Sugeno type controllers are universal controllers
Fuzzy Sets and Systems
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IEEE Transactions on Fuzzy Systems
Combinatorial rule explosion eliminated by a fuzzy rule configuration
IEEE Transactions on Fuzzy Systems
General SISO Takagi-Sugeno fuzzy systems with linear rule consequent are universal approximators
IEEE Transactions on Fuzzy Systems
Comments on “Combinatorial rule explosion eliminated by a fuzzy rule configuration” [and reply]
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Comment on “Combinatorial rule explosion eliminated by a fuzzy rule configuration” [and reply]
IEEE Transactions on Fuzzy Systems
Analysis and design of hierarchical fuzzy systems
IEEE Transactions on Fuzzy Systems
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An efficient tool to deal with the 'rule explosion' problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low-dimensional systems. In this paper a generalized hierarehical Tagaki-Sugeno (TS) system is built. It is shown that the input-output (I/O) relationship of this generalized hierarehical system can be represented as one of a standard TS fuzzy system. And the system approximation capability is analyzed by taking piecewise linear functions as a bridge. By constructive method it is proven that the hierarchical fuzzy systems (HFS's) can be universal approximators. For the given approximation accuracy, an estimation formula about the number of the rules needed in the HFS is established. Finally some simulation examples confirm that the HFS's with smaller size rule base can approximate the given functions with high accuracy. The results obtained here provide us with the theoretical basis for various applications of HFS's.