Tytuł artykułu
Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
One of the simplest ways of representation of uncertain or inexact data, as well as inexact computations with them, is based on interval arithmetic. In this approach, an uncertain (real) number is represented by an interval (a continuous bounded subset) of real numbers which presumably contains the unknown exact value of the number in question. Despite its simplicity, it conforms very well to many practical situations, like tolerance handling or managing rounding errors in numerical computations. Also, the so-called alfa-cut method of handling fuzzy sets membership functions is based on replacing a fuzzy set problem with a set of interval problems.
Rocznik
Tom
Strony
443--477
Opis fizyczny
Bibliogr. 35 poz., rys., tab., wykr.
Twórcy
autor
- Institute of Fundamental Technological Research, Polish Academy of Sciences, Polish Academy of Sciences, ul. Świętokrzyska 21, 00-049 Warsaw, Poland
autor
- Chair of Theoretical Mechanics, Silesian Technical University, ul. Krzywoustego 7, 44-100 Gliwice, Poland
autor
- Department of Management, Academy of Mining and Metallurgy, ul. Gramatyka 10, 30-067 Cracow, Poland
Bibliografia
- [1] G. Alefeld, J. Herzberger. Introduction to Interval Computations. Academic Press, New York 1983.
- [2] H. Beeck. Zur Problematik der Hüllenbestimmung von Intervallgleichungssystemen. In: K. Nickel, ed., Interval Mathematics 1975. Lecture Notes in Computer Science, 29: 150-159. Springer Verlag, Berlin 1975.
- [3] J.J. Buckley, Y. Qu. On using a-cuts to evaluate fuzzy equations. Fuzzy Sets and Systems, 38: 309-312, 1990.
- [4| Z. Cywiński. Mechanika budowli w zadaniach. [Exercises in Structural Mechanics, in Polish]. Polish Scientific Publishers (PWN), Warszawa 1984.
- [5] A.S. Deif. Singular values of an interval matrix. Lin. Alg. Appl., 151: 125-133, 1991.
- [6] K.D. Forbus. Qualitative physics: past, present, and future. In: H.E. Shrobe, ed., Exploring Artificial Intelligence, 239-296. Morgan Kaufmann, San Mateo, CA, 1988.
- [7] A. Gatnar. Metody modelowania jakościowego. [Methods of Qualitative Modelling, in Polish]. Akademicka Oficyna Wydawnicza PLJ, Warszawa 1994.
- [8] E. Hansen. Global Optimization Using Interval Analysis. Marcel Dekker, New York 1992.
- [9] D.J. Hartfiel. Concerning the solution set of Ax = b where P ≤ A≤ Q and p≤b≤q. Numerische Mathematik, 35: 355-359, 1980.
- [10] C. Jansson. Interval linear systems with symmetric matrices, skew-symmetric matrices and dependencies in the right hand side. Computing, 46: 265-274, 1991.
- [11] M. Kleiber, Z. Kulpa. Computer-assisted hybrid reasoning in simulation and analysis of physical systems. CAMES, 2(3): 165-186, 1995. [PostScript file: see http://www.ippt.gov.pl/~zkulpa/zkpubl.html#quaphys|
- [12] H.U. Köylüoglu, A.Ş. Cakmak, S.R.K. Nielsen. Interval mapping in structural mechanics. In: Spanos, ed., Computational Stochastic Mechanics. 125-133. Balkema, Rotterdam 1995.
- [13] B. Kuipers. Qualitative Reasoning: Modeling and Simulation with Incomplete Knowledge. The MIT Press, Cambridge, MA, 1994.
- [14] Z. Kulpa. Diagrammatic representation of interval space in proving theorems about interval relations. Reliable Computing, 3(3): 209-217, 1997.
- [15] Z. Kulpa. Diagrammatic representation for a space of intervals. Machine GRAPHICS 6 VISION, 6(1): 5-24, 1997. [PostScript file: see http://www.ippt.gov.pl/~zkulpa/zkpubl.html#diagrammatic]
- [16] Z. Kulpa, A. Radomski, O. Gajl, M. Kleiber, I. Skalna. Hybrydowy system ekspertowy jakościowo-ilościowej analizy układów mechanicznych [Hybrid expert system for qualitative/quantitative analysis of mechanical struc- tures, in Polish]. In: Z. Bubnicki, A. Grzech, eds., Inżynieria wiedzy i systemy ekspertowe [Knowledge Engineering and Expert Systems, in Polish], Vol. 2, 135-142. (Proc. IIIrd Natl. Scientific Conference, Wroclaw, June 10-12, 1997), Oficyna Wydawnicza Politechniki Wrocławskiej, Wrocław 1997.
- [17] Z. Kulpa, A. Radomski, O. Gajl, M. Kleiber, I. Skalna. Hybrid expert system for qualitative and quantitative analysis of mechanical structures. In: L. Ironi, ed., Qualitative Reasoning: 11th International Workshop (Cortona, Italy, June 3-6, 1997), 287-293. Istituto di Analisi Numerica C.N.R., Pavia, Italy, 1997. [PostScript file: see http://www.ippt.gov.pl/~zkulpa/zkpubl.html#quaphys]
- [18] S.E. Laveuve. Definition einer Kahan-Arithmetik und ihre Implementierung. In: K. Nickel, ed., Interval Mathemattcs 1975. Lecture Notes in Computer Science, 29: 236-245. Springer Verlag, Berlin 1975.
- [19] R.E. Moore. Interval Anałysis. Prentice Hall, Englewood Clifis, NJ, 1966.
- [20] A. Neumaier. Interval Methods for Systems of Equations. Cambridge University Press, Cambridge 1990.
- [21] W. Oettli. On the solution set of linear system with inaccurate coefficients. S[AM J. Numer. Anal., Series 8, 2(1): 115-118, 1965.
- [22] W. Oettli, W. Prager. Compatibility of approximate solution of linear equations with given error bounds for coefficients and right-hand sides. Numer. Math., 6: 405-409, 1964.
- [23] A. Pownuk. Przedziałowe metody w rozwiazywaniu układów równań liniowych rozmytych. [Interval methods in solving linear fuzzy systems of equations, in Polish]. Konferencja Naukowo-Dydaktyczna “Nowe Tendencje w Nauczaniu Mechaniki” (Kołobrzeg, 25-26.10.1996), 175-184. Wyd. INNOWEX, Koszalin 1996.
- [24] W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. (2nd ed.), Cambridge University Press, Cambridge 1993.
- [25] S.S. Rao, L. Berke. Analysis of uncertain structural systems using interval analysis. AJAA Journal, 35(4): 727-735, 1997.
- (26] J. Rohn. Systems of linear interval equations. Lin. Alg. Appl., 126: 39-78, 1989.
- [27] J. Rohn. Cheap and tight bounds: The recent result by E. Hansen can be made more efficient. Interval Computations, 4: 13-21, 1993.
- [28] J. Rohn. Linear interval equations: Computing enclosures with bounded relative overestimation is NP-hard. In: R.B. Kearfott, V. Kreinovich, eds., Applications of Interval Computations. 81-89, Kluwer Academic Publishers, 1996.
- [29] J. Rohn. [Untitled]. A letter to the Reliable-Computing e-mail discussion list, August 1997.
- [30] J. Rohn, V. Kreinovich. Computing exact componentwise bounds on solutions of linear systems with interval data is NP-hard. SIAM J. Matr. Anal. Appl., 16: 415-420, 1995.
- [31] S.M. Rump. Verification methods for dense and sparse systems of equations. In: J. Herzberger, ed., Topics in Validated Computations. 63-135, Elsevier Science B.V., 1994.
- [32] S. P. Shary. Algebraic approach to the interval linear static identification, tolerance, and control problems, or one more application of Kaucher arithmetic. Reliable Computing, 2(1): 3-33, 1996.
- [33] Yu. I. Shokin. On interval problems, interval algorithms and their computational complexity. In: G. Alefeld, A. Frommer and B. Lang, eds., Scientific Computing and Validated Numerics. 314-328, Akademie-Verlag, Berlin 1996.
- [34] J. Skrzypczyk. Fuzzy finite element methods - A new methodology. In: Computer Methods in Mechanics (Proc. XIII Polish Conference on Computer Methods in Mechanics, Poznań, Poland, May 5-8, 1997), 4: 1187-1194. Poznań University of Technology, Poznań 1997.
- [35] M. Warmus. Calculus of approximations. Bull. Acad. Pol. Sci., CI. III, 4(5): 253-259, 195
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB2-0001-0113
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.