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SIMULATING CONTINUOUS FUZZY SYSTEMS: I | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 2، دوره 2، شماره 1، تابستان 2005، صفحه 1-17 اصل مقاله (190.29 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2005.471 | ||
| نویسندگان | ||
| J. J. Buckley1؛ K. D. Reilly2؛ L. J. Jowers* 2 | ||
| 1Department of Mathematics, University of Alabama at Birmingham, Birmingham, Alabama, 35294, USA | ||
| 2Department of Computer and Information Sciences, University of Alabama at Birmingham, Birmingham, Alabama, 35294, USA | ||
| چکیده | ||
| In previous studies we first concentrated on utilizing crisp simulation to produce discrete event fuzzy systems simulations. Then we extended this research to the simulation of continuous fuzzy systems models. In this paper we continue our study of continuous fuzzy systems using crisp continuous simulation. Consider a crisp continuous system whose evolution depends on differential equations. Such a system contains a number of parameters that must be estimated. Usually point estimates are computed and used in the model. However these point estimates typically have uncertainty associated with them. We propose to incorporate uncertainty by using fuzzy numbers as estimates of these unknown parameters. Fuzzy parameters convert the crisp system into a fuzzy system. Trajectories describing the behavior of the system become fuzzy curves. We will employ crisp continuous simulation to estimate these fuzzy trajectories. Three examples are discussed. | ||
| کلیدواژه‌ها | ||
| Fuzzy systems؛ Fuzzy differential equations؛ Simulation؛ Uncertainty | ||
| مراجع | ||
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[1] J. J. Buckley, Fuzzy statistics, Springer-Verlag, Heidelberg, Germany, (2004). [2] J. J. Buckley, Fuzzy probabilities and fuzzy sets for web planning, Springer-Verlag, Heidelberg, Germany, (2004). [3] J. J. Buckley, Simulating Fuzzy Systems, Springer-Verlag, Heidelberg, Germany, To appear. [4] J. J. Buckley, Fuzzy systems, Soft Computing, To appear. [5] J. J. Buckley and T. Feuring, Fuzzy initial value problem for nth order linear differential equations, Fuzzy Sets and Systems, 121(2001) 247-255. [6] J. J. Buckley, E. Eslami and T. Feuring, Fuzzy mathematics in economics and engineering, Springer-Verlag, Heidelberg, Germany, (2002). [7] J. J. Buckley, T. Feuring and Y. Hayashi, Linear systems of first order ordinary differential equations: Fuzzy initial conditions, Soft Computing, 6(2002) 415-421. [8] J. J. Buckley, K. Reilly and X. Zheng, Simulating fuzzy systems I, Applied Research in Uncertainty Modelling and Analysis, Eds. N.O.Attoh-Okine, B.Ayyub, Kluwer, (2004), To appear. [9] J. J. Buckley, K. Reilly and X. Zheng, Simulating fuzzy systems II, Applied Research in Uncertainty Modelling and Analysis, Eds. N.O.Attoh-Okine, B.Ayyub, Kluwer, (2004), To appear. [10] Maple 9, Waterloo Maple Inc., Waterloo, Canada. [11] M. Olinick, An introduction to mathematical models in the social and life sciences, Addison- Wesley, Reading, MA, (1978). [12] scilabsoft.inria.fr [13] solutions.iienet.org [14] M. R. Spiegel, Applied differential equations, Third Edition, Prentice-Hall, Englewood Cliffs, NJ, (1981). [15] H. A. Taha, Operations research, Fifth Edition, Macmillan, N.Y., (1992). [16] H. M. Wagner, Principles of operations research, Second Edition, Prentice Hall, Englewood Cliffs, N.J.. (1975). [17] www.mathworks.com [18] D. G. Zill, A First course in differential equations, Brooks/Cole, Pacific Grove, CA, (1997).tt | ||
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