Theory of fuzzy systems
type: Item
instance of: scholarly article
title: Theory of fuzzy systems
zbMATH Open document ID: 0536.93002
DOI: 10.1016/S0165-0114(83)80105-5
author: Michel de Glas
published in: Fuzzy Sets and Systems
publication date: 1983-01-01T00:00:00Z
review text: A systematic theory of ''fuzzy systems'' is proposed, this ''fuzzy system'' being a mathematical model for the evolution, in time, of a ''fuzzy set'' (not well defined set). For any given t, the set x(t) is a fuzzy subset of some state space X, and this subset is given by a function \(\mu_{x(t)}:X\to [0,1]\), which reminds a measure of the likelihood that a given point \(u\in X\) belongs to the set x(t). The strong deviation from the usual probabilistic approach lies in the law of composition, which is defined on the basis of a min-max property. The usual differential equation defining the dynamical system, \(\dot x(t)=f(t,x(t))\) is substituted by a differential relation \(\dot x(t)=x(t){\mathbb{O}}R,\) where R is a ''fuzzy relation'' and \({\mathbb{O}}\) is a law of composition. Some basic properties (which are quite different from the usual probabilistic process) are obtained in this paper, and more are promised in a forthcoming paper.
Mathematics Subject Classification ID: 93A10
Mathematics Subject Classification ID: 93E99
Mathematics Subject Classification ID: 94D05
zbMATH DE Number: 3852870
zbMATH Keywords: fuzzy flow
zbMATH Keywords: fuzzy orbit
zbMATH Keywords: fuzzy systems
zbMATH Keywords: fuzzy relation
MaRDI profile type: Publication
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full work available at URL: s0165-0114(83)80105-5
OpenAlex ID: W2150976614
description: scientific article; zbMATH DE number 3852870