The interaction between humans and mobile robots in shared areas requires adequate control for both humans and robots.The online path planning of the robot depending on the estimated or intended movement of the person is crucial for the obstacle avoidance and close cooperation between them. The velocity obstacles method and its fuzzification optimizes the relationship between the velocities of a robot and a human agent during the interaction. In order to find the estimated intersection between robot and human in the case of positions/orientations disturbed by noise, analytical and fuzzified versions are presented. The orientation of a person is estimated by eye tracking, with the help of which the intersection area is calculated. Eye tracking leads to clusters of fixations that are condensed into cluster centers by fuzzy-time clustering to detect the intention and attention of humans.