A. O. Atagun, A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011), 592-601.
[5] P. Corsini, V. Leoreanu, Applications of Hyperstructure Theory, Advances in Math-ematics, 5, Kluwer Academic Publishers Boston, Mass, 2003.
[6] F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008), 2621-2628.
[7] S. Hoskova-Mayerova, Topological Hypergroupoids, Comput. Math. Appl. 64 (9) (2012), 2845-2849.
[8] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (4-5) (2003), 555-562.
[9] F. Marty, Sur une Generalisation de la Notion de Groupe, 8th Congress Mathematiciens Scandinaves, Stockholm, (1934), 45-49.
[10] W. K. Min, A Note on Soft Topological Spaces, Comput. Math. Appl. 62 (2011), 3524-3528.
[11] D. A. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37(4-5) (1999), 19-31.
[12] G. Oguz, B. Davvaz, Soft topological hyperstructure, J. Intell. Fuzzy Sys. 40 (2021), 8755-8764
[13] Z. Pawlak, Rough sets, Int. J. Infor. Comp. Sci. 11 (1982), 341-356.
[14] T. Shah, S. Shaheen, Soft topological groups and rings, Ann. Fuzzy Math. Inform. 7 (5) (2014), 725-743.
[15] M. S. Tallini, Hypervector Spaces, Proceedings of the Fourth International Congress on Algebraic Hyperstructures and Applications, Xanthi, Greece, 1990.
[16] M. S. Tallini, Weak Hypervector Space and Norms in such Spaces, Algebraic Hyper Structures and Applications, Jast, Rumania, Hadronic Press, 1994.
[17] J. Wanga, M. Yin, W. Gua, Soft polygroups, Comput. Math. Appl. 62 (2011), 3529-3537.
[18] S. Yamak, O. Kazanci, B. Davvaz, Soft hyperstructure, Comput. Math. Appl. 62 (2) (2011), 797-803.
[19] L. A. Zadeh, Fuzzy sets, Infor. Contr. 8 (1965), 338-353.
