This study addresses the challenge of solving real-world multi-objective optimization problems under uncertainty, where data is often vague or incomplete. Existing fuzzy models, such as intuitionistic and Pythagorean fuzzy sets, may not fully capture high levels of hesitancy. A Fermatean fuzzy environment is adopted to better represent uncertainty and support more reliable decision-making.
A novel multi-objective linear programming model is developed with Fermatean fuzzy coefficients in both objectives and constraints. The model is converted into a crisp form using an accuracy function, followed by component-wise optimization. The Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is then used to determine efficient solutions. Various linear and nonlinear membership functions, including linear, parabolic and hyperbolic, are employed to represent satisfaction levels. A numerical example from the agricultural sector is provided.
The approach effectively identifies an efficient compromise solution. Among the membership functions tested, the hyperbolic function yields more flexible and balanced results. The method handles higher uncertainty levels better than conventional fuzzy techniques.
The methodology supports decision-making under uncertainty in domains like agriculture, finance and healthcare.
This study proposes a novel integration of Fermatean fuzzy theory, component-wise optimization and TOPSIS, offering a robust framework for solving uncertain multi-objective problems.
