On soft computing and modelling

• Autorzy: Kosiński W.
• Języki publikacji: EN

Abstrakty

EN

In real-life problems both parameters and data used in mathematical modelling are vague. The vagueness can be described by fuzzy numbers and sets. Pattern recognition, system modelling, diagnosis, image analysis, fault detection and others are fields where soft calculation with unprecise, fuzzy, objects plays an important role. In the presentation after a short review of the recent result in the theory of ordered fuzzy numbers and their normed algebra, specific applications in finance, dynamical systems and mechanics are presented. From the classical framework known algebraic and evolution equations describing such systems are transformed to their fuzzy versions. Their solvability is shortly presented together with the specially dedicated problem solutions.

Słowa kluczowe

EN

ordered fuzzy numbers; Banach space; defuzzyfication; modelling; dynamic systems; finance

PL

przestrzeń Banacha; modelowanie; układ dynamiczny; finanse

• Wydawca: Instytut Telekomunikacji i Informatyki Uniwersytetu Technologiczno-Przyrodniczego w Bydgoszczy
• Czasopismo: Image Processing & Communications
• Rocznik: 2006
• Tom: Vol. 11, no 1
• Strony: 71--82
• Opis fizyczny: Bibliogr. 34 poz., wykr.

Twórcy

autor

Kosiński W.

• Institute of Environmental Mechanics and Applied Computer Science, Kazimierz Wielki University, Chodkiewicza 30, 85-072 Bydgoszcz, Poland,

Bibliografia

• [1] Alexiewicz A. (1969), Functional Analysis (In Polish: Analiza funkcjonalna), Monografie Matematyczne, Tom 49, PWN, Warszawa.
• [2] Buckley James J. (1992), Solving fuzzy equations in economics and finance, Fuzzy Sets and Systems, 48, 289-296.
• [3] Buckley James J. and Eslami E. (2005), An Introduction to Fuzzy Logic and Fuzzy Sets, Physica-Verlag, A Springer-Verlag Company, Heidelberg.
• [4] Chen Guanrong, PhamTrung Tat, (2001), Fuzzy Set's, Fuzzy Logic, and Fuzzy Control, Systems, CRS Press, Boca Raton, London, New York, Washington, D.C.
• [5] Czogała E., Pedrycz W. (1985), Elements and Methods of Fuzzy Set Theory (in Polish), PWN, Warszawa, Poland.
• [6] Drewniak J.(2001), Fuzzy numbers (In Polish), in: Fuzzy Sets and their Applications, (In Polish), J. Chojcan, J. Leski (Eds.), WPS, Gliwice, Poland, pp. 103-129.
• [7] Dubois D., H. Prade H. (1978), Operations on fuzzy numbers, Int. J. System Science, 9 (6), 613-626.
• [8] Goetschel R. Jr., Voxman W. (1986), Elementary fuzzy calculus, Fuzzy Sets and Systems, 18 (1), 31-43.
• [9] Kaucher E. (1980), Interval analysis in the extended interval space IR, Computing, Suppl. 2, 33-49 .
• [10] Kaufman A. and Gupta M. M. (1991), Introduclion to Fuzzy Arithmetic, Van Nostrand Reinhold, New York.
• [11] Klir G.J. (1997), Fuzzy arithmetic with requisite constraints, Fuzzy Sets and Systems, 91(2), 165-175.
• [12] Kosiński W. (2006), Defuzzyfication operators of ordered fuzzy numbers, submitted/or publication.
• [13] Kosiński W. (2006), On fuzzy number calculus, Int. J. Appl. Math. Comput. Sci., 16 (1). 51-57.
• [14] Kosiński W. (2004), On defuzzyfication of ordered fuzzy numbers, in: ICAISC 2004, 7th Int. Conference, Zakopane, Poland, June 2004, L. Rutkowski, Jörg Siekmann, Ryszard Tadeusiewicz, Lofti A. Zadeh (Eds.) LNAI, vol. 3070, pp. 326-331, Springer-Verlag, Berlin, Heidelberg.
• [15] Kosiński W., Prokopowicz P. (2004), Algebra of fuzzy numbers (In Polish: Algebra liczb rozmytych), Matematyka Stosowana. Matematyka dla Społeczeństwa, 5 (46), 37-63 .
• [16] Kosiński W., Piechór K., Prokopowicz P. (2001), Tyburek K.: On algorithmic approach to operations on fuzzy numbers, in: Methods of Artificial Intelligence in Mechanics and Mechanical Engineering, T. Burczyński, W. Cholewa (Eds.), pp. 95-98, PACM, Gliwice, Poland.
• [17] Kosiński W., Prokopowicz P. (2002), Ślęzak D.: Fuzzy numbers with algebraic operations: algorithmic approach, in: Intelligent Information Systems 2002, M. Kłopotek, S.T. Wierzchoń, M. Michalewicz (Eds-) Proc.IIS'2002, Sopot, June 3-6, 2002, Poland, pp. 311-320, Physica Verlag, Heidelberg.
• [18] Kosiński W., Prokopowicz P., Ślęzak D. (2002), Drawback of fuzzy arithmetics -new intutions and propositions, in: Proc. Methods of Artificial Intelligence, T. Burczyński, W. Cholewa, W. Moczulski (Eds-), pp. 231-237, PACM, Gliwice, Poland.
• [19] Kosiński W., P. Prokopowicz P., Ślęzak D. (2003), On algebraic operations on fuzzy numbers, in Intelligent Information Processing and Web Mining, Proc. of the International US: IIPWM,03 Conference held in Zakopane, Poland, June 2-5,2003, M. Kłopotek, S.T. Wierzchoń, K. Trojanowski (Eds.), pp. 353-362, Physica Verlag, Heidelberg.
• [20] Koleśnik R., Prokopowicz P., Kosiński W. (2004), Fuzzy Calculator - usefull tool for programming with fuzzy algebra, in Artificial Intelligence and Soft Computing -ICAISC 2004, 7th Int. Conference, Zakopane, Poland, June 2004, L. Rutkowski, Jörg Siekmann, Ryszard Tadeusiewicz, Lofti A. Zadeh (Eds.) LNAI, vol. 3070, pp. 320-325, Springer-Verlag, Berlin, Heidelberg.
• [21] Kosiński W., Prokopowicz P., Ślęzak D.(2003), Ordered fuzzy numbers, Bulletin of the Polish Academy of Sciences, Ser. Sci. Math., 51 (3), 327-338.
• [22] Kosiński W., Weigl M ., General mapping approximation problems solving by neural networks and fuzzy inference systems, Systems Analysis Modelling Simulation, 30 (1), (1998) 11-28.
• [23] Lachwa A., Rozmyty świat zbiorów, liczb, relacji, faktów, reguł i decyzji, Akademicka Oficyna Wydawnicza EXIT, Warszawa 2001.
• [24] Łojasiewicz S. (1973), Introduction to the Theory of Real Functions (In Polish) Wstęp do teorii funkcji rzeczywistych, Biblioteka Matematyczna, Tom 46, PWN, Warszawa.
• [25] Martos B. (1983), Nonlinear Programming - Theory and Methods, PWN, Warszawa, Poland (Polish translation of the English original published by Akademiai Kiado, Budapest, 1975).
• [26] Mostowski A., Stark M. (1965) Elements of Higher Algebra (In Polish: Elementy algebry wyższej), Państwowe Wydawnictwo Naukowe, Warszawa.
• [27] Nguyen H.T. (1978), A note on the extension principle for fuzzy sets, J. Math. Anal. Appl. 64, 369-380 .
• [28] Piegat A., Modelowanie i sterowanie rozmyte, Akademicka Oficyna Wydawnicza PLJ, Warszawa, 1999.
• [29] Prokopowicz P. (2005), Algorithmization of Operations on Fuzzy Numbers and its Applications (In Polish: Algorytmizacja dzialań na liczbach rozmytych i jej zastosowania), Ph. D. Thesis, IPPT PAN, kwiecień 2005.
• [30] Wagenknecht M. (2001), On the approximate treatment of fuzzy arithmetics by inclusion, linear regression and information content estimation, in: Fuzzy Sets and their Applications (In Polish), J. Chojcan, J. Leski (eds.), Wydawnictwo Politechniki Śląskiej, Gliwice, 291-310.
• [31] Wagenknecht M., Hampel R., Schneider V.(2001), Computational aspects of fuzzy arithmetic based on archimedean t-norms, Fuzzy Sets and Systems, 123 (1), 49-62.
• [32] Zadeh L. A.(1965), Fuzzy sets, Information and Control, 8 (3), 338-353.
• [33] Zadeh L. A. (1975), The concept of a linguistic variable and its application to approximate reasoning, Part I, Information Sciences, 8(3), 199-249.
• [34] Zadeh L. A. (1983), The role of fuzzy logic in the management of uncertainty in expert systems, Fuzzy Sets and Systems,