Approximate bisimulation relations for fuzzy automata

作者：Yang, Chao; Li, Yongming^*

来源：Soft Computing, 2018, 22(14): 4535-4547.

DOI：10.1007/s00500-017-2913-z

• Fuzzy automata
• Approximate bisimulation relation
• The greatest approximate bisimulation relation
• Ultra-metric

In this paper, for an ultra-metric D on the unit interval and a small positive real number , we firstly define the concept of approximate bisimulation relations between two fuzzy automata and prove that the behavior of a fuzzy automaton differs by from the behavior of a fuzzy automaton 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 and and approximate bisimulation relations for 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.

• 出版日期2018-7
• 单位陕西师范大学