Decoupling in fuzzy systems: A cascade compensation approach
type: Item
instance of: scholarly article
title: Decoupling in fuzzy systems: A cascade compensation approach
zbMATH Open document ID: 0672.93040
DOI: 10.1016/0165-0114(89)90192-9
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: The paper addresses a problem of decoupling in systems described by fuzzy relational equations, \(y_ 1=x_ 1\circ x_ 2\circ R_ 1\), \(y_ 2=x_ 1\circ x_ 2\circ R_ 2\) where \(x_ 1,x_ 2\) stand for input fuzzy sets, \(x_ 1:X\to [0,1]\), \(x_ 2:x_ 2\to [0,1]\), \(y_ 1,y_ 2\) are output fuzzy sets described in the appropriate spaces whereas \(R_ 1\) and \(R_ 2\) are fuzzy relations of the system. A compensator working in cascade structure is given by formulas, \(x_ 1=u_ 1\circ u_ 2\circ \tilde R_ 1\), \(x_ 2=u_ 1\circ u_ 2\circ \tilde R_ 2\) where \(u_ 1\) and \(u_ 2\) denote inputs of the compensator and \(\tilde R_ 1\) and \(\tilde R_ 2\) are two fuzzy relations which are looked for in order to compensate the previous system. A necessary and sufficient condition for the existence of a solution of the decoupling problem is studied.
Mathematics Subject Classification ID: 93C30
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 4101043
zbMATH Keywords: decoupling
zbMATH Keywords: fuzzy relational equations
zbMATH Keywords: compensator
zbMATH Keywords: cascade structure
author: Chen Wei Xu
author: Yong-Zai Lu
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90192-9
OpenAlex ID: W2025653556
cites work: Fuzzy sets and systems. Theory and applications
cites work: Q3949028
cites work: An identification algorithm in fuzzy relational systems
cites work: When is a fuzzy relation decomposable in two fuzzy sets?
cites work: Resolution of composite fuzzy relation equations
Recommended article: Q3758630
Recommended article: Q3476657
Recommended article: Q4292507
Recommended article: Q4489371
Recommended article: Q3086628
Recommended article: Q5499270
Recommended article: DECENTRALIZED STABILIZATION OF COMPLEX SYSTEMS BY COMBINATION OF CONVENTIONAL AND FUZZY CONTROLS
Recommended article: Decomposition of multivariable systems for distributed fuzzy control
Recommended article: Decentralized fuzzy control of multivariable systems by active decomposition of control laws
Recommended article: Q5467114
description: scientific article; zbMATH DE number 4101043