Fuzzy Random Weighted Weber Problems in Facility Location

Abstract This article considers facility location in a Weber problem with weights including both uncertainty and vagueness. By representing its weights as fuzzy random variables, it can be extended to a fuzzy random weighted Weber problem, and then formulated as a fuzzy random programming problem. By introducing possibility and necessity measures and chance constraints, the extended problem is reformulated to new two types of Weber problems. Based upon characteristics of facility location, theorem for solving the reformulated problems are shown.