Transportation Problems Using Triangular Type-2 Intuitionistic Fuzzy Numbers

This study introduces the structure of normalized Triangular Type-2 Intuitionistic Fuzzy Numbers (TrT2IFNs), a relatively recent concept with strong potential to enhance the modeling and analysis of uncertainty. The study also presents basic arithmetic operations and ranking functions for these fuzzy parameters. The arithmetic operations are defined using the (α, β)-cut technique, where fuzzy numbers are decomposed into α- and β-level sets to enable systematic computation. In addition, a new ranking function is developed based on a mean interval approach, enabling effective comparison of these fuzzy numbers. To validate the proposed methods, a Transportation Problem (TP) is formulated, where cost parameters are represented by TrT2IFNs. The model is illustrated through numerical examples, and the results are analyzed. The findings show that the proposed approach addresses uncertainty in transportation problems more effectively than existing methods. Applying TrT2IFNs improves the representation of cost uncertainty, supporting better decision-making in logistics and supply chain optimization. The numerical results indicate reduced transportation costs compared to current approaches, demonstrating the practical value of the proposed framework in operations research under real-world uncertainty.