Document Type : Research Paper

Authors

Department of Mathematics, Kocaeli University, 41001, Kocaeli, Turkey

Abstract

In this work, we intend to introduce and study another algebraic structure of single-valued neutrosophic sets called neutrosophic field as a continuation of our investigations on neutrosophic algebraic structures. For this goal, we define the concept of neutrosophic fields and observe some of their basic characteristics and properties. Then we give the definition of a neutrosophic linear space over the proposed neutrosophic field and consider its fundamental properties.

Keywords

Main Subjects

###### ##### References
[1] I. Arockiarani, I. R. Sumathi, J. Martina Jency, Fuzzy neutrosophic soft topological spaces, Inter J. Math Arhchive. 4 (10) (2013), 225-238.
[2] R. A. Borzooei, H. Farahani, M. Moniri, Neutrosophic deductive filters on BL-algebras, J. Intel. Fuzzy. Sys. 26 (6) (2014), 2993-3004.
[3] V. Cetkin, H. Aygun, An approach to neutrosophic subgroup and its fundamental properties, J. Intel. Fuzzy. Sys. 29 (2015), 1941-1947.
[4] V. Cetkin, H. Aygun, An approach to neutrosophic subrings, Sakarya Univ. J. Sci. 23 (3) (2019), 472-477.
[5] V. Cetkin, B. Pazar Varol, H. Aygün, On neutrosophic submodules of a module, Hacet. J. Math. Stat. 46 (5) (2017), 791-799.
[6] T. Eswarlal, R. Ramakrishma, Vague fields and vague vector spaces, Inter. J. Pure Appl. Math. 94 (3) (2014), 295-305.
[7] Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, Vol. 73, Springer, 1974.
[8] V. Kandasamy, F. Smarandache, Some Neutrosophic Algebraic Structures and Neutrosophic N-algebraic Structures, Hexis, Phoenix, Arizona, 2006.
[9] P. Majumdar, S. K. Samanta, On similarity and entropy of neutrosophic sets, J. Intel. Fuzzy. Sys. 26 (3) (2014), 1245-1252.
[10] S. Nanda, Fuzzy fields and fuzzy linear spaces, Fuzzy Sets. Sys. 19 (1986), 89-94.
[11] A. A. Salama, S. A. Al-Blowi, Neutrosophic set and neutrosophic topological spaces, IOSR J. Math. 3 (4) (2012), 31-35.
[12] M. Shabir, M. Ali, M. Naz, F. Smarandache, Soft neutrosophic group, Neutrosophic Sets. Sys. 1 (2013), 13-25.
[13] F. Smarandache, A Unifying Field in Logics. Neutrosophy/ Neutrosophic Probability, Set and Logic, Rehoboth: American Research Press, 1998.
[14] H. Wang, F. Smarandache, Y. Zhang, R. Sunderraman, Single Valued Neutrosophic sets, Proceedings of 10th International Conference on Fuzzy Theory & Technology, Salt Lake City, Utah, 2005.
[15] G. Wenxiang, L. Tu, Fuzzy linear spaces, Fuzzy Sets. Sys. 49 (1992), 377-380.
[16] K. M. Zhang, Y. Bai, X. L. Li, Y. F. Qin, Intuitionistic Fuzzy Subfield and its Characterizations, Second International Conference on Intelligent Human-Machine Systems and Cybernetics, (2010), 58-61.