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Gardeñes, Ernest; Saínz, Miguel; Jorba, Lambert; Calm, Remei; Estela, Rosa; Mielgo, Honorino; Trepat, Albert

doi:10.1023/a:1011465930178

Cited by 82 publications

(42 citation statements)

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“…The outer approximation of x(13) is 7.7003 − 0.005278ε1 − 0.4234ε2 + 1.3824η3. It proves that x(13) ∈ [5.8891, 9.5114] if we ignore the mode change, and if not, that is if we take into account ε1 > −0.84, we get a slightly tighter value: x(13) ∈ [5.8891, 9.5106]. From the first-order generalized affine form, we also deduce that the inner interval range for x(13) is in all cases [7.369694594, 8.030894409]: this is still a fairly wide inner approximation even in the case of the mode change.…”

Section: Guard Conditions In Hybrid Automatamentioning

confidence: 95%

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Inner approximated reachability analysis

Goubault

Mullier

Putot

et al. 2014

Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control

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Computing a tight inner approximation of the range of a function over some set is notoriously difficult, way beyond obtaining outer approximations. We propose here a new method to compute a tight inner approximation of the set of reachable states of non-linear dynamical systems on a bounded time interval. This approach involves affine forms and Kaucher arithmetic, plus a number of extra ingredients from set-based methods. An implementation of the method is discussed, and illustrated on representative numerical schemes, discrete-time and continuous-time dynamical systems.

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Section: Guard Conditions In Hybrid Automatamentioning

confidence: 95%

“…A modal interval [9] is an interval supplemented by a quantifier. Extensions of modal intervals were proposed in the framework of generalized intervals, and called AE extensions because universal quantifiers (All) always precede existential ones (Exist) in the interpretations.…”

Section: Modal Intervals and Generalized Intervalsmentioning

confidence: 99%

Inner approximated reachability analysis

Goubault

Mullier

Putot

et al. 2014

Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control

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“…The semantic tolerance model is based on modal interval analysis (MIA) [30,31,32], which is an algebraic and semantic extension of the classic interval analysis (IA) [33].…”

Section: Generalized Intervalsmentioning

confidence: 99%

Interpretable Interval Constraint Solvers in Semantic Tolerance Analysis

Wang¹

2008

Computer-Aided Design and Applications

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A semantic tolerance modeling scheme based on generalized intervals was recently proposed to allow for embedding more tolerancing intents in specifications with a combination of numerical intervals and logical quantifiers. By differentiating a priori and a posteriori tolerances, the logic relationships among variables can be interpreted, which is useful to verify completeness and soundness of numerical estimations in tolerance analysis. In this paper, we present a semantic tolerance analysis approach to estimate tolerance stack-ups. New interpretable linear and nonlinear constraint solvers are developed to ensure interpretability of variation estimations. This new approach enhances traditional numerical analysis methods by preserving logical information during computation such that more semantics can be derived from numerical results.

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“…Some of the problems inherent to classical intervals are solved by their reticular completion using modal intervals [9].…”

Section: Introductionmentioning

confidence: 99%

Quantified trapezoidal fuzzy numbers

Adillon

Jorba

2017

IFS

Self Cite

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The aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoidal fuzzy number may also be improper intervals. In addition, this paper addresses the inclusion relationship which is deduced from the inclusion of modal intervals and is related to the classical setinclusion relationship between trapezoidal fuzzy numbers as well as the extensions of real continuous functions over the set of quantified trapezoidal fuzzy numbers.Using the semantic interpretation of the calculations over modal intervals will enable us to interpret the meaning of the calculus accurately over quantified trapezoidal fuzzy numbers.With quantified trapezoidal fuzzy numbers, we will be able to overcome some operational limitations that are usually faced when working with trapezoidal fuzzy numbers from a classical point of view. In order to show the applicability of quantified trapezoidal fuzzy numbers, we propose fuzzy equations which have no solution in the set of proper fuzzy numbers yet do have solutions that are improper fuzzy numbers. We also propose two applications of quantified trapezoidal fuzzy numbers, one of them about financial calculations and the other one in an optical problem.

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Cited by 82 publications

References 0 publications

Inner approximated reachability analysis

Inner approximated reachability analysis

Interpretable Interval Constraint Solvers in Semantic Tolerance Analysis

Quantified trapezoidal fuzzy numbers

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