An approach for solving transportation problem using possibility interval valued intuitionistic fuzzy soft sets

The transportation problem is a fundamental optimization technique used to efficiently allocate resources by determining the best way to transport goods from multiple suppliers to multiple consumers. The primary goal is to reduce transportation costs or increase overall profit while satisfying supply and demand constraints. However, in real-world scenarios, transportation costs, availability of resources, and demand often contain uncertainties, making it challenging to represent them with precise numerical values. Traditional optimization methods struggle to handle such imprecision, necessitating the application. Intuitionistic fuzzy sets (IFS) offer an advanced approach by incorporating both membership and non-membership functions, allowing for a more flexible and realistic representation of uncertain data.In this research study, we initiate the idea of the possibility interval-valued intuitionistic fuzzy triangular number (PIV-IFTN) to address uncertainty in transportation problems. This approach is particularly useful when exact transportation costs or profit values are unknown but can be estimated within a specific range. By defining operations and properties for PIV-IFTNs, we establish a robust mathematical foundation for their practical application. To find an optimal transportation strategy, we employ the zero ranking technique, which enables us to systematically evaluate and prioritize different possible solutions. This methodology ensures that transportation costs are minimized while profits are maximized, making it an effective tool for handling uncertain real-life transportation scenarios and enhancing decision-making processes.