An Optimization View On Intuitionistic Fuzzy Three-Way Decisions

From an optimization point of view, we propose a new method to determine the loss funtion of intuitionistic fuzzy three-way decisions. First, two linear programming models are constructed to determine a pair of thresholds in three-way decisions based on their practical semantics. Meanwhile, the validity of the models is verified by KKT conditions. Second, the models are further extended to intuitionistic fuzzy three-way decisions (IF-3WD) and the corresponding nonlinear models are established. Third, the uniqueness of solution for models is proven and a LINGO software is employed to solve the models. We then obtain both thresholds of IF-3WD and its decision rules. Finally, an example is given to show the effectiveness of our method.