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This paper deals with representation and reasoning on information concerning the evolution of a physical parameter by means of a model based on the Fuzzy Constraint Satisfaction Problem formalism, and with which it is possible to define what we call Fuzzy Temporal Profiles (FTP). Based on fundamentally linguistic information, this model allows the integration of knowledge on the evolution of a set of parameters into a knowledge representation scheme in which time plays a fundamental role.The FTP model describes the behaviour of a physical parameter on the basis of a set of signal events, and which allows the evolution of the parameter between each pair of events to be modelled as signal episodes. Given the fundamentally linguistic nature of the information represented, the consistency analysis of this information is an essential task. Nevertheless, the obtention of the minimal representation of the network that defines an FTP is an NP-hard problem. In spite of this, we supply algorithms guaranteeing local levels of consistency that allow to correct a large proportion of the errors committed by a human expert in the linguistic description of the profile. Furthermore, we propose a new topology whose consistency can be guaranteed in polynomial time. We also study the applicability of this model in the recognition of signal patterns.