1 **Affiliation :
**

** Email : **

2 **Affiliation :
**Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan

** Email : **naveedjafar@lgu.edu.pk

3 **Affiliation :
**Department of Mathematics, TED University, Ön Cebeci, Ziya Gökalp Cd. 48/A, 06420 Çankaya/Ankara, Turkey

** Email : **ezgi.turkarslan@tedu.edu.tr

4 **Affiliation :
**Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan

** Email : **

5 **Affiliation :
**Department of Mathematics Lahore Garrison University, Av-4, Sec-C, DHA Phase VI, 54000 Lahore Pakistan

** Email : **sarahwaad470@gmail.com

Received: April 08, 2020 Accepted: August 09, 2020

**Abstract : **

The concept of neutrosophic become really handy now a days and based on non-standard analysis to mention mathematical outcomes, uncertainty, non-completed situations, inconsistency, distinctness. The main concept of Neutrosophic set based on membership values of truth, indeterminacy and falsity, which are independent, and which play vital role in situations like uncertainty, incomplete and inconsistence. From triangular to octagonal Neutrosophic number. They play vital role in modeling problems, science, biology and many more. Hence it is clear that these are necessary and have real life applications, but some real-life problems have more edges and their triangular to octagonal fail to overcome this situation (mention in table 1). Hence, nonagonal neutrosophic numbers give a wide scope of utilizations while managing more variances in the decision-making condition with nine edges for membership values of truth, indeterminacy and falsity. In this current article we present compression between triangular to nonagonal neutrosophic number and their requirement, explore differential equations in Neutrosophic environment as Linear, symmetric and asymmetric types further, their ∂-*cute* and then we present a real-life problem and solved it with TOPSIS technique of MCDM.

**Keywords : **

Accuracy function , Neutrosophic number , Nonagonal Neutrosophic numbers (NNN) , MCDM , TOPSIS.

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