Bisimulation of type 2 for BL-general fuzzy automata

  • Marzieh Shamsizadeh
  • Mohammad Mehdi ZahediEmail author


In this note, first, we define bisimulation of type 2 for a basic logic general fuzzy automaton and show that if there exists a bisimulation of type 2 between two basic logic general fuzzy automata, then they have the same behavior. Also, by using the greatest bisimulation of type 2, we obtain a quotient basic logic general fuzzy automaton in which this quotient is minimal. Moreover, we prove that if there exists a bisimulation of type 1 between two automata, then there is a bisimulation of type 2 between them, but the converse is not valid. Moreover, we give an algorithm, which determines the bisimulation of type 2 between any two basic logic general fuzzy automata and show that the time complexity of this algorithm is so better than the time complexity of the algorithm computing bisimulation of type 1. After that, we present some examples to clarify the notions and results of this paper.


BL-general fuzzy automata Bisimulation of type 2 Quotient automata Minimal automata 



The authors wish to thank Iran National Science Foundation (INSF) for financial support.

Compliance with ethical standards

Conflict of interest

None of the authors have a conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of MathematicsGraduate University of Advanced TechnologyKermanIran

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