Possibilistic linear programming with globally interactive fuzzy numbers

We treat possibilistic linear programming problems whose uncertain parameters are globally interactive. We assume that the possible range of globally interactive uncertain parameters can be expressed by a fuzzy set whose h-level sets are polytopes. We consider three models, i.e., fractile optimization, modality optimization and symmetric models using a necessity measure. To those models, we discuss solution algorithms. We show that the fractile optimization model is reduced to a semi-infinite linear programming problem and solved by a relaxation procedure developed for semi-infinite linear programming problems. Moreover, we show that the other models are reduced to semi-infinite programming problems and solved by a relaxation procedure together with a bisection method. As a result, the three models are solved by iterative use of linear programming techniques.