Mudasir Nazar (FA20-BSM-031 : Umer Farooq (FA20-BSM-059)Dr. Madiha KhalidLHR TP 99232026-01-062025https://repository.cuilahore.edu.pk/handle/123456789/205This thesis introduces the concept of neutrosophic heptagonal numbers and presents a novel approach for their ranking. Neutrosophic heptagonal numbers extend the realm of neutrosophic numbers to a seven-dimensional space, offering a more comprehensive representation of uncertainty in various real-world appli cations. The developed ranking method provides a structured framework to assess and order these complex numbers, facilitating decision-making processes in uncertain environments. To demonstrate the practical utility of this approach, we apply it to solve a transportation problem framed within the context of a cost matrix. By lever aging the ranking methodology on the cost matrix, we effectively address the uncertainties inherent in transportation planning, optimizing routes, and mini mizing costs. Through computational experiments, we validate the effectiveness and efficiency of the proposed method in handling real-world scenarios charac terized by intricate uncertainties. This research contributes to advancing the understanding and application of neutrosophic heptagonal numbers in decision sciences, offering a valuable tool for analyzing complex systems where uncertainty plays a significant roleenDr. Madiha KhalidMATHEMATICSTransportation ProblemThesis