Optimization of Transportation Problems under Type-2 Fuzzy Uncertainty: A Novel Algorithm and Application

Abstract

The transportation problem is the optimization challenge where the goal is to minimize the expense of transporting products from multiple sources to diverse destinations while satisfying all supply and demand needs. In real-world problems, transportation costs are often uncertain due to factors such as fluctuating fuel prices, traffic conditions, and weather. This paper proposes a novel approach to solving the transportation problem (TP) under Type-2 Fuzzy Uncertainty, provides a more robust framework for handling complex and layered uncertainty. We introduce a systematic algorithm that involves defuzzification of Type-2 Fuzzy Numbers (T2FN), followed by the application of Vogel's Approximation Method (VAM) and the Modified Distribution Method (MODI) to find the optimal solution. Demonstrate the efficacy of the suggested approach, a numerical example has given. The results demonstrate that the Type-2 Fuzzy approach offers greater flexibility and accuracy in modeling real-world transportation problems compared to traditional fuzzy methods. This research contributes to the field of fuzzy optimization by providing a new tool for decision-makers to handle complex uncertainty in transportation and logistics.