Preventive health care is unlike health care for acute ailments, as people are less alert to their unknown medical problems. In order to motivate public and to attain desired participation levels for preventive programs, the attractiveness of the health care facility is a major concern. Health economics literature indicates that attractiveness of a facility is significantly influenced by proximity of the clients to it. Hence attractiveness is generally modelled as a function of distance. However, abundant empirical evidence suggests that other qualitative factors such as perceived quality, attractions nearby, amenities, etc. also influence attractiveness. Therefore, a realistic measure should incorporate the vagueness in the concept of attractiveness to the model. The public policy makers should also maintain the equity among various neighborhoods, which should be considered as a second objective. Finally, even though the general tendency in the literature is to focus on health benefits, the cost effectiveness is still a factor that should be considered. In this paper, a fuzzy bi-objective model with budget constraints is developed. Later, by modelling the attractiveness by means of fuzzy triangular numbers and treating the budget constraint as a soft constraint, a modified (and more realistic) version of the model is introduced. Two solution methodologies, namely fuzzy goal programming and fuzzy chance constrained optimization are proposed as solutions. Both the original and the modified models are solved within the framework of a case study in Istanbul, Turkey. In the case study, the Microsoft Bing Map is utilized in order to determine more accurate distance measures among the nodes. © 2014, Springer Science+Business Media New York.