Gaze control is one of the essential functions of a mobile robot to acquire limited information from the environment using a local vision sensor, and enable robust navigation in a dynamic environment. Gaze control should be performed considering various criteria, including obstacle avoidance, map building, localization, path planning, etc. The fuzzy measure and the fuzzy integral could be used to represent the user's preference for the criteria, and to globally evaluate the candidate gaze directions, respectively. In the authors' previous research, gaze control was implemented to navigate a humanoid robot using a fixed preference for the criteria in a dynamic environment. It incorporated SLAM-based localization and modified univector field-based path generation. This paper proposes a gaze control-based navigation architecture with a situation-specific preference approach. This approach switches preference degrees specific to the changed situation in a dynamic environment. This paper also proposes a novel motion model for the unscented Kalman filter-based SLAM, which is synchronized with the walking pattern generator of a humanoid robot. The proposed architecture is verified through comparisons with four other architectures each with a different approach by carrying out experiments using the small-sized humanoid robot, HanSaRam-IX, developed in the Robot Intelligence Technology Laboratory, Korea Advanced Institute of Science and Technology.