A Three-Dimensional Product-Based Circular Intuitionistic Fuzzy Potential Method for Transportation Problems

Transportation problems constitute a fundamental class of optimization models; however, real-world applications involve uncertainty, hesitation, and expert disagreement that cannot be adequately captured by deterministic or classical fuzzy approaches. This paper proposes a three-dimensional circular intuitionistic fuzzy potential method (3D–CIFMODI), which extends the classical MODI framework to Circular Intuitionistic Fuzzy Triples (C-IFTs) through radius-aware operations and indexed matrix representations. Unlike existing circular intuitionistic fuzzy transportation methods, which are primarily feasibility-driven, the proposed approach introduces a dual-based optimality framework based on circular reduced costs, preserving the full structure of uncertainty without reducing it to crisp equivalents. The method retains polynomial-time computational complexity O(mn(m+n)), i.e., O(n3) for square problems, with only a constant computational overhead due to circular operations. A numerical case study demonstrates the effectiveness and robustness of the proposed framework. Furthermore, a comparative analysis between classical intuitionistic fuzzy (IFS) and circular intuitionistic fuzzy (C-IFS) representations shows that incorporating the radius parameter significantly improves discrimination capability, solution stability, and interpretability. The results confirm that the proposed method provides a unified, interpretable, and computationally efficient framework for solving multi-layer transportation problems under circular intuitionistic fuzzy uncertainty.