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In order to determine the parameters of belief-rule-base (BRB) accurately, several optimization methods have been proposed for training BRB, on the basis of a generic rule-base inference methodology using the evidential reasoning (RIMER) approach. These optimization methods are implemented offline, and such are not suitable for training BRB in a dynamic fashion. In this paper, two recursive algorithms are proposed to update BRB online that can simulate dynamic systems. The main feature of the proposed algorithms is that only partial input and output information is required, which can be incomplete or vague, numerical or judgmental, or mixed. If the internal structure of a BRB is initially decided using expert judgments, domain-specific knowledge and/or commonsense rules, the proposed algorithms can be used to fine-tune the initial BRB online, once input and output datasets become available. Using the proposed algorithms, there is no need to collect a complete set of data before a BRB can be trained, which is necessary if the BRB is used to simulate a dynamic system. A numerical example and a case study are reported to demonstrate the potential of the algorithms for online fault diagnosis.