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    Wyświetlanie 1-11 z 11
    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:
    Computing with words with the use of inverse RDM models of membership functions
    Autorzy:
    Piegat, A.
    Pluciński, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/330406.pdf
    Data publikacji:
    2015
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    computing with words
    fuzzy arithmetic
    RDM fuzzy arithmetic
    granular computing
    Opis:
    Computing with words is a way to artificial, human-like thinking. The paper shows some new possibilities of solving difficult problems of computing with words which are offered by relative-distance-measure RDM models of fuzzy membership functions. Such models are based on RDM interval arithmetic. The way of calculation with words was shown using a specific problem of flight delay formulated by Lotfi Zadeh. The problem seems easy at first sight, but according to the authors’ knowledge it has not been solved yet. Results produced with the achieved solution were tested. The investigations also showed that computing with words sometimes offers possibilities of achieving better problem solutions than with the human mind.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2015, 25, 3; 675-688
    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:
    Fuzzy-Arithmetic-Based Lyapunov Synthesis in the Design of Stable Fuzzy Controllers: a Computing-With-Words Approach
    Autorzy:
    Zhou, C.
    Powiązania:
    https://bibliotekanauki.pl/articles/908020.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    informatyka
    fuzzy control
    standard fuzzy arithmetic
    constrained fuzzy arithmetic
    Lyapunov synthesis
    stability
    computing with words
    perception-based information
    pole balancing mobile robot
    Opis:
    A novel approach to designing stable fuzzy controllers with perception-based information using fuzzy-arithmetic-based Lyapunov synthesis in the frame of computing with words (CW) is presented. It is shown that a set of conventional fuzzy control rules can be derived from the perception-based information using the standard-fuzzy-arithmetic-based Lyapunov synthesis approach. On the other hand, a singleton fuzzy controller can be devised by using a constrained-fuzzy-arithmetic-based Lyapunov synthesis approach. Furthermore, the stability of the fuzzy controllers can be guaranteed by means of the fuzzy version of Lyapunov stability analysis. Moreover, by introducing standard and constrained fuzzy arithmetic in CW, the "words" represented by fuzzy numbers could be efficiently manipulated to design fuzzy controllers. The results obtained are illustrated with the design of stable fuzzy controllers for an autonomous pole balancing mobile robot.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 3; 411-421
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Implementation of Adaptive Generalized Sidelobe Cancellers Using Efficient Complex Valued Arithmetic
    Autorzy:
    Glentis, G. O.
    Powiązania:
    https://bibliotekanauki.pl/articles/908084.pdf
    Data publikacji:
    2003
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    elektronika
    adaptive beamforming
    generalized sidelobe canceller
    LMS algorithm
    complex valued arithmetic
    Opis:
    Low complexity realizations of Least Mean Squared (LMS) error, Generalized Sidelobe Cancellers (GSCs) applied to adaptive beamforming are considered. The GSC method provides a simple way for implementing adaptive Linear Constraint Minimum Variance (LCMV) beamformers. Low complexity realizations of adaptive GSCs are of great importance for the design of high sampling rate, and/or small size and low power adaptive beamforming systems. The LMS algorithm and its Transform Domain (TD-LMS) counterpart are considered for the adaptive processing task involved in the design of optimum GSC systems. Since all input signals are represented by complex variables, complex valued arithmetic is utilized for the realization of GSC algorithms, either on general purpose computers, or on dedicated VLSI ASICs. Using algorithmic strength reduction (SR) techniques, two novel algorithms are developed for efficient realizations of both LMS GSCs and TD-LMS GSC schemes. Both of the proposed algorithms are implemented using real valued arithmetic only, whilst reducing the number of multipliers by 25% and 20%, respectively. When VLSI implementation aspects are considered, both the proposed algorithms result in reduced power dissipation and silicon area realizations. The performance of the proposed realizations of the LMS based GSC methods is illustrated in the context of typical beamforming applications.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2003, 13, 4; 549-566
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A New Definition of the Fuzzy Set
    Autorzy:
    Piegat, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908479.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    zbiór rozmyty
    prawdopodobieństwo
    arytmetyka rozmyta
    fuzzy set theory
    fuzzy arithmetic
    possibility
    Opis:
    The present fuzzy arithmetic based on Zadeh's possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in comparison with the results produced by the present fuzzy arithmetic.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 1; 125-140
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi-objective linear programming problem
    Autorzy:
    Vidhya, R.
    Irene Hepzibah, R.
    Powiązania:
    https://bibliotekanauki.pl/articles/330813.pdf
    Data publikacji:
    2017
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fuzzy number
    fuzzy arithmetic
    linear programming problem
    liczba rozmyta
    arytmetyka rozmyta
    programowanie liniowe
    Opis:
    In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2017, 27, 3; 563-573
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Hierarchical residue number systems with small moduli and simple converters
    Autorzy:
    Tomczak, T.
    Powiązania:
    https://bibliotekanauki.pl/articles/907828.pdf
    Data publikacji:
    2011
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    arytmetyka cyfrowa
    układ cyfrowy
    resztowy system liczbowy
    digital arithmetic
    digital circuits
    residue number system
    VLSI
    Opis:
    In this paper, a new class of Hierarchical Residue Number Systems (HRNSs) is proposed, where the numbers are represented as a set of residues modulo factors of 2k š 1 and modulo 2k. The converters between the proposed HRNS and the positional binary number system can be built as 2-level structures using efficient circuits designed for the RNS (2k - 1, 2k, 2k +1). This approach allows using many small moduli in arithmetic channels without large conversion overhead. The advantages resulting from the use of the proposed HRNS depend on the possibility of factorisation of moduli [...].
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2011, 21, 1; 173-192
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    What is not clear in fuzzy control systems?
    Autorzy:
    Piegat, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/908467.pdf
    Data publikacji:
    2006
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie rozmyte
    system rozmyty
    arytmetyka rozmyta
    logika rozmyta
    możliwość
    fuzzy control
    fuzzy systems
    fuzzy arithmetic
    fuzzy logic
    necessity
    possibility
    Opis:
    The paper presents a number of unclear, unsolved or partly solved problems of fuzzy logic, which hinder precise transformation of expert knowledge about proper control of a plant in a fuzzy controller. These vague problems comprise the realization of logical and arithmetic operations and another basic problem, i.e., the construction of membership functions. The paper also indicates how some of the above problems can be solved.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2006, 16, 1; 37-49
    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 1-11 z 11

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