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Fuzzy modelling of measurements acquired by an intelligent ultrasonic telemeter

The measurement uncertainty in physical sensors is often represented by a probabilistic statistical approach, but such a representation is not always adapted to the treatment of information and a fuzzy representation, based on possibility theory, can sometimes be preferred. That is why we have proposed a truncated triangular probability-possibility transformation, to be applied to the four most encountered symmetric probability laws, and to any unimodal and symmetric probability distribution which can be assimilated to one of these four probability laws. In this paper, we propose to build a fuzzy model of measurement sensors by applying this transformation. For this, a minimum of knowledge about the probabilistic modeling of sensors is required. In fact, according to the measurement context of the sensor considered, a more or less spread probabilistic modeling of the measurement will be available. In this paper, three main situations will be considered and for each situation, an adapted fuzzy model will be proposed. Finally, an application to distance measurements provided by two ultrasonic sensors, a pulse telemeter and a frequency modulated telemeter, is presented.