A Solid Transportation Problems under a Picture Fuzzy Environment

Abstract: In real-world shipping, companies often use different modes of transport like trucks, trains, or planes, to move goods from factories to markets which is called a Solid Transportation Problem. However, real shipping data like costs, supplies and demands are rarely exact because of changing market conditions. Mostly in many decision-making problems uncertainty, hesitation and refusal information cannot be effectively represented by classical fuzzy models. To solve this problem, the concept of Picture Fuzzy Sets (PFS) has been used. This approach includes positive, neutral, and negative membership degrees, creating a much better and more complete framework for managing real-world data uncertainty. In this paper a new model is introduced to solve Solid Transportation Problem under a Picture Fuzzy Environment. Here, all costs, supplies and demands are written as Picture Fuzzy Numbers to handle real-world uncertainty perfectly. In this model, a standard score function is used to change the fuzzy numbers into crisp numbers. A numerical example is provided to demonstrate the applicability, effectiveness and computational efficient of proposed method.

Keywords: Picture Fuzzy Sets, Solid Transportation Problems, Score Function