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SVD Based Complexity Reduction of Rule Bases with Non-Linear Antecedent Fuzzy Sets

TitleSVD Based Complexity Reduction of Rule Bases with Non-Linear Antecedent Fuzzy Sets
Publication TypeJournal Article
Year of Publication2002
AuthorsTakács, O., and A. Várkonyi-Kóczy
JournalIEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT
Volume51
Issue2
Pagination217 - 221
Date Published2002
Publication Languageeng
Abstract

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.