Abstract

The concept of ‘Field’ plays an important role in defining the algebraic structure ‘Linear Space’. Following the definition of neutrosophic soft field and it's element namely neutrosophic soft scalar introduced in [29], their structural characteristics have been investigated in the present paper. Then the neutrosophic soft function over a crisp field is defined and illustrated by suitable examples. In continuation, the nature of neutrosophic soft homomorphic image and pre-image of a neutrosophic soft field are studied here. Finally, the concept of neutrosophic soft algebra over a neutrosophic soft field has been proposed along with the establishment of some related theorems.

References

[1] D. Molodtsov, Soft set theory- First results, Computer and Mathematics with Applications, 37(4-5), 19-31, (1999).
[2] A. Rosenfeld, Fuzzy groups, Journal of mathematical analysis and applications, 35, 512-517, (1971).
[3] N. P. Mukherjee and P. Bhattacharya, Fuzzy groups: Some group -Theoretic analogs, Information sciences, 39, 247-268, (1986).
[4] P. K. Sharma, Intuitionistic fuzzy groups, IFRSA International journal of data warehousing and mining, 1(1), 86-94, (2011).
[5] H. Aktas and N. Cagman, Soft sets and soft groups, Information sciences, 177, 2726-2735, (2007).
[6] P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, The journal of fuzzy mathematics, 9(3), 589-602, (2001).
[7] P. K. Maji, R. Biswas and A. R. Roy, Intuitionistic fuzzy soft sets, The journal of fuzzy mathematics, 9(3), 677-692, (2001).
[8] P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computer and Mathematics with Applications, 45, 555-562, (2003).
[9] P. K. Maji, R. Biswas and A. R. Roy, On intuitionistic fuzzy soft sets, The journal of fuzzy mathematics, 12(3), 669-683, (2004).
[10] A. Aygunoglu and H. Aygun, Introduction to fuzzy soft groups, Computer and Mathematics with Applications, 58, 1279-1286, (2009).
[11] N. Yaqoob, Md. Akram and Md. Aslam, Intuitionistic fuzzy soft groups induced by (t,s) norm, Indian Journal of Science and Technology, 6(4), 4282-4289, (2013).
[12] B. P. Varol, A. Aygunoglu and H. Aygun, On fuzzy soft rings, Journal of Hyperstructures, 1(2), 1-15, (2012).
[13] Z. Zhang, Intuitionistic fuzzy soft rings , International Journal of Fuzzy Systems, 14(3), 420-431, (2012).
[14] S. Nanda, Fuzzy algebras over fuzzy fields, Fuzzy Sets and Systems, 37, 99-103, (1990).
[15] G. Wenxiang and L. Tu, Fuzzy algebras over fuzzy fields redefined, Fuzzy Sets and Systems, 53, 105-107, (1993).
[16] F. Smarandache, Neutrosophy, Neutrosophic Probability, Set and Logic, Amer. Res. Press, Rehoboth, USA., (1998), p. 105, http://fs.gallup.unm.edu/eBook-neutrosophics4.pdf (fourth version).
[17] F. Smarandache, Neutrosophic set, a generalisation of the intuitionistic fuzzy sets, Inter. J. Pure Appl. Math., 24, (2005), 287-297.
[18] P. K. Maji, Neutrosophic soft set, Annals of Fuzzy Mathematics and Informatics, 5(1), 157-168, (2013).
[19] S. Broumi, F. Smarandache and P. K. Maji, Intuitionistic neutrosophic soft set over rings, Mathematics and Statistics 2(3), 120-126, (2014), DOI: 10.13189/ms.2014.020303.
[20] V. Cetkin and H. Aygun, An approach to neutrosophic subgroup and its fundamental properties, J. of Intelligent and Fuzzy Systems 29, 1941-1947, (2015).
[21] V. Cetkin and H. Aygun, A note on neutrosophic subrings of a ring, 5th international eurasian conference on mathematical sciences and applications, 16-19 August 2016, Belgrad-Serbia.
[22] I. Deli and S. Broumi, Neutrosophic Soft Matrices and NSM-decision Making, Journal of Intelligent and Fuzzy Systems, 28(5), 2233-2241, (2015).
[23] I. Deli and S. Broumi, Neutrosophic soft relations and some properties, Annals of Fuzzy Mathematics and Informatics, 9(1), 169-182, (2015).
[24] T. Bera and N. K. Mahapatra, Introduction to neutrosophic soft groups, Neutrosophic Sets and Systems, 13, 118-127, (2016), doi.org/10.5281/zenodo.570845.
[25] T. Bera and N. K. Mahapatra

[26] T. Bera and N. K. Mahapatra, On neutrosophic soft rings, OPSEARCH, 1-25, (2016), DOI 10.1007/ s12597-016-0273-6.

[27] T. Bera and N. K. Mahapatra, On neutrosophic normal soft groups, Int. J. Appl. Comput. Math., 2(4), (2016), DOI 10.1007/s40819-016-0284-2.

[28] T. Bera and N. K. Mahapatra, Introduction to neutrosophic soft topological spaces, OPSEARCH, (March, 2017), DOI 10.1007/s12597-017-0308-7.

[29] T. Bera and N. K. Mahapatra, On neutrosophic soft linear spaces, Fuzzy Information and Engineering, 9, 299-324, (2017).