Une approche paramétrique de la régression linéaire floue - Formalisation par intervalles

Abstract : System identification is a term gathering tools that identify mathematical models from observations. Within this framework, regression techniques are frequently used. This Ph. D. thesis deals with the study of parametrical linear regression in an imprecise context. So, measurements and model parameters are imprecise and represented using fuzzy set theory, while inputs are crisp numbers. Existing fuzzy regression techniques present two main limits. On the one hand, the imprecision of identified models is too important, mainly due to the link between imprecision variation and input sign. On the other hand, inclusion is not guaranteed even when a triangular fuzzy model, which should include observations, is identified. In this context, several improvements are introduced and illustrated. Inclusion is guaranteed by the identification of trapezoidal fuzzy models. By applying a shift term to inputs, the model output imprecision becomes independent of input sign, while model linear structure is preserved. Lastly, an optimization criterion which represents the global fuzziness of the model on its definition domain is introduced. It is then possible to improve the precision of the identified model as well as its representativeness. All these concepts are extended to piecewise and multi-inputs linear model identification. The potential of the proposed method is tested on realistic data sets, concerning the identification of polynomial models with appropriate order and multi-linear models. By identifying dynamical models from variations of a market index, problems related to fuzzy regressive models with imprecise inputs are also introduced
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Amory Bisserier. Une approche paramétrique de la régression linéaire floue - Formalisation par intervalles. Intelligence artificielle [cs.AI]. Université de Savoie, 2010. Français. ⟨tel-01222338⟩

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