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arXiv · 1103.5078

Algorithms for computing the greatest simulations and bisimulations between fuzzy automata

Miroslav Ćirić·Jelena Ignjatović·Ivana Jančić·Nada Damljanović
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Abstract

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, and backward-forward bisimulations) between fuzzy automata have been introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of this kind. In the present paper, for any of the above-mentioned types of simulations/bisimulations we provide an effective algorithm for deciding whether there is a simulation/bisimulation of this type between the given fuzzy automata, and for computing the greatest one, whenever it exists. The algorithms are based on the method developed in [J. Ignjatović, M. Ćirić, S. Bogdanović, On the greatest solutions to certain systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081-3113], which comes down to the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations.

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Miroslav Ćirić, Jelena Ignjatović, Ivana Jančić, Nada Damljanović. 2011-03-25. Algorithms for computing the greatest simulations and bisimulations between fuzzy automata. https://doi.org/10.1016/j.fss.2012.05.006

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