Competitive analysis for the on-line fuzzy shortest path problem

In this paper, based on the traditional shortest path problem in the domain of the operations research and the theory of the on-line algorithms, the on-line fuzzy shortest path problem (OFSP) is originally proposed by our team. In this realistic model, two kinds of uncertainties, namely on-line and fuzzy, are combined to be considered at the same time. Firstly, some preliminaries concerning the competitive analysis and shortest path problem and then the model of OFSP are established. Following that, some on-line fuzzy algorithms are designed to handle the problem of OFSP and the rigorous proofs for the competitive ratio are given. Finally, conclusions are made and some possible research directions are discussed.