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Equivalence conditions for binary-tree-type hierarchical fuzzy systems. (Chinese. English summary) Zbl 1150.93478
Summary: To prove whether hierarchical fuzzy systems can be solved as the number of parameters exponentially increases when the number of input variables increases. This paper analyzes the problem of the number of fuzzy rules exponentially increasing as the number of input variables increases. This analysis gives equivalence conditions for a binary-tree-type hierarchical fuzzy system and a typical multi-input-single output (MISO) fuzzy system by deriving their input-output expressions. The analysis shows that to reach the same approximation accuracy, the number of parameters used by the binary-tree-type hierarchical fuzzy system must not be less than of the typical fuzzy system. This example casts doubt on whether hierarchical fuzzy systems can ultimately solve the “curse of dimensionality” problem of general MISO fuzzy systems.
MSC:
93C42 Fuzzy control/observation systems
03E72 Theory of fuzzy sets, etc.
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