Several real-world situations can be modeled as maximal covering location problem (MCLP), which is focused on finding the best locations for a certain number of facilities that maximizes the coverage of demand nodes located within a given exact coverage distance (or travel time). In a real scenario, such distance as well as other elements of the location problem can be uncertain or linguistically (vaguely) defined by the decision maker. In this paper, we manage flexibility in the coverage distance through a fuzzy constraint. So, an extension of the original MCLP model is proposed, which is solved by using a parametric approach. Computational experiments have been conducted to analyze how the proposed model can be solved and what kind of information can be obtained to help a potential decision maker to take a more informed decision.

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