Computation of the greatest simulations and bisimulations between fuzzy automata

  • Authors:

  • Miroslav ĆIri;Jelena Ignjatovi;Ivana JančI;Nada Damljanovi

  • Affiliations:

  • University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;University of Niš, Faculty of Sciences and Mathematics, Višegradska 33, 18000 Niš, Serbia;University of Kragujevac, Technical Faculty in Čačak, Svetog Save 65, P. O. Box 131, 32000 Čačak, Serbia

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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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 efficient 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 Ignjatovic et al. [On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets Syst. 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.