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Personalized route problem with fuzzy constraints

The Personalized Route Problem resembles the so-called multi-criteria Shortest Path Problem where every arc (street) of the graph (map) has a set of costs (values) associated to a set of criteria (features). The personalization of the path comes when the user a) determines how important is each criterion according to personal preferences and b) indicates constraints on the criteria values. The preferences are often uncertain, imprecise or inexact. Also, it seems reasonable to allow some relaxation on the constraints. We propose and define a new model for the Personalized Route Problem with fuzzy constraints. As an example, we show its application to the Shortest Path Route with fuzzy constraints on the slopes values.