An approach for solving transportation problem under Pythagorean fuzzy environment

Introduction/purpose: In this paper, we introduce a new defuzzification function for trapezoidal Pythagorean fuzzy numbers (TrPFNs) and develop arithmetic operations associated with these numbers. Since the transportation problem is closely related to linear programming problems, we construct a transportation model in which all parameters are represented using TrPFNs. The purpose of this work is to address uncertainty and imprecision that often occur in real-life transportation planning. Methods: A transportation model with trapezoidal Pythagorean fuzzy parameters is formulated. The proposed defuzzification function, along with the mathematical properties of TrPFNs, is used to transform the fuzzy transportation model into an equivalent deterministic model. The resulting deterministic problem is then solved using MATLAB. Results: To demonstrate the effectiveness of the proposed approach, a case study involving the transportation of goods between factories and warehouses is presented. The example preserves the fuzzy nature of the parameters throughout the solution process. A sensitivity analysis is also conducted to examine the robustness of the model. Furthermore, the results obtained from the proposed method are compared with existing approaches to verify consistency. Conclusion: The study shows that the proposed defuzzification function and the developed transportation model effectively handle uncertainty in transportation problems. The approach provides reliable and consistent results, indicating its potential usefulness for solving real-world fuzzy transportation problems.