In this paper, we present the notion of m-polar fuzzy number(m-PFN) along with some properties. Further, we describe the m-polar fuzzy linear system of equations (m-PFLSEs) along with weak and strong solutions. Moreover, we characterize a new technique to find the solution of fully m-PFLSE using one-cut extension. By applying this technique, we calculate the minimal and maximal symmetric solutions (SSs) of the fully m-PFLSEs which based on a controllable solution set (CSS) and a tolerable solution set (TSS), respectively. We consider an example to find the solutions of fully m-PFLSEs. In the end, we prove some elementary results on the base of our proposed method.
AbbasbandyS., EzzatiR. and JafarianA., LU decomposition method for solving fuzzy system of equations, Applied Mathematics and Computation172 (2006), 633–643.
2.
AbbasbandyS. and JafarianA., Steepest descent method for system of fuzzy linear equations, Applied Mathematics and Computation175 (2006), 823–833.
3.
AkramM., Bipolar fuzzy graphs, Information Sciences181 (2011), 5548–5564.
4.
AkramM., m-Polar fuzzy graphs: Theory, methods and applications, Studies in Fuzziness and Soft Computing371 (2019), Springer, 1–284.
5.
AkramM., AliG., WaseemN. and DavvazB., Decisionmaking methods based on hybrid mF models, Journal of Intelligent and Fuzzy Systems35(3) (2018), 3387–3403.
6.
AkramM., MuhammadG. and AllahviranlooT., Bipolar fuzzy linear system of equations, Computational and Applied Mathematics38(2) (2019), 69.
7.
AkramM. and WaseemN., Similarity measures for new hybrid models: mF sets and mf soft sets, Punjab University Journal of Mathematics51(6) (2019), 115–130.
8.
AkramM., AdeelA. and AlcantudJ.C.R., Multi-criteria group decision-making using an m-polar hesitant fuzzy topsis approach, Symmetry11(6) (2019), 795.
9.
AkramM., AdeelA. and AlcantudJ.C.R., Hesitant fuzzy Nsoft sets: A new model with applications in decision-making, Journal of Intelligent and Fuzzy Systems36(6) (2019), 6113–6127.
10.
AkramM., MuhammadG., KoamA.N. and HussainN., Iterative methods for solving a system of linear equations in a bipolar fuzzy environment, Mathematics7(8) (2019), 728.
11.
AllahviranlooT., A comment on fuzzy linear systems, Fuzzy Sets and Systems140 (2003), 559.
12.
AllahviranlooT. and SalahshourS., Fuzzy symmetric solutions of fuzzy linear systems, Journal of Computational and Applied Mathematics235(16) (2011), 4545–4553.
13.
AllahviranlooT., Successive over relaxation iterative method for fuzzy system of linear equations, Applied Mathematics and Computation162 (2005), 189–196.
14.
AllahviranlooT. and KermaniM.A., Solution of a fuzzy system of linear equation, Applied Mathematics and Computation175 (2006), 519–531.
15.
AllahviranlooT., AhmadyE., AhmadyN. and AlketabyK.S., Block Jacobi two-stage method with Gauss-Sidel inner iterations for fuzzy system of linear equations, Applied Mathematics and Computation175 (2006), 1217–1228.
16.
AllahviranlooaT., SalahshourS. and KhezerlooaM., Maximaland minimal symmetric solutions of fully fuzzy linear systems, Journal of Computational and Applied Mathematics235 (2011), 4652–4662.
17.
ChenJ., LiS., MaS. and WangX., m-polar fuzzy sets: An extension of BFSs, The Scientific World Journal (2014), 1–8.
18.
FriedmanM., MingM. and KandelA., Fuzzy linear system, Fuzzy Sets and Systems96 (1998), 209–261.
19.
LeeK.-M., Bipolar-valued fuzzy sets and their basic operations, Proc Int Conf, Bangkok, Thailand, 2000, 307–317.
20.
MoghadamK.G., GhanbariR. and AmiriN.M., Duality in bipolar triangular fuzzy number quadratic programming problems, Proceedings of the International Conference on Intelligent Sustainable Systems (2017), 1236–1238.
21.
TahmasbpourA. and BorzooeiR.A., Chromatic number of bipolar fuzzy graphs, Journal of Applied Mathematics and Informatics34 (2016), 49–60.
22.
TangX. and
WeiG., Multiple attribute decision-making with dual hesitant Pythagorean fuzzy information, Cognitive Computation11(2) (2019), 193–211.
23.
WangJ., GaoH. and WeiG., The generalized Dice similarity measures for Pythagorean fuzzy multiple attribute group decision making, International Journal of Intelligent Systems34(6) (2019), 1158–1183.
24.
WeiG., AlsaadiF.E., HayatT. and AlsaediA., A linear assignment method for multiple criteria decision analysis with hesitant fuzzy sets based on fuzzy measure, International Journal of Fuzzy Systems19(3) (2017), 607–614.
25.
ZhangW.R., Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, Proceedings of IEEE Conference (1994), 305–309.
26.
ZadehL.A., Fuzzy sets, Informtion and Control8 (1965), 338–353.
27.
ZhanJ., AkramM. and SitaraM., Novel decision-making method based on bipolar neutrosophic information, Soft Computing (2018). DOI 10.1007/s00500-018-3552-8.
28.
ZhanJ., MasoodH. and AkramM., Novel decision-making algorithms based on intuitionistic fuzzy rough environment, International Journal of Machine Learning and Cybernetics, DOI 10.1007/s13042-018-0827-4, 2018.
29.
ZhanJ. and XuW., Two types of coverings based multigranulation rough fuzzy sets and applications to decision making, Artificial Intelligence Review, DOI: 10.1007/s10462-018-9649-8.
30.
ZhangL., ZhanJ., XuZ.X. and AlcantudJ.C.R., Coveringbased general multigranulation intuitionistic fuzzy rough sets and corresponding applications to multiattribute group decision-making, Information Sciences, DOI 10.1016/j.ins.2019.04.054.
31.
ZhanJ., SunB. and AlcantudJ.C.R., Covering based multigranulation (I, T)-fuzzy rough set models and applications in multi-attribute group decision-making, Information Sciences476 (2019), 290–318.
32.
ZhangK., ZhanJ. and WuW.Z., Novel fuzzy rough set models and corresponding applications to multicriteria decision-making, Fuzzy Sets and Systems2019, 10.1016/j.fss.2019.06.019.
