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In this study, we derive a simple transportation scheme by post-optimizing the costs of a modified problem. The strategy attempts to make the original (mainly feasible) option more practicable by adjusting the building components’ costs. Next, we employ the previously mentioned cell or area cost operators to gradually restore the modified costs to their initial levels, while simultaneously implementing the necessary adjustments to the “optimal” solution. This work presents a multi-goal, multi-item substantial transportation problem with interval-valued fuzzy variables, such as transportation costs, supplies, and demands, as parameters to maintain the transportation cost. This research addresses two circumstances where task ambiguity may occur: the interval solids transportation problem and the fuzzy substantial transportation issue. In the first scenario, we express data problems as intervals instead of exact values using an interval-valued fermatean neutrosophic number; in the second case, the information is not entirely obvious. We address both models when uncertainty solely affects the constraint set. For the interval scenario, we define an additional problem to solve. Our existing efficient systems have dependable transportation, so they are also capable of handling this new problem. In the fuzzy case, a parametric technique generates a fuzzy solution to the preceding problem. Since transportation costs have a direct impact on market prices, lowering them is the primary goal. Using parametric analysis, we provide optimal parameterization solutions for complementary situations. We provide a recommended algorithm for determining the stability set. In conclusion, we offer a sensitivity analysis and a numerical example of the transportation problem involving both balanced and imbalanced loads.
Kamran et al. (Tue,) studied this question.