During the last few decades, as a part of effort to enhance natural human robot interaction (HRI), considerable research has been carried out to develop human-like gaze control. However, most studies did not consider hardware implementation, real-time processing, and the real environment, factors that should be taken into account to achieve natural HRI. This paper proposes a fuzzy integral-based gaze control algorithm, operating in real-time and the real environment, for a robotic head. We formulate the gaze control as a multicriteria decision making problem and devise seven human gaze-inspired criteria. Partial evaluations of all candidate gaze directions are carried out with respect to the seven criteria defined from perceived visual, auditory, and internal inputs, and fuzzy measures are assigned to a power set of the criteria to reflect the user defined preference. A fuzzy integral of the partial evaluations with respect to the fuzzy measures is employed to make global evaluations of all candidate gaze directions. The global evaluation values are adjusted by applying inhibition of return and are compared with the global evaluation values of the previous gaze directions to decide the final gaze direction. The effectiveness of the proposed algorithm is demonstrated with a robotic head, developed in the Robot Intelligence Technology Laboratory at Korea Advanced Institute of Science and Technology, through three interaction scenarios and three comparison scenarios with another algorithm.