Nonagonal Neutrosophic Number: Analytical Aspects and its Role in Optimization technique for transportation problem

Neutrosophic numbers have received increasing attention from researchers and industrialists to address the indeterminacy and uncertainty inherent in real-life decision-making. This study aims to solve the transportation problem where supply, demand and transportation costs are Nonagonal Neutrosophic Numbers (NNNs). In the existing literature, various methods have been introduced to solve transportation problems (TPs) involving neutrosophic parameters. The application of Nonagonal Neutrosophic Numbers to transportation problems is a relatively recent development. NNNs offer a more detailed and adaptable representation of uncertainty by utilizing a nine-parameter structure that captures the degrees of truth, indeterminacy, and falsity. Therefore, in this paper, we solve the transportation problem using Nonagonal Neutrosophic Numbers for the first time. To facilitate this, we introduce two novel score functions for converting NNNs into crisp values. Based on these, we propose an algorithmic framework to obtain the optimal solution effectively. To exemplify the effectiveness of the proposed method, we solved a numerical example, and the obtained results are presented and compared with those in the existing literature. Finally, the significance of this study and potential directions for future research are mentioned.