Approximation theory of fuzzy systems based upon genuine many-valued implications -- SISO cases
type: Item
instance of: scholarly article
title: Approximation theory of fuzzy systems based upon genuine many-valued implications -- SISO cases
zbMATH Open document ID: 1017.93056
DOI: 10.1016/S0165-0114(01)00166-X
author: Yongming Li
author: Zhongke Shi
author: Zhihui Li
published in: Fuzzy Sets and Systems
publication date: 2003-02-05T00:00:00Z
review text: The authors prove that the single input and single output (SISO) fuzzy systems based upon genuine many-valued implications are universal approximators [for the MIMO cases, see ibid. 130, 159-174 (2002; Zbl 1017.93057), reviewed below]. The study on approximation theory of fuzzy systems is very important and necessary. In most applications of fuzzy systems, the main design objective can be transformed to finding a designed mapping from the input spaces to the output spaces, which may also be denoted as a function. Thus, the problem of designing fuzzy systems can be considered as approximation problems of functions. It is shown theoretically that fuzzy control systems based upon genuine many-valued implications are equivalent to those based upon t-norm implications, and the general approach to construct fuzzy systems is given. It is also shown that a defuzzifier based upon the center of areas is not appropriate for fuzzy systems based upon genuine many-valued implications.
Mathematics Subject Classification ID: 93C42
Mathematics Subject Classification ID: 93A30
zbMATH DE Number: 1864830
zbMATH Keywords: fuzzy system
zbMATH Keywords: Boolean implication
zbMATH Keywords: universal approximator
zbMATH Keywords: many-valued implications
zbMATH Keywords: \(t\)-norm implications
Wikidata QID: Q62038267
reviewed by: George S. Stavrakakis
MaRDI profile type: Publication
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full work available at URL: s0165-0114(01)00166-x
OpenAlex ID: W2138579452
DBLP publication ID: journals/fss/LiSL02
description: scientific article; zbMATH DE number 1864830