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.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
