A Belief Rule Base Considering Random Variables of Adaptive Membership Functions

With its inherent causal reasoning and superior capacity for handling uncertainty, the belief rule base (BRB) has been widely applied in complex systems modeling. As a generalization of fuzzy systems, selecting appropriate membership functions (MFs) to fuzzify input data and accurately calculating rule matching degree are crucial for the inference calculation of BRB. However, the original MF of BRB lacks flexibility and statistical properties. Thus, a BRB considering random variables of adaptive MF (BRB-RAMF) is proposed. First, the adaptive coefficient is defined, which can flexibly adjust the shape of the MF. With this definition, the adaptive coefficient is represented as a random variable with specific probability distribution, and the adaptive MF with continuous probability distribution is proposed to enhance its statistical properties. Moreover, the rule matching degree calculation of two attributes is discussed in detail, and then the multiple attributes are extended to demonstrate its universality. The fundamental performance of the model is investigated to confirm its rationality. Finally, the effectiveness of the BRB-RAMF model is demonstrated by taking the health status assessment of aerospace relays and spacecraft flywheel systems as examples.