Self-tuning method for fuzzy rule base with belief structure

A framework for modelling the safety of an engineering system using a fuzzy rule-based evidential reasoning (FURBER) approach has been proposed recently, where a fuzzy rule-base designed on the basis of a belief structure (called a belief rule expression matrix) forms a basis in the inference mechanism of FURBER. In this paper, a learning method for optimally training the elements of the belief rule expression matrix and other knowledge representation parameters in FURBER is proposed. This process is formulated as a nonlinear objective function to minimize the differences between the output of a belief rule base and given data. The optimization problem is solved using the optimization tool provided in MATLAB. A numerical example is provided to demonstrate how the method can be implemented