This paper presents a novel method to develop a human-robot attitudinal relationship based on intimacy. For a robot to estimate human's intimacy, we propose a fuzzy space model to classify intimate human behavioral patterns. Proxemic, tactile, and oculesic behavioral features, which are dominantly used for intimacy exchange in human-human communication, are analyzed to develop the 3-D intimacy space. The proposed model provides social standards to develop an intimacy-based attitudinal relationship between a human and a robot. We analyze the generality of our model through a sample interaction scenario and discuss how intimacy can be incrementally learnt for a long-term interaction between a robot and a human.