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Arithmétique floue phi-calcul : applications à la classification et à la commande

Abstract : The presented Ph.D. thesis proposes a practical arithmetic to calculate fuzzy intervals and quantities. The latter are modelled by an accumulative distribution function based on classical statistics instead of classical membership functions. This innovative work effectively deals with imprecise data and uncertainties by exploiting some ideas in the direction described above.Existing methods found in the specialized literature are not disregarded, though this thesis intends to present another way of reasoning and solving certain problems with a simpler implementation.Since the proposed method is close to probability and classical statistics, it has lead –at a first stage-to stressing the analysis of imprecise data as well as to extend the statistical tools. Nevertheless, a complete and coherent arithmetic based on fuzzy logic techniques and interval analysis has been proposed.A number of illustrative examples have been presented through this work to facilitate the understanding of our approach. The thesis’ objective is to show the feasibility and applicability of our claims.Results obtained in applications, both on the analysis of objective-subjective data and on the internal nonlinear model control (with special emphasis on a real-time application for a non-linear imprecise system) have proved the effectiveness of j-calculus. Other mathematical developments and extensions to other areas suggest that interesting perspectives in the future will arrive
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Submitted on : Tuesday, November 10, 2020 - 1:56:55 PM
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  • HAL Id : tel-02998162, version 1


Hakim Lamara. Arithmétique floue phi-calcul : applications à la classification et à la commande. Automatique / Robotique. Université de Valenciennes et du Hainaut-Cambrésis, UVHC, (France), 2007. Français. ⟨NNT : 2007VALE0038⟩. ⟨tel-02998162⟩



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