Mudasir Nazar, Umer FarooqCIIT/FA22-BSM-031/LHR, CIIT/FA22-BSM-59/LHRDr. Madiha KhalidLHR TP 99242026-01-192024https://repository.cuilahore.edu.pk/handle/123456789/726This 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 roleenDepartment of MathematicsFA20MAthematicsRanking Heptagonal NeutrosophicFuzzy NumbersTransportation ProblemReport Presented Dr. Madiha KhalidThesis