Generalized Linear Transformation Algorithm for Solving Fully Fuzzy Transportation Problems

Marwah Misbah; Mohamed Muamer

المؤلفون

Marwah Misbah Author
Mohamed Muamer Author

الكلمات المفتاحية:

Fuzzy Linear Programming، Fuzzy Transportation Problem، Triangular Fuzzy Numbers، Ranking Function، Generalized Linear Transportation Algorithm

الملخص

This paper proposes a generalized linear transformation algorithm for solving fully fuzzy transportation problems, where all parameters costs, supplies, and demands are represented as triangular fuzzy numbers. Unlike existing methods that rely on fixed ranking functions or require solving multiple models for different (α- cuts), the proposed algorithm transforms the fuzzy problem into a single crisp linear programming model using a flexible ranking function with an adjustable parameter λ. This allows decision-makers to continuously explore solutions ranging from pessimistic (λ = 0) to optimistic (λ = 1) without re-solving the model. The theoretical properties of the algorithm feasibility preservation, ranking consistency, and crisp consistency are rigorously established. The algorithm is validated through a numerical example (Dali company problem) and compared with recent methods. Results demonstrate that the proposed approach achieves a balance between computational efficiency and solution accuracy while offering superior flexibility for real-world decision-making under uncertainty.

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