Paper Info
Title
Approximation Capabilities of Hierarchical Fuzzy Systems
Abstract
Derived from practical application in location analysis and pricing, and based on the approach of hierarchical structure analysis of continuous functions, this paper investigates the approximation capabilities of hierarchical fuzzy systems. By first introducing the concept of the natural hierarchical structure, it is proved that continuous functions with natural hierarchical structure can be naturally and effectively approximated by hierarchical fuzzy systems to overcome the curse of dimensionality in both the number of rules and parameters. Then, based on Kolmogorov's theorem, it is shown that any continuous function can be represented as a superposition of functions with the natural hierarchical structure and can then be approximated by hierarchical fuzzy systems to achieve the universal approximation property. Further, the conditions under which the hierarchical fuzzy approximation is superior to the standard fuzzy approximation in overcoming the curse of dimensionality are analyzed
Year
DOI
Venue
2005
10.1109/TFUZZ.2005.856559
IEEE T. Fuzzy Systems
Keywords
Field
DocType
approximation capability,hierarchical fuzzy system,continuous function,universal approximation property,natural hierarchical structure,location analysis,standard fuzzy approximation,practical application,hierarchical structure analysis,hierarchical fuzzy systems,hierarchical fuzzy approximation,approximation capabilities,fuzzy system,approximation theory,fuzzy systems,curse of dimensionality,approximation property,pricing
Continuous function,Superposition principle,Mathematical optimization,Fuzzy logic,Approximation theory,Curse of dimensionality,Artificial intelligence,Fuzzy control system,Fuzzy number,Approximation property,Mathematics,Machine learning
Journal
Volume
Issue
ISSN
13
5
1063-6706
Citations 
PageRank 
References 
51
1.88
20
Authors
2
Name
Order
Citations
PageRank
Xiao-jun Zeng12282125.89
J. A. Keane2967.33