Competitive facility location problem with fuzzy relative distance Journal of Nonlinear Convex Analysis

Abstract. This paper investigate a competitive facility location problem wherethere are two facilities on alinear market. Customers at ademand point utilizethe facility which seems to be the nearest one from them. We assume that they donot distinguish the small difference between two distances, i.e., they do not always utilize the nearest facility by strictly measuring physical distance. We formulatethis preference by introducing fuzzy difference of the actual distance between twopoints. $\mathrm{h} $ our model, two companies, the leader and the follower, establish their facil-mulate these problems as amedianoid problem and a centroid problem respectively, and show the domains which contain the solutions for these problems