1060 704
Full Length Article
International Journal of Neutrosophic Science
Volume 8 , Issue 2, PP: 118-127 , 2020 | Cite this article as | XML | Html |PDF


A Note on Neutrosophic Submodule of an R-module M

Authors Names :   Binu R   1 *  

1  Affiliation :  Rajagiri School of Engineering and Technology, Kerala, India

    Email :  1984binur@gmail.com

Doi   :   https://doi.org/10.54216/IJNS.080205

Abstract :

The paper focuses on the applications of neutrosophic set theory in the domain of classical algebraic structures, especially R-module. This study discusses some algebraic operations of neutrosophic sets of an R-moduleM, induced by the operations in M and demonstrates certain properties of the neutrosophic submodules of an R-module. The ideas of R module’s non-empty arbitrary family of neutrosophic submodules are characterized, and related outcomes are proved. The last section of this paper also derives a necessary and sufficient condition for a neutrosophic set of an R-module M.

Keywords :

R-module , Neutrosophic Set , Neutrosophic Submodule , Support , Neutrosophic Point

References :

[1]   L. A. Zadeh, “Fuzzy sets,” Informtaion and Control, vol. 8, no. 3, pp. 338–353, 1965.

[2]  K. T. Atanassov, “New operations defined over the intuitionistic fuzzy sets,” Fuzzy Sets and Systems,vol. 61, no. 2, pp. 137–142, 1994.

[3]  F. Smarandache, “Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & syntheticanalysis,” 1998.

[4]  F. Smarandache, “Neutrosophic set-a generalization of the intuitionistic fuzzy set,” International Journalof Pure and Applied Mathematics, vol. 24, no. 3, p. 287, 2005.

[5]  M. Machover and J. Hirschfeld, Lectures on non-standard analysis, vol. 94. Springer, 2007.

[6]  S. Aggarwal, R. Biswas, and A. Ansari, “Neutrosophic modeling and control,” in 2010 InternationalConference on Computer and Communication Technology (ICCCT), pp. 718–723, IEEE, 2010.

[7]  A. Rosenfeld, “Fuzzy groups,” Journal of Mathematical Analysis and Applications, vol. 35, no. 3,pp. 512–517, 1971.

[8]  W.-j. Liu, “Fuzzy invariant subgroups and fuzzy ideals,” Fuzzy Sets and Systems, vol. 8, no. 2, pp. 133–139, 1982.

[9]  J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra. World scientific, 1998.

[10]                 C. V. Negoit¸a and D. A. Ralescu, ˘ Applications of fuzzy sets to systems analysis. Springer, 1975.

[11]                 M. Mashinchi and M. Zahedi, “On l-fuzzy primary submodules,” Fuzzy Sets and Systems, vol. 49, no. 2,pp. 231–236, 1992.

[12]                  P. Isaac, “Semisimple l-modules and split exact sequences of l-modules,” Journal of Fuzzy Mathematics,vol. 15, no. 2, p. 345, 2007.

[13]                 P. Isaac and P. P. John, “On intuitionistic fuzzy submodules of a module,” Int. J. of Mathematical Sciences and Applications, vol. 1, no. 3, pp. 1447–1454, 2011.

[14]                 I. Deli, M. Ali, and F. Smarandache, “Bipolar neutrosophic sets and their application based on multicriteria decision making problems,” in 2015 International Conference on Advanced Mechatronic Systems(ICAMechS), pp. 249–254, IEEE, 2015.

[15]                 I. Deli and S. Broumi, “Neutrosophic soft relations and some properties,” Annals of fuzzy mathematicsand informatics, vol. 9, no. 1, pp. 169–182, 2015.

[16]                 V. Torra, “Hesitant fuzzy sets,” International Journal of Intelligent Systems, vol. 25, no. 6, pp. 529–539,2010.

[17]                 W. V. Kandasamy and F. Smarandache, Basic neutrosophic algebraic structures and their application tofuzzy and neutrosophic models, vol. 4. Infinite Study, 2004.

[18]                 V. C¸ etkin and H. Aygun, “An approach to neutrosophic subrings,” ¨ Sakarya University Journal of Science,vol. 23, no. 3, pp. 472–477, 2019.

[19]                 V. Cetkin, B. P. Varol, and H. Aygun, On neutrosophic submodules of a module. Infinite Study, 2017.

[20]                 N. Olgun and M. Bal, “Neutrosophic modules,” Neutrosophic Oper. Res, vol. 2, pp. 181–192, 2017.

[21]                 M. Artin, Algebra. Pearson Prentice Hall, 2011.

[22]                 D. Dummit and R. Foote, Abstract Algebra. Wiley, 2003.

[23]                 W. Haibin, F. Smarandache, Y. Zhang, and R. Sunderraman, Single valued neutrosophic sets. InfiniteStudy, 2010.

[24]                 F. Smarandache, “A unifying field in logics: Neutrosophic logic.,” in Philosophy, pp. 1–141, AmericanResearch Press, 1999.

[25]                  F. Smarandache and M. Ali, Neutrosophic Sets and Systems, book series, Vol. 9, 2015. 

[26]                  N. Set, “Neutrosophic probability and statistics,” Univcrsity of New Mexico, Gallup, Deccmber, 200

[27]                  C. Kahraman and ˙ I. Otay, Fuzzy multi-criteria decision-making using neutrosophic sets. Springer, 2019.


[28]                 F. Smarandache, “Neutrosophic set-a generalization of the intuitionistic fuzzy set,” tech. rep.,math/0404520, 2004.

Cite this Article as :
Binu R, A Note on Neutrosophic Submodule of an R-module M, International Journal of Neutrosophic Science, Vol. 8 , No. 2 , (2020) : 118-127 (Doi   :  https://doi.org/10.54216/IJNS.080205)