Abstract
Based on some results of the fuzzy network computation and competitive analysis, the online fuzzy most reliable path problem (OFRP) is originally proposed by our team. In this paper, the preliminaries about the fuzzy most reliable path and competitive analysis are given first. Following that, the mathematical model of OFRP is established. In this realistic model, two kinds of uncertainties, namely online and fuzzy, are combined to be considered at the same time. Then some online fuzzy algorithms are developed to address the OFRP and the rigorous proofs of the competitive analysis are given in detail. Finally, some possible research directions about the OFRP are discussed and the conclusions are made
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