Fuzzy shortest path problem in cyclic weighted multi-graphs

This paper addresses the shortest path problem in a fuzzy directed graph. Unlike the previous approaches, the proposed approach can be applied for networks which may consist of cycles and parallel arcs that each arc length is defined by a fuzzy number. It should be noted that the crisp shortest path problem has already been solved however in many real world applications the exact value of arcs is not clear and hence there is a need to model uncertainty. A fuzzy set, "traffic-free", is defined in order to define arcs membership function values. The approach seeks for a minimal path that meets the designed traffic ratio. In order to formulate the problem, credibility measure is used. For solving the formulated problem, a hybrid intelligent algorithm integrating fuzzy simulation and genetic algorithm is designed. Results show that the algorithm converges in a more reasonable time in comparison with conventional approaches.