Abstract. The concepts of forti cation and partial interdiction have not been considered concurrently in previous studies. In this paper, we added the forti cation and partial interdiction concepts to interdiction problem for the rst time; the reason is that in interdiction situations, defenders decide to protect some important facilities according to their budgets, and attackers like to destroy most unprotected facilities according to their resources, and therefore, to cripple the defenders' systems. Moreover, we use the advantages of credibility-based fuzzy mathematical programming and introduce an integrated model based on uncertainty contexts. In this bi-objective model, decision-maker gives satisfaction degrees for constraints, and then we use the interactive possibility model to solve the bi-objective model with varying con dence levels. These con dence levels specify the knowledge of attacker and defender about themselves. In addition, we propose Genetic Algorithm (GA) to solve the suggested model. In the experiments, we generate problem instances and solve them by Multi-Objective Mixed-Integer Non-Linear Programming (MOMINLP) and the proposed genetic algorithm for various settings.