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Wyszukujesz frazę "interval arithmetic" wg kryterium: Temat

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    Wyświetlanie 1-4 z 4
    Tytuł:
    A decomposition approach to type 2 interval arithmetic
    Autorzy:
    Piegat, Andrzej
    Dobryakova, Larisa
    Powiązania:
    https://bibliotekanauki.pl/articles/330100.pdf
    Data publikacji:
    2020
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    multidimensional RDM interval arithmetic
    type 2 interval arithmetic
    RDM type 2 interval arithmetic
    decomposition type 2 interval arithmetic
    interval arithmetic
    Opis:
    The classic interval has precise borders A = [a, ā] . Therefore, it can be called a type 1 interval. Because of great practical importance of such interval data, several versions of type 1 interval arithmetic have been created. However, sometimes precise borders a and ā of intervals cannot be determined in practice. If the borders are uncertain, then we have to do with type 2 intervals. A type 2 interval can be denoted as AT2 = [aL, aR], [āL, āR]. The paper presents multidimensional decomposition RDM type 2 interval arithmetic (D-RDM-T2-I arithmetic), where RDM means relative-distance measure. The decomposition approach considerably simplifies calculations and is transparent for users. Apart from this arithmetic, examples of its applications are also presented. To the authors’ best knowledge, no papers on this arithmetic exist. D-RDM-T2-I arithmetic is necessary to create type 2 fuzzy arithmetic based on horizontal µ-cuts, which the authors aim to do.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 185-201
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Is an interval the right result of arithmetic operations on intervals?
    Autorzy:
    Piegat, A.
    Landowski, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/330098.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    interval arithmetic
    one dimensional interval arithmetic
    multidimensional interval arithmetic
    RDM interval arithmetic
    arytmetyka interwałowa
    arytmetyka interwałowa jednowymiarowa
    arytmetyka interwałowa wielowymiarowa
    Opis:
    For many scientists interval arithmetic (IA, I arithmetic) seems to be easy and simple. However, this is not true. Interval arithmetic is complicated. This is confirmed by the fact that, for years, new, alternative versions of this arithmetic have been created and published. These new versions tried to remove shortcomings and weaknesses of previously proposed options of the arithmetic, which decreased the prestige not only of interval arithmetic itself, but also of fuzzy arithmetic, which, to a great extent, is based on it. In our opinion, the main reason for the observed shortcomings of the present IA is the assumption that the direct result of arithmetic operations on intervals is also an interval. However, the interval is not a direct result but only a simplified representative (indicator) of the result. This hypothesis seems surprising, but investigations prove that it is true. The paper shows what conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations. Examples illustrate the proposed method of interval computations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 575-590
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A realistic tolerant solution of a system of interval linear equations with the use of multidimensional interval arithmetic
    Autorzy:
    Piegat, Andrzej
    Pluciński, Marcin
    Powiązania:
    https://bibliotekanauki.pl/articles/11542697.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    interval arithmetic
    interval linear equation
    tolerable solution
    multidimensional interval arithmetic
    arytmetyka interwałowa
    równanie liniowe przedziałowe
    arytmetyka interwałowa wielowymiarowa
    Opis:
    The paper presents a method of determining the robustness of solutions of systems of interval linear equations (ILEs). The method can be applied also for the ILE systems for which it has been impossible to find solutions so far or for which solutions in the form of improper intervals have been obtained (which cannot be implemented in practice). The research conducted by the authors has shown that for many problems it is impossible to arrive at ideal solutions that would be fully robust to data uncertainty. However, partially robust solutions can be obtained, and those with the highest robustness can be selected and put into practice. The paper shows that the degree of robustness to the uncertainty of the entire system can be calculated on the basis of the degrees of robustness of individual equations, which greatly simplifies calculations. The presented method is illustrated with a series of examples (also benchmark ones) that facilitate its understanding. It is an extension of the authors’ previously published method for first-order ILEs.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 2; 229--247
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Verification techniques for sensitivity analysis and design of controllers for nonlinear dynamic systems with uncertainties
    Autorzy:
    Rauh, A.
    Minisini, J.
    Hofer, E. P.
    Powiązania:
    https://bibliotekanauki.pl/articles/930112.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    arytmetyka przedziałowa
    analiza osiągalności
    sterowanie odporne
    interval arithmetic
    reachability analysis
    observability analysis
    robust stability
    model-based design of optimal controllers
    Opis:
    Control strategies for nonlinear dynamical systems often make use of special system properties, which are, for example, differential flatness or exact input-output as well as input-to-state linearizability. However, approaches using these properties are unavoidably limited to specific classes of mathematical models. To generalize design procedures and to account for parameter uncertainties as well as modeling errors, an interval arithmetic approach for verified simulation of continuoustime dynamical system models is extended. These extensions are the synthesis, sensitivity analysis, and optimization of open-loop and closed-loop controllers. In addition to the calculation of guaranteed enclosures of the sets of all reachable states, interval arithmetic routines have been developed which verify the controllability and observability of the states of uncertain dynamic systems. Furthermore, they assure asymptotic stability of controlled systems for all possible operating conditions. Based on these results, techniques for trajectory planning can be developed which determine reference signals for linear and nonlinear controllers. For that purpose, limitations of the control variables are taken into account as further constraints. Due to the use of interval techniques, issues of the functionality, robustness, and safety of dynamic systems can be treated in a unified design approach. The presented algorithms are demonstrated for a nonlinear uncertain model of biological wastewater treatment plants.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 425-439
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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