Solving Combinatorial Optimization Problems with Fuzzy Weights

In this paper a combinatorial optimization problem with fuzzy weights is discussed. In order to choose a solution the concept of a necessary soft optimality is adopted. It is shown that the fuzzy problem can be reduced to solving a family of interval problems with the maximal regret criterion. Two general methods of solving the interval problems are presented. The first one is based on a branch and bound technique and the second method is based on a mixed integer programming formulation. Both techniques are general and can be applied if the underlying interval problem is NP-hard.