Weighting of constraints in fuzzy optimization

Many practical optimization problems are characterized by some flexibility in the problem constraints, where this flexibility can be exploited for additional trade-off between improving the objective function and satisfying the constraints. Fuzzy sets have proven to be a suitable representation for modeling this type of soft constraints. The paper proposes an extension of this model for satisfying the problem constraints and the goals, where preference for different constraints and goals can be specified by the decision-maker. The difference in the preference for the constraints is represented by a set of associated weight factors, which influence the amount of trade-off between improving the optimization objectives and satisfying various constraints. Simultaneous weighted satisfaction of the problem constraints and goals are demonstrated by using a fuzzy linear programming problem.