Adaptation of SVD-based fuzzy reduction via minimal expansion

Most adopted fuzzy inference techniques do not hold the universal approximation property if the numbers of antecedent sets are limited. This fact and the exponential complexity problem of widely adopted fuzzy logic techniques show the contradictory features of fuzzy rule bases in pursuit of good approximation. As a result, complexity reduction emerged in fuzzy theory. The natural disadvantage of using complexity reduction is that the adaptivity property of the reduced approximation becomes highly restricted. This paper proposes a technique for the singular value decomposition (SVD) based reduction developed by Yam et al. (see IEEE Trans. Fuzzy Syst., vol. 7, p. 120-131, Feb. 1999), which may alleviate the adaptivity restriction.