A novel aspect of Human-Robot Interaction (HRI) can be put on the basis, that the robot side is implemented on a state-machine (fuzzy automaton), which reacts the human intervention as a function of the robot state and the human action. This platform is suitable for implementing quite complicated action-reaction sequences, like the interaction of human and an animal, e.g. a behaviour of an animal companion to the human. According to this paradigm the robot can follow the existing biological examples and form inter-species interaction. The 20.000 year old human-dog relationship is a good example for this paradigm of the HRI, as interaction of different species. In this paper, for ethologically inspired HRI model implementation, a fuzzy model structure built upon the framework of low computational demand Fuzzy Rule Interpolation (FRI) methods and fuzzy automaton is suggested. For demonstrating the applicability of the proposed structure, some components of a human-dog interaction FRI model, which also suitable for HRI, will be briefly introduced in this paper.