An Enhanced Framework for fuzzy transportation problems using enneadecagon fuzzy numbers with dual ranking and stepping stone optimization

The Enneadecagon Fuzzy Number (EDGFN) is a 19-point symmetric fuzzy representation that offers a more precise modelling and granularity than traditional triangular or trapezoidal forms. In this paper, we present a novel methodology for resolving fuzzy transportation problems. Fuzzy costs, inventories, and demands are transformed into precise equivalents using two fuzzy ranking techniques, Graded Mean Integration Representation (GMIR) and the widely used Centroid method. The transportation problem is solved using Vogel’s Approximation Method (VAM) with these crisp values as inputs to acquire an initial basic feasible solution. The solution is subsequently evaluated for optimality and improved iteratively using the stepping stone Method. The final transportation cost and the number of iterations necessary to achieve optimality are assesses through a comparative study of each ranking method. The results suggest that the combination of EDGFN with centroid method and GMIR provides a precise control over uncertainty representation. This framework facilitates more exact and informed decision-making in ambiguous environments, including resource allocation and supply chain logistics.