Cyclic classes and an ergodic theorem in dynamic fuzzy systems
type: Item
instance of: scholarly article
title: Cyclic classes and an ergodic theorem in dynamic fuzzy systems
zbMATH Open document ID: 0951.54037
DOI: 10.1016/S0165-0114(96)00303-X
author: Yuji Yoshida
published in: Fuzzy Sets and Systems
publication date: 1999-06-17T00:00:00Z
review text: This study is concerned with a dynamic fuzzy system governed by the equation \[ S_{n+1}(y)=\sup_{x\in E}\biggl[ \min\bigl( S_n(x), Q(x,y) \bigr)\biggr],\;y\in E \] where a state space \(E\) is a complete metric space and \(Q\) is a normal semi-continuous fuzzy relation defined in \(E\times E\). \(\{S_n\}\) is a sequence of fuzzy states. The paper provides a detailed discussion of the limiting behavior of fuzzy states of the system and analyzes the cyclic behavior of the system. Finally, an ergodic theorem is formulated. A brief illustrative example is provided.
reviewed by: Witold Pedrycz
Mathematics Subject Classification ID: 54H20
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1305155
zbMATH Keywords: fuzzy relations
zbMATH Keywords: sup-min composition
zbMATH Keywords: recurrence
zbMATH Keywords: dynamic fuzzy system
zbMATH Keywords: ergodic theorem
MaRDI profile type: Publication
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full work available at URL: s0165-0114(96)00303-x
OpenAlex ID: W2007172959
description: scientific article; zbMATH DE number 1305155