254 135
Full Length Article
Volume 10 , Issue 1, PP: 23-35 , 2020

Title

A Note on Neutrosophic Polynomials and Some of Its Properties

Authors Names :   Somen Debnath   1     Anjan Mukherjee   2  

1  Affiliation :  Department of Mathematics, Umakanta Academy, Agartala-799001; Tripura, INDIA

    Email :  somen008@rediffmail.com


2  Affiliation :  Department of Mathematics, Tripura University, Agartala -799022; Tripura, INDIA

    Email :  mukherjee123anjan@gmail.com



Doi   :  10.5281/zenodo.4001128


Abstract :

The purpose of this article is to study neutrosophic polynomials i.e. polynomials which are Neutrosophic in nature and study its properties with the help of  neutrosophic numbers. Apart from this we discuss different types of neutrosophic polynomials with concrete examples and establish some theorems and results which will be useful for the further study. We also give a solution method to find the approximate roots of a neutrosophic polynomial equation.

Keywords :

Neutrosophic numbers; Neutrosophic polynomials; Synthetic division;  Multiple roots

References :

[1]   L.  A.   Zadeh, “  Fuzzy  sets”, Inform. Control,Vol 8, pp.338-353, 1965.

[2]  W. L. Gau,  and  D. J. Buehrer, “ Vague sets”, IEEE Transactions on Systems, Man and Cybernetics, Vol 23, pp. 610-614, 1993.

[3]  J. Goguen,  “ L-fuzzy sets”,  Journal of Mathematical Analysis and  Applications, Vol 18, pp. 145-174, 1967.

[4] Z. Pawlak,  “Rough sets”,  International Journal of Computing and Information Sciences, Vol 11, pp. 341-356, 1982.

[5]  K . Atanassov,  “ Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol 20, pp. 87-96, 1986.

[6]  M. Gorzalczany, “ A method of inference in approximate reasoning based on interval-valued fuzzy sets”, Fuzzy Sets and Systems, Vol 21, pp. 1-17, 1987.

[7] K. Atanassov and  G. Gargov, “Interval-valued intuitionistic fuzzy sets”, Fuzzy Sets and Systems, Vol 31, pp. 343-349, 1989.

[8] F. Smarandache, “ Neutrosophic set-a generalization of the intuitionistic fuzzy sets”, International Journal of Pure and Applied Mathematics,Vol 24, pp. 287–297, 2005.

[9] T. Mitra Basu and S. K. Mondal, “ Neutrosophic soft matrix and its application in solving group decision making problems from medical science” , Computer Communication and Collaboration ,Vol 3, pp. 1-31, 2015.

[10] K. Mondal, S. Pramanik and B.C. Giri, “ Hybrid binary logarithm similarity measure for MAGDM problems under SVNS assessments” , Neutrosophic Sets and Systems, Vol 20, pp. 12-25, 2018.

[11] K. Mondal, S. Pramanik and B.C. Giri, “Single valued neutrosophic hyperbolic sine similarity measure based MADM strategy”,  Neutrosophic Sets and Systems , Vol 20, pp. 3-11, 2018.

[12]  M. Sahin, S. Alkhazaleh and V. Ulucay, “ Neutrosophic soft expert sets”,  Applied Mathematics,Vol  6, pp.116-127, 2015.

[13] F.Smarandache, “ Neutrosophy, neutrosophic probability, set and logic”,Amer.Res.Press, Rehoboth,USA, ISBN 978-1879585638, pp. 1-105, 1998.

[14]  D.Molodtsov, “ Soft set theory-first results” Computers and Mathematics with Application,Vol 37, pp.19-31, 1999.

[15] P. K Maji, R. Biswas and A. R.  Roy, “ Soft set theory”, Computers and Mathematics with Applications, Vol 45, pp. 555-562, 2003.

[16]  P. K. Maji, “ Neutrosophic soft set”, Annals of Fuzzy Mathematics and   Informatics,Vol  5, pp.157-168, 2013. 

[17] P. K. Maji, “ A neutrosophic soft set approach to a decision making problem”, Annals of Fuzzy mathematics and Informatics, Vol 3, pp. 313-319, 2012.

[18] A.A.A. Agboola, “ On Refined Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems, Vol 10, pp. 99-101, 2015.

[19] E.O. Adeleke, A.A.A. Agboola and F. Smarandache, “Refined Neutrosophic Rings I”, International Journal of Neutrosophic Sciences, Vol 2, pp. 77-81, 2020.

[20] ] E.O. Adeleke, A.A.A. Agboola and F. Smarandache, “Refined Neutrosophic Rings II”, International Journal of Neutrosophic Sciences, Vol 2, pp. 89-94, 2020.

[21] A.A.Salma, S.A.Alblowi,”Neutrosophic set and neutrosophic topological spaces”, IOSR J. Math, Vol 3, pp.31-35, 2012.