Fuzzy facility location problem with preference of candidate sites

Models so far considered as facility location problems treat either min–max or max–min criterion, that is, the facility is either desirable or undesirable. We propose the following model considering the satisfaction degree with respect to the distance from the facility for each customer (residents) and preference of the site in an urban area. The objective is to find the site of the facility which maximizes the minimal satisfaction degree among all demand points and maximizes the preference of the site. Since generally speaking, there exists no site that maximizes both criteria, we seek non-dominated sites after defining non-domination.