Generating consistent fuzzy belief rule base from sample data

A fuzzy rule-based evidential reasoning approach and it corresponding optimization algorithm have been proposed recently, where a fuzzy rule-base with a belief structure, called a fuzzy belief rule base (FBRB), forms a basis in the inference mechanism. In this paper, a new learning method for optimally generating a consistent FBRB based on the given data is proposed. The main focus is given on the consistency of FBRB knowing that the consistency conditions are often violated if the system is generated from real world data. The measurement of inconsistency of FBRB is provided and finally is incorporated in the objective function of the optimization algorithm. This process is formulated as a nonlinear constraint optimization problem and solved using the optimization tool provided in MATLAB. A numerical example is provided to demonstrate the effectiveness of the proposed algorithm.