The maximal covering location problem (MCLP) seeks location of facilities on a network, so as to maximize the total demand within a pre-defined distance or travel time of facilities (which is called coverage radius). Most of the real-world applications of MCLP comprise many demand nodes to be covered. Moreover, uncertainty is ubiquitous in most of the real-world covering location problems, which are solved for a long-term horizon. Therefore, this paper studies a large-scale MCLP on the plane with fuzzy coverage radii under the Hurwicz criterion. In order to solve the problem, a combination of variable neighborhood search (VNS) and fuzzy simulation is offered. Test problems with up to 2500 nodes and different settings show that VNS is competitive, since it is able to find solutions with gaps all below 1.5% in much less time compared to exact algorithms.