NDLI: Conditions for Equivalence of Hierarchical Fuzzy Systems and Zero-Order TS Fuzzy Systems

Content Provider	IEEE Xplore Digital Library
Author	Xinyu Du Hao Ying Naiyao Zhang
Copyright Year	2005
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Wayne State Univ., Detroit, MI (Xinyu Du; Hao Ying)
Abstract	For conventional fuzzy systems, Mamdani type or TS type, it is; well known that the number of fuzzy rules and adjustable parameters exponentially increases with the number of input variables. This problem is often referred as curse of dimensionality. Hierarchical fuzzy systems have been proposed to resolve this problem. At present, however, it is unclear whether or not hierarchical fuzzy systems can truly resolve this issue. In this paper, we investigate the zero-order TS fuzzy systems and their corresponding hierarchical fuzzy systems. We rigorously prove that to approximate any continuous functions with the same degree of accuracy, the number of parameters used by the hierarchical fuzzy systems are exactly the same as those employed by the TS systems. This result implies that the hierarchical fuzzy systems do not offer a real solution, at least for the zero-order TS fuzzy systems
Sponsorship	IEEE IEEE Neural Networks Soc
Starting Page	939
Ending Page	944
File Size	1951179
Page Count	6
File Format	PDF
ISBN	0780391594
DOI	10.1109/FUZZY.2005.1452520
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2005-05-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Fuzzy systems Input variables Automation Sensitivity analysis Stability analysis
Content Type	Text
Resource Type	Article

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