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Soft Computing
Published in: Soft Computing 14/2018

09-11-2017 | Foundations

Approximate bisimulation relations for fuzzy automata

Authors: Chao Yang, Yongming Li

Published in: Soft Computing | Issue 14/2018

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Abstract

In this paper, for an ultra-metric D on the unit interval and a small positive real number \(\epsilon \), we firstly define the concept of approximate bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton \(A_1\) differs by \(\epsilon \) from the behavior of a fuzzy automaton \(A_2\) under an approximate bisimulation relation between them. Then we put forward the notion of surjective functional approximate bisimulation relations between two fuzzy automata. A connection between surjective functional approximate bisimulation relations between two fuzzy automata \(A_1\) and \(A_2\) and approximate bisimulation relations for \(A_1\) is also discussed. Finally, we give a method to construct the greatest approximate bisimulation relation for a fuzzy automaton and point out that bisimulation relations for a fuzzy automaton are also approximate bisimulation relations.
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Metadata
Title
Approximate bisimulation relations for fuzzy automata
Authors
Chao Yang
Yongming Li
Publication date
09-11-2017
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 14/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-017-2913-z

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