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Approximate bisimulation relations for fuzzy automata

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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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Acknowledgements

This study was supported by the Fundamental Research Funds for the Central Universities (Grant No.2017TS047). This study was funded by National Science Foundation of China (Grant No. 11671244).

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Authors and Affiliations

  1. College of Computer Science, Shaanxi Normal University, Xi’an, 710062, China

    Chao Yang & Yongming Li

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  1. Chao Yang
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  2. Yongming Li
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Correspondence to Yongming Li.

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Communicated by A. Di Nola.

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Yang, C., Li, Y. Approximate bisimulation relations for fuzzy automata. Soft Comput 22, 4535–4547 (2018). https://doi.org/10.1007/s00500-017-2913-z

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