SVD-based complexity reduction of "near PSGS" fuzzy systems

Abstract

With the help of the SVD-based (singular value decomposition) complexity reduction method, not only the redundancy of fuzzy rule-bases are eliminated, but also further, nonexact reduction are made, considering the allowable error. Namely, in case of higher allowable error, the result is 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 in time-critical applications and makes possible the combining of fuzzy systems with anytime techniques to cope with the changing circumstances during the operation of the system. However, while the SVD-based reduction can be applied to PSGS fuzzy systems, in case of rule-bases, constructed from expert knowledge, the input fuzzy sets are not always in Ruspini-partition. This paper extends the SVD-based reduction to "near PSGS" fuzzy systems, where the input fuzzy sets are not in Ruspini-partition.