Singular value-based reduction of fuzzy rule base with non-singleton support
Yeung Yam, Péter Bárányi, Chi Tin Yang · 1999
Applies a singular value based method for the reduction of fuzzy rule base with non-singleton support. The method characterizes membership functions by the conditions of sum normalization (SN), non-negativeness (NN), and normality (NO), and conducts singular value decomposition on a matrix comprising rule consequents and support factors. The singular values serve to indicate the important components to keep, and the orthogonal matrices can be tailored to yield linear combinations to form membership functions for the reduced set. Membership functions as obtained generally satisfy the SN and NN conditions but not the NO, in which case close-to-NO solution would be adopted.