An optimal learning method for constructing belief rule bases

A belief rule-base inference methodology using the evidential reasoning approach (RIMER) has been developed where a new rule-base designed on the basis of a belief structure forms a basis in the inference mechanism of RIMER. A rule-base with both subjective and analytical elements may be difficult to build in particular for a complex system. A learning method for optimally training the elements of belief rules and other knowledge representation parameters is proposed. Nonlinear multiobjective optimization models are proposed to minimize the differences between the outputs of a belief rule base and given data. The problems are solved using the optimization toolbox provided in MATLAB. The optimization models are extended to hierarchical knowledge based systems. A numerical example for a hierarchical rule-base is examined to demonstrate the new method.