INTERNATIONAL JOURNAL OF ADVANCE RESEARCH
IN MULTIDISCIPLINARY

Unbalanced transportation problems become more difficult when costs, capacities and requirements are imprecise and when available evidence contains both support and rejection. This paper presents a rank-assisted solution framework based on triangular intuitionistic fuzzy numbers (TIFNs). Each uncertain parameter is represented by a lower, modal and upper value together with membership and non-membership grades. A centroid-like magnitude is used for operational comparison, while score and hesitation provide secondary information. Supply-demand imbalance is corrected through a dummy destination or source whose economic interpretation is made explicit. A direct zero-suffix procedure constructs the initial basis and the Modified Distribution Method (MODI) supplies the optimality certificate. In a surplus-supply example, the direct basis has representative cost 535; one MODI loop reduces the cost to 525, and reconstruction with the original TIFN route costs gives the intuitionistic fuzzy objective <(460, 525, 590); 0.90, 0.05>. A shortage example requires a 10-unit dummy source with destination-specific penalties and yields a representative optimum of 595, with the dummy allocation identifying the destination exposed to shortage or emergency procurement. The framework demonstrates that ranking, balancing, allocation, optimality and uncertainty interpretation should be separated rather than merged into one opaque calculation.