Numerical techniques for solving bipolar neutrosophic system of linear equations

محورهای موضوعی : Numerical analysis

M. Gulistan ¹ , I. Beg ² , A. Malik ³

1 - Hazara University, Mansehra, Pakistan
2 - Lahore School of Economics, Lahore, Pakistan
3 - Hazara University, Mansehra, Pakistan

تاریخ دریافت : 1399/11/21 تاریخ پذیرش : 1400/02/10 تاریخ انتشار : 1400/03/11

کلید واژه: Richardson iterative method, Gauss Seidel method, Successive Over Relaxation (SOR) method, Bipolar neutrosophic system of linear equations,

چکیده مقاله :

In this paper, based on embedding approach three numericalmethods namely Richardson, Gauss-Seidel, and successive over relaxation (SOR)have been developed to solve bipolar neutrosophic system of linear equations.To check the accuracy of these newly developed schemes an example with exactand iterative solution is given.

منابع و مأخذ:

[1] S. Abbasbandy, A. Jafarian, Steepest descent method for system of fuzzy linear equations, Appl. Math. Compute. 175 (1) (2006) 823-833.

[2] M. Akram, Bipolar fuzzy graphs, Inf. Sci. 181 (2011), 5548-5564.

[3] M. Akram, G. Muhammad, A. N. A. Koam, N. Hussain, Iterative methods for solving a system of linear equations in a bipolar fuzzy environment, Mathematics. 7 (2019), 8:728.

[4] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Appl. Math. Compute. 155 (6) (2004), 493-502.

[5] T. Allahviranloo, Successive over relaxation iterative method for fuzzy system of linear equations, Appl. Math. Compute. 162 (1) (2005), 189-196.

[6] S. Amrahov, I. Askerzade, Strong solution of fuzzy linear system, Compute. Model. Eng. Sci. 76 (2011), 207-2016.

[7] B. Bede, Product type operations between fuzzy numbers and their application in geology, Acta polytech. Hung. 3 (2006), 123-139.

[8] S. Broumi, A. Bakali, M. Talea, F. Samarandache, R. Verma. Inter. J. Model. Optim. 7 (5) (2017), 300-304.

[9] D. Dubois, H. Prade, An introduction to bipolar representation of information and preference, Int. J. Intell. syst. 23 (2008), 866-877.

[10] D. Dubios, H. Prade, Operations on fuzzy numbers, Int. J. Syst. Sci. 9 (6) (1978), 613-626.

[11] D. Dubios, H. Prade, Fuzzy number: An overview in The Analysis of fuzzy Information, 1: Mathematics, J.C. Bezdek, Ed. CRC Press: Boca Raton, FL, USA. (1987), 3-39.

[12] M. Dehghan, B. Hashemi, Iterative solution of fuzzy linear systems, Appl. Math. Compute. 175 (1) (2006), 645-674.

[13] S. A. Edalatpanah, Systems of neutrosophic linear equations, Neutrosophic Sets. Sys. 33 (2020).

[14] M. Friedman, M. Ming, A. Kandel, Fuzzy linear systems, Fuzzy Sets. Syst. 96 (1998), 201-209.

[15] R. Goetschel, W. Voxman, Elementary calculus, Fuzzy Sets Syst. 18 (1986), 31-43.

[16] L. Ineirat, Numerical methods for solving fuzzy system of linear equations, Master thesis, An-Najah National University, Nebulas, Palestine, 2017.

[17] M. Mizumoto, K. Tanaka, The four operations of arithmetic on fuzzy numbers, Syst. Comput. Controls. 7 (1976), 73-81.

[18] G. Muhammad, M. Akram, Iterative method for solving a system of linear equation in Bipolar Fuzzy environment, Mathematics. 7 (2019), 8:728.

[19] S. Muzzioli, H. Reynaerts, Fuzzy linear systems of the form $A_1x + b_1 = A_2x + b_2$, Fuzzy Sets Sys. 157 (7) (2006), 939-951.

[20] M. Shoaib, M. Aslam, R. A. Borzooei, M. Taheri, S. Broumi, A study on bipolar single valued neutrosophic graphs with novel application, Neutrosophic Set. Sys. 32 (2020), 1:15.

[21] S. Samanta, H. Rashmanlou, M. Pal, R. A. Borzooei, A study on bipolar fuzzy graps, J. Intel. Fuzzy. Sys. 28 (2) (2015) 571-580.

[22] F. Smarandache. Neutrosophy, Neutrosophic Probability set and logic, ProQuest Information and Learning, 1998.

[23] J. Ye, Neutrosophic linear equations and application in traffic flow problems, Algorithms. 4 (2017), 10:133.

[24] J. Ye, W. Cui, Neutrosophic state feedback design method for SISO neutrosophic linear system, Cognative Systems Research. 52 (2018), 1056-1065.

[25] L. A. Zadeh, Fuzzy sets, Inf. Control. 8 (3) (1965), 338-353.

[26] W. R. Zhang, Bipolar suzzy sets, Proceedings of the IEEE & International Conference on Fuzzy Systems Proceedings. 4-9 May (1998), 835-840.

[27] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis, Proceedings of the First International Joint Conference of the North American & Fuzzy Information Processing Society Biannual Conference, (1994), 305-309.