SVD-based complexity reduction of rule-bases with nonlinear antecedent fuzzy sets

With the help of the singular value decomposition (SVD) based complexity reduction method, not only can the redundancy of fuzzy rule-bases be eliminated, but further reduction can also be made, considering the allowable error. Namely, in the case of higher allowable error, the result may be a less complex fuzzy inference system, with a smaller rule-base. This property of the SVD-based reduction method makes possible the usage of fuzzy systems, even in cases when the available time and resources are limited. The original SVD-based reduction method was proposed for rule-bases with linear antecedent fuzzy sets. This limitation remained valid in the later extensions, as well. The purpose of this paper is to give a formal mathematical proof for the original formulas with nonlinear antecedent fuzzy sets and thus to end this limitation.