Graded Tolerant Inclusion and its Axiomatization

Patrick BOSC, Allel HADJALI and Olivier PIVERT.

In this paper, a revisited approach for possibilistic fuzzy regression methods is proposed. Indeed, a new modified fuzzy linear model form is introduced where the identified model output can envelope all the observed data and ensure a total inclusion property. Moreover, this model output can have any kind of spread tendency. In this framework, the identification problem is reformulated according to a new criterion that assesses the model fuzziness independently of the collected data. The proposed concepts are used in a global identification process in charge of building a piecewise model able to represent every kind of output evolution.

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