Numerical techniques for solving bipolar neutrosophic system of linear equations

Subject Areas : Numerical analysis

M.  Gulistan ¹ (Hazara University, Mansehra, Pakistan)
I.  Beg ² (Lahore School of Economics, Lahore, Pakistan)
A.  Malik ³ (Hazara University, Mansehra, Pakistan)

Received: 2021-02-09 Accepted : 2021-04-30 Published : 2021-06-01

Keywords:

References:

[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.