Interactive decision making for a shortest path problem with interval arc lengths

This paper considers a shortest path problem with interval costs for directed arcs and reliability for networks, and proposes a bi-objective interval shortest path problem. The proposed model is not well-defined due to interval costs, and so the deterministic constrained shortest path problem is obtained by introducing the order relation of interval values. In order to solve this bi-objective problem, a solution algorithm based on interactive fuzzy satsificing method in terms of multi-objective programming is developed.