基于模糊概率的多状态贝叶斯网络可靠性分析

利用贝叶斯网络对多状态系统进行可靠性分析时，各根节点不同状态的精确概率难以获得。因此提出了把模糊理论与贝叶斯网络方法相结合，将不同专家给出的根节点各状态发生概率的语言变量转化为三角模糊数，并经过均值化、解模糊和归一化得到不同状态的发生概率的精确值。将其代入多状态贝叶斯网络中，计算叶节点不同状态的发生概率，进而计算各根节点的后验概率及风险增加当量重要度。通过实例分析验证了该方法的可行性。应用该方法能够提高贝叶斯网络处理不确定性问题的能力，使其在解决多状态不确定性系统可靠性和安全性问题时发挥更大的作用。

Reliability analysis of multi-state Bayesian networks based on fuzzy probability

In the course of reliability analysis on multi-state systems by using Bayesian networks, it is difficult to obtain the precision probability of different states of root nodes. So a method combining fuzzy theory with Bayesian networks is proposed. The linguistic variables from different experts, which denote the probability of different states of root nodes, are translated into triangular fuzzy-numbers. By steps viz. equalization, defuzzification and normalization, the precision probabilities are got. Inputting them into multistate Bayesian networks, the probabilities of leaf nodes in different states are calculated. And then, the posterior probability and risk achievement worth (RAW) importance of root node are got. The feasibility of this method is validated by an example. The application of this method can improve the ability of Bayesian networks to deal with uncertainty issues and make it play a greater role in improving the reliability and security of the multi-state uncertainty system.