Singular Value-Based Fuzzy Reduction With Relaxed Normality Condition

This work extends the results of a recent reduction method for fuzzy rule bases. The original approach conducts singular value decomposition (SVD) on the rule consequents and eliminates the weak and redundant components according to the magnitudes of the resulting singular values. The number of reduced rules as resulted depends on the number of singular values retained in the process. Conditions of sum normalization (SN), non-negativeness (NN) and Normality (NO) are imposed to ensure properly interpretable membership functions for the reduced rules. In this work, a new concept of relaxed Normality (RNO) condition is presented to enhance the interpretability of membership functions in situations where the NO condition cannot be strictly satisfied. The price to pay is an increase in the number of reduced rules and errors.