This paper considers a facility construction problem in a rectangular urban area with some barriers and rectilinear distance. There exist some demand points and possible construction sites with preference of construction. For each site, its construction cost is a fuzzy random variable due to the change of the situation and difficulty of estimation after planning. Therefore in this case the total cost is also a fuzzy random variable and so probability that the cost becomes below the budget should not be below the fixed level from randomness of the total cost. We should decide suitable facility construction places under the condition that each demand point is covered within some distance from at least one facility. Under this condition, the possibility that the above chance constraint is satisfied should be maximized and minimal preference among facility constructed sites maximized. We seek some non-dominated solutions after definition of non-domination.