Hierarchical neuro-fuzzy quadtree models
type: Item
instance of: scholarly article
title: Hierarchical neuro-fuzzy quadtree models
zbMATH Open document ID: 1035.93007
DOI: 10.1016/S0165-0114(01)00145-2
author: Flávio Joaquim de Souza
author: Marley M. R. Vellasco
author: Marco Aurélio C. Pacheco
published in: Fuzzy Sets and Systems
publication date: 2003-02-05T00:00:00Z
review text: The authors propose a new hybrid fuzzy model named hierarchical neuro-fuzzy quadtree (HNFQ) which is based on a recursive partitioning method of the input space called quadtree. In this partitioning and contrary to the usual binary partitioning, the \(n\)-dimensional space is successively subdivided in quadrants that, in turn, can be again subdivided in four regions. Thus, the learning capacity of artificial neural networks is maintained, and the theory of fuzzy sets makes it possible to present the information learned in a format which is well interpretable. The article describes the architecture of this new model, presenting its basic cell and its learning algorithm. Further, it is evaluated in three well-known benchmark applications; i.e., the approximation of the function sinc\((x,y)=\sin(x)\sin(y)/(xy)\) -- which yields a shape resembling a Mexican hat --, the Mackey Glass chaotic series forecast and the two spirals problem. When compared to other neuro-fuzzy systems, the HNFQ exhibits competing results with two major advantages: it creates automatically its own structure and it is not limited to few input variables.
Mathematics Subject Classification ID: 93A30
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 92B20
Mathematics Subject Classification ID: 93C35
Mathematics Subject Classification ID: 93B11
zbMATH DE Number: 1864833
zbMATH Keywords: neuro-fuzzy system
zbMATH Keywords: fuzzy system model
zbMATH Keywords: quadtree recursive partitioning
zbMATH Keywords: learning
zbMATH Keywords: hierarchical neuro-fuzzy quadtree
zbMATH Keywords: QNFQ
reviewed by: Inge Troch
describes a project that uses: NEFCLASS-X
describes a project that uses: ANFIS
describes a project that uses: C4.5
MaRDI profile type: Publication
cites work: Q4946089
cites work: Quad trees: A data structure for retrieval by composite keys
cites work: Q4936225
cites work: Q4023089
cites work: Neuro-fuzzy systems for function approximation
cites work: Neural-network-based fuzzy logic control and decision system
cites work: Q4341166
full work available at URL: s0165-0114(01)00145-2
OpenAlex ID: W2025535886
description: scientific article; zbMATH DE number 1864833