aspg-21-3612-1791472392 20261008151312 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 1 Yuvashri P. Department of Mathematics, Rajalakshmi Engineering College , Rajalakshmi Nagar, Thandalam, Mevalurkuppam, Tamil Nadu 602105, India Saraswathi A. Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu- 603203, India broumi said Faculty of Science Ben MSik, University Hassan II, Casablanca, Morocco Linear programming is an effective way in mathematical programming for solving optimization problems with linear objectives and linear constraints. There is determinant and indeterminant information in the actual world. As a result, the indeterminate problem is veritable and must be considered in the optimization problem,To handle this situation the neutrosophic theory is formed from extension of fuzzy set theory and is a helpful tool for dealing with inconsistent, indeterminate, and incomplete information.In this paper, we examine the coefficient of single valued triangular neutrosophic numbers to solve the neutrosophic integer programming problem.The neutrosophic integer programming problem are formulated with highest truth membership (T), indeterminancy membership and falsity membership function. The neutrosophic objective function involving a neutrosophic number, and then constructs a neutrosophic integer programming problem technique to handle neutrosophic optimization.In this paper we propose a strategy by using lexicographic approach in fractional dual algorthim to obtaining the basic solution and optimal solution as single valued neutrosophic triangular numbers.To gauge the efficacy of the model we solved few examples. 2025 15 32 3612 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260102 https://www.americaspg.com/journal/21/article/3612 https://www.americaspg.com/storage/91740122702.pdf