Asia Mathematika

An International Journal. ISSN: 2457-0834 (online)

Volume 3, Issue 2, August 2019, Pages: 1-18

Study of the group theory in neutrosophic soft sense

Tuhin Bera1* and Nirmal Kumar Mahapatra2

1Department of Mathematics, Boror S. S. High School, Bagnan, Howrah-711312, WB, India.
2Department of Mathematics, Panskura Banamali College, Panskura RS-721152, WB, India.


The purpose of this paper is to cultivate the group theory by means of neutrosophic soft sense in a different way. The concepts of neutrosophic soft coset, neutrosophic normal soft group, neutrosophic soft quotient group, direct product of neutrosophic soft groups and simple neutrosophic soft group have been presented in a new approach. These are illustrated by suitable examples. Their structural characteristics are investigated here in the parlance of group theory in classical sense. Two kinds of composition namely binary composition ‘o’ between the elements of a classical group and neutrosophic soft composition / neutrosophic soft product ‘o’ between the neutrosophic soft elements of neutrosophic soft groups are used to practice here. Following the classical group theory, the concepts have been developed by using the neutrosophic soft composition directly


Neutrosophic soft coset, Neutrosophic normal soft group, Neutrosophic soft quotient group, Direct product, Simple neutrosophic soft groups.


▷Download pdf


[1] Aktas H, Cagman N. Soft sets and soft groups. Information sciences, 2007; 177: 2726-2735.
[2] Aygunoglu A, Aygun H. Introduction to fuzzy soft groups. Computer and Mathematics with Applications, 2009; 58: 1279-1286.
[3] Atanassov K. Intuitionistic fuzzy sets. Fuzzy sets and systems, 1986; 20(1): 87-96.
[4] Bera T, Mahapatra NK. (α, β, γ) -cut of neutrosophic soft set and it’s application to neutrosophic soft groups. Asian Journal of Math. and Compt. Research, 2016; 12(3): 160-178.
[5] Bera T, Mahapatra NK. Introduction to neutrosophic soft groups. Neutrosophic Sets and Systems, 2016; 13: 118- 127,
[6] Bera T, Mahapatra NK. On neutrosophic normal soft groups. Int. J. Appl. Comput. Math., 2016; 2(4): DOI 10.1007/s40819-016-0284-2.
[7] Bera T, Mahapatra NK. On neutrosophic soft rings. OPSEARCH, 2016; 1-25, DOI 10.1007/ s12597-016-0273-6.
[8] Bera T, Mahapatra NK. Introduction to neutrosophic soft topological spaces. OPSEARCH, 2017; DOI 10.1007/s12597-017-0308-7.
[9] Broumi S, Smarandache F, Maji PK. Intuitionistic neutrosophic soft set over rings. Mathematics and Statistics, 2014; 2(3): 120-126, DOI : 10.13189/ms.2014.020303.
[10] Cetkin V, Aygun H. An approach to neutrosophic subgroup and its fundamental properties. J. of Intelligent and Fuzzy Systems, 2015; 29: 1941-1947.
[11] Deli I, Broumi S. Neutrosophic Soft Matrices and NSM-decision Making. Journal of Intelligent and Fuzzy Systems, 2015; 28(5): 2233-2241.
[12] Maji PK. Neutrosophic soft set. Annals of Fuzzy Mathematics and Informatics, 2013; 5(1): 157-168.
[13] Molodtsov D. Soft set theory - First results. Computer and Mathematics with Applications, 1999; 37(4-5): 19-31.
[14] Rosenfeld A. Fuzzy groups. Journal of mathematical analysis and applications, 1971; 35: 512-517.
[15] Sharma PK. Intuitionistic fuzzy groups. IFRSA International journal of data warehousing and mining, 2011; 1(1): 86-94.
[16] Smarandache F. Neutrosophic set, A generalisation of the intuitionistic fuzzy sets. Inter. J. Pure Appl. Math., 2005; 24: 287-297.
[17] Varol BP, Aygunoglu A, Aygun H. On fuzzy soft rings. Journal of Hyperstructures, 2012; 1(2): 1-15.
[18] Yaqoob N, Akram M, Aslam M. Intuitionistic fuzzy soft groups induced by (t,s) norm. Indian Journal of Science and Technology, 2013; 6(4): 4282-4289.
[19] Zadeh LA. Fuzzy sets. Information and control, 1965; 8: 338-353

Visitors count

Join us