A novel interactive satisfying method via goal programming with alternative tolerance for fuzzy multi-objective optimization

A novel interactive satisfying method via goal programming with alternative tolerance is proposed for fuzzy multi-objective optimization problem with progressive preference. According to decision maker, the new tolerances of all the objectives are generated to modify the membership functions or add the objective constraints through the auxiliary programming. The optimization models based on goal programming are presented to handle three types of fuzzy relations. The dissatisfying objectives are improved iteratively till the satisfying result is acquired. Numerical example shows power of the proposed method.