1 Affiliation : Department of Mathematics, Lahore Garrison University, Lahore, Pakistan
Email : email@example.com
2 Affiliation : Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA
Email : firstname.lastname@example.org
To deal with fluctations in decision-making, fuzzy / neutrosophic numbers are used. The problem having more fluctuations are difficult to sovle. Thus it is a dire need to define higher order number, also It is a very curious question by researchers all around the world that how octagonal neutrosophic number can be represented and how to be graphed? In this research article, the primarily focused on the representation and graphs of octagonal neutrosophic number. at last, a case study is done using VIKOR method based on octagonal neutrosophic number. These representations will be helpful in multi-criteria decision making problems in the case that there are large number of fluctuations. Finally, concluded the present work with future directions.
Neutrosophic Number , Octagonal Number , VIKOR Method , MCDM , Uncertainty , Indeterminacy , Accuracy Function , De-neutrosophication
 Zadeh LA. Fuzzy Sets. Inform Control. 1965;8(3):338–353.
 Atanassov, K. Intuitionistic fuzzy sets. Fuzzy Sets Syst. (1986), 20, pp.87–96.
 Smarandache, F. Neutrosophy/neutrosophic probability, set, and logic. American Research Press, Rehoboth. (1998).
 Chakraborty, A.; Mondal, S. P.; Ahmadian, A.; Senu, N.; Alam, S.; and Salahshour, S.; Different Forms of Triangular Neutrosophic Numbers, De-Neutrosophication Techniques, and their Applications, Symmetry, vol 10, 327, 2018.; doi:10.3390/sym10080327.
 Chakraborty, A.; Mondal, S. P.;Mahata, A.; Alam, S.; Different linear and non-linear form of Trapezoidal Neutrosophic Numbers, De-Neutrosophication Techniques and its Application in time cost optimization technique, sequencing problem; RAIRO Operation Research, vol 11, 327, 2018. doi:10.1051/ro/2019090.
 Chakraborty. A., Sankar P. Mondal, Shariful A. Ali A., Norazak S., Debashis De. and Soheil S., The Pentagonal Fuzzy Number: Its Different Representations, Properties, Ranking, Defuzzification and Application in Game Problems, Symmetry, vol 10, pp 248, 2018.
 A. Chakraborty, S. Broumi, P.K Singh,”Some properties of Pentagonal Neutrosophic Numbers and its Applications in Transportation Problem Environment,” Neutrosophic Sets and Systems, vol.28, pp.200-215, 2019.
 A. Chakraborty, S. Mondal, S. Broumi, “De-Neutrosophication technique of pentagonal neutrosophic number and application in minimal spanning tree,” Neutrosophic Sets and Systems, vol. 29, pp. 1-18,2019. doi: 10.5281/zenodo.3514383.
 Chakraborty, A. “A New Score Function of Pentagonal Neutrosophic Number and its Application in Networking Problem,” International Journal of Neutrosophic Science, Volume 1, Issue 1, pp. 40-51, 2020.
 Edalatpanah, S. A., “A Direct Model for Triangular Neutrosophic Linear Programming,”
International Journal of Neutrosophic Science, Volume 1, Issue 1, pp. 19-28, 2020.
 Saqlain, M., Jafar, M. N., Riaz, M. A New Approach of Neutrosophic Soft Set with Generalized Fuzzy TOPSIS in Application of Smart Phone Selection, Neutrosophic Sets and Systems, vol. 32, pp. 307-316, 2020. DOI: 10.5281/zenodo.3723161
 Saqlain. M., Jafar. N. and Riffat. A., Smart phone selection by consumers’ in Pakistan: FMCGDM fuzzy multiple criteria group decision making approach, Gomal University Journal of Research, vol 34(1), pp. 27-31, 2018.
 Riaz. M., Saqlain. M. and Saeed. M. Application of Generalized Fuzzy TOPSIS in Decision Making for Neutrosophic Soft set to Predict the Champion of FIFA 2018: A Mathematical Analysis, Punjab University Journal of Mathematics, vol 51(8), pp.111-126, 2019.
 Abdel-Basset, M., Saleh, M., Gamal, A., & Smarandache, F. An approach of the TOPSIS technique for developing supplier selection with group decision making under type-2 neutrosophic number. Applied Soft Computing, vol77, pp. 438-452, 2019.
 Abdel-Baset, M., Chang, V., Gamal, A., & Smarandache, F. An integrated neutrosophic ANP and VIKOR method for achieving sustainable supplier selection: A case study in the importing field. Computers in Industry, vol 106, pp. 94-110, 2019.
 Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. A hybrid approach of neutrosophic sets and DEMATEL method for developing supplier selection criteria. Design Automation for Embedded Systems, pp.1-22, 2018.
 Abdel-Basset, M., Manogaran, G., Gamal, A., & Smarandache, F. A group decision-making framework based on the neutrosophic TOPSIS approach for smart medical device selection. Journal of medical systems, vol 43, issue 2, pp. 38-43, 2019.
 Nabeeh, N. A., Smarandache, F., Abdel-Basset, M., El-Ghareeb, H. A., & Aboelfetouh, A. An Integrated Neutrosophic-TOPSIS Approach and Its Application to Personnel Selection: A New Trend in Brain Processing and Analysis. IEEE Access, vol 7, pp. 29734-29744. 2019.
 K. Mondal, and S. Pramanik. Neutrosophic decision making model of school choice. Neutrosophic Sets and Systems, vol 7, pp. 62-68, 2015.
 M. Saqlain, A. Hamza, and S. Farooq, “Linear and Non-Linear Octagonal Neutrosophic Numbers: Its Representation, α-Cut and Applications,” International Journal of Neutrosophic Science, vol. 3, no. 1, pp. 29–43, 2020.
 Saqlain M, Saeed M, Ahmad M. R, Smarandache F, (2019), Generalization of TOPSIS for Neutrosophic Hypersoft set using Accuracy Function and its Application, Neutrosophic Sets and Systems (NSS), 27: 131-137.