Fuzzy controllers design via fixed point theorem
type: Item
instance of: scholarly article
title: Fuzzy controllers design via fixed point theorem
zbMATH Open document ID: 0613.93011
DOI: 10.1016/0165-0114(86)90072-2
published in: Fuzzy Sets and Systems
publication date: 1986-01-01T00:00:00Z
review text: The paper is dedicated to a problem of control of a system described by the input-output equation \(y=f(x)\) which is realized in presence of fuzziness. Fuzziness is attached to the problem formulated by introducing a fuzzy relation \(\mu_{\epsilon}\) defined in the Cartesian product of the output space (equipped with a metric d(\(\cdot,\cdot))\), say \(\mu_{\epsilon}:\) \b{Y}\(\times \underline Y\to [0,1]\). This relation expresses a grade of satisfaction of the inequality \(d(y,z)<\delta\), with \(\epsilon\) standing for a nonnegative constant for any pair of elements y,z\(\in \underline Y\). In such a framework a control formula \(u=r(y)\), u being an element of the space of controls, is derived by means of a fixed point theorem.
Mathematics Subject Classification ID: 93B15
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 3993381
zbMATH Keywords: input-output equation
zbMATH Keywords: Fuzziness
zbMATH Keywords: fuzzy relation
zbMATH Keywords: fixed point theorem
author: Andrzej Świerniak
MaRDI profile type: Publication
full work available at URL: 0165-0114(86)90072-2
OpenAlex ID: W2124781398
cites work: Outline of a New Approach to the Analysis of Complex Systems and Decision Processes
cites work: Q4063083
description: scientific article; zbMATH DE number 3993381