International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/313 2020 2020 Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Muhammad* * Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Ali .. Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Sara Farooq In this paper, the primarily focus is to extend the concept of Octagonal Neutrosophic Numbers (ONN) since these numbers provide a wide range of applications while dealing with more fluctuations in the linguistic environment. Firstly, mathematical notions and definitions of Linear, Symmetric and Asymmetric types are proposed. Secondly, α-Cut is defined. Finally, a case study is done by using the TOPSIS technique of MCDM.        2020 2020 29 43 10.54216/IJNS.030101 https://www.americaspg.com/articleinfo/21/show/313