Based on some results of the fuzzy network computation and competitive analysis, the Online Fuzzy Most Reliable Path Problem (OFRP), which is one of the most important problems in network optimization with uncertainty, has been originally proposed by our team. In this paper, the preliminaries about fuzzy and the most reliable path and competitive analysis are given first. Following that, the mathematical model of OFRP, in which two kinds of uncertainties, namely online and fuzzy, are combined to be considered at the same time, is established. 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 of the OFRP are discussed and the conclusions are drawn.
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