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An identification model for a fuzzy time based stationary discrete process | ||
Iranian Journal of Fuzzy Systems | ||
مقاله 14، دوره 19، شماره 1، فروردین و اردیبهشت 2022، صفحه 171-188 اصل مقاله (251.31 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22111/ijfs.2022.6559 | ||
نویسنده | ||
G. Sirbiladze* | ||
Department of Computer Sciences, Ivane Javakhishvili Tbilisi State University, University St. 13, Tbilisi 0186, Georgia | ||
چکیده | ||
A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic System (SDEFDS) in extremal fuzzy time intervals, are considered. A fuzzy-integral representation of a stationary discrete extremal fuzzy process is given. A method and an algorithm for identifying the transition operator of SDEFDS are developed. The SDEFDS transition operator is restored by means of expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimator of the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states. | ||
کلیدواژهها | ||
Sugeno's type extremal fuzzy measures and integrals؛ extremal fuzzy time intervals؛ SDEFDS؛ identification of the SDEFDS integral model | ||
مراجع | ||
[1] S. Abbaszadeh, M. Eshaghi, M. de la Sen, The Sugeno fuzzy integral of log-convex functions, Journal of Inequalities and Applications, (2015), 12 pages, Doi: 10.1186/s13660-015-0862-6.
[2] R. P. Agarwal, D. Baleanu, J. J. Nieto, D. F. Torres, Y. Zhou, A survey on fuzzy fractional differential and optimal control nonlocal evolution equations, Journal of Computational and Applied Mathematics, 339 (2018), 3-29.
[3] Z. Alijani, D Baleanu, B. Shiri, G. C. Wu, Spline collocation methods for systems of fuzzy fractional differential equations, Chaos Solitons Fractals, 131 (2020), 12 pages.
[4] Z. Alijani, U. Kangro, Collocation method for fuzzy Volterra integral equations of the second kind, Mathematical Modelling and Analysis, 25(1) (2020), 146-166.
[5] A. A. Ashtiani, M. B. Menhaj, Fuzzy relational dynamic system with smooth fuzzy composition, Journal of Mathematics and Computer Science, 2(1) (2011), 1-8.
[6] A. B. Badiru, Dynamic fuzzy systems modeling, in: Systems Engineering Models, 1st ed. (2019), 19-53.
[7] R. E. Bellman, L. A. Zadeh, Decision-making in a fuzzy environment, Manage Sciences, Ser. B., 17 (1970), 141-164.
[8] J. J. Buckley, J. Feuring, Fuzzy differential equations, Fuzzy Sets and Systems, 110(1) (2000), 43-54.
[9] O. Castillo, P. Melin, Soft computing for control of non-linear dynamic systems, Studies in Fuzziness and Soft Computing, 73, Physica-Verlag, Wulzburg, 2001.
[10] S. Chakraverty, S. Tapaswini, D. Behera, Fuzzy differential equations and applications for engineers and scientists, Taylor and Francis Group, 2016.
[11] Z. Ding, M. Ma, A. Kandel, On the observativity of fuzzy dynamical control systems (I), Fuzzy Sets and Systems, 95 (1998), 53-65.
[12] D. Dubois, H. Prade, Possibility theory, Plenum Press, New York, 1988.
[13] Y. Feng, Mean-square integral and differential of fuzzy stochastic processes, Fuzzy Sets and Systems, 102(2) (1999), 271-280.
[14] R. Ghanbari, K. Ghorbani-Moghadam, N. Mahdavi-Amiri, B. D. Baets, Fuzzy linear programming problems: Models and solutions, Soft Computing, 24 (2020), 10043-10073.
[15] L. T. Gomes, L. Barros, B. Bede, Fuzzy differential equations in various approaches, Springer Briefs in Mathematics, Springer, Cham, 2015.
[16] M. Grabisch, Fuzzy integral in multicriteria decision making, Fuzzy Sets and Systems, 69 (1995), 279-298.
[17] M. Grabisch, Fuzzy measures and integrals: Recent developments, Fifty years of fuzzy logic and its applications, 125–151, Stud. Fuzziness Soft Computing., 326, Springer, Cham, 2015.
[18] M. Grabisch, T. Murofushi, M. Sugeno (eds.), Fuzzy measures and integrals. Theory and applications, Studies in Fuzziness and Soft Computing, 40. Physica-Verlag, Heidelberg, 2000.
[19] M. Higashi, G. J. Klir, Identification of fuzzy relation systems, IEEE Transactions on Systems Man Cybernet., 14(2) (1984), 349-355.
[20] H. Jafari, M. T. Malinowski, M. J. Ebadi, Fuzzy stochastic differential equations driven by fractional Brownian motion, Advances in Difference Equations, 16 (2021), 2-17.
[21] J. Kacprzyk, A. Wilbik, S. Zadrozny, Linguistic summarization of time series using a fuzzy quantifier driven aggregation, Fuzzy Sets and Systems, 159(12) (2011), 1485-1499.
[22] O. Kaleva, Fuzzy differential equations, Fuzzy Sets and Systems, 24(3) (1987), 301-317.
[23] J. M. Keller, D. Liu, D. B. Fogel, Fuzzy measures and fuzzy integrals, in: Fundamentals of Computational Intelligence: Neural Networks, Fuzzy Systems, and Evolutionary Computation, Wiley-IEEE Press, 2016, 183-205.
[24] G. J. Klir, Fuzzy measure theory, Plenum Press, New York, 1992.
[25] P. E. Kloeden, Fuzzy dynamical systems, Fuzzy Sets and Systems, 7(3) (1982), 275-296.
[26] M. Kurano, M. Yasuda, J. Nakagami, Y. Yoshida, A fuzzy relational equation in dynamic fuzzy systems, Fuzzy Sets and Systems, 101 (1999), 439-443.
[27] X. Li, X. Zhang, Sugeno integral of set-valued functions with respect to multi-submeasures and its application in MADM, International Journal of Fuzzy Systems, 20(8) (2018), 2534-2544.
[28] B. Liu, Toward fuzzy optimization without mathematical ambiguity, Fuzzy Optimization and Decision Making, 1(1) (2002), 43-63.
[29] T. Loganathan, K. Ganesan, A solution approach to fully fuzzy linear fractional programming problems, Journal of Physics, 1377 (2019), 012040.
[30] P. Melin, O. Castillo Modelling, simulation and control of non-linear dynamical systems, an intelligent approach using soft computing and fractal theory, With 1 IBM-PC floppy disk (3.5 inch; HD). Numerical Insights, 2. Taylor and Francis, Ltd., London, 2002.
[31] M. Michta, Fuzzy stochastic differential equations driven by semimartingales-different approaches, Mathematical Problems of Engineering, 3 (2015), 23-65.
[32] E. Pap, Null-additive set functions, Mathematics and its Applications, 337. Kluwer Academic Publishers Group, Dordrecht; Ister Science, Bratislava, 1995.
[33] B. Shiri, I. Perfilieva, Z. Alijani, Classical approximation for fuzzy Fredholm integral equation, Fuzzy Sets and Systems, 404 (2021), 159-177.
[34] G. Sirbiladze, Modeling of extremal fuzzy dynamic systems, I. Extended extremal fuzzy measures, International Journal of General Systems, 34(2) (2005), 107-138.
[35] G. Sirbiladze, Modeling of extremal fuzzy dynamic systems. II. Extended extremal fuzzy measures on composition products of measurable spaces, International Journal of General Systems, 34(2) (2005), 139-167.
[36] G. Sirbiladze, Modeling of extremal fuzzy dynamic systems. III. Modeling of extremal and controllable extremal fuzzy processes, International Journal of General Systems, 34(2) (2005), 169-198.
[37] G. Sirbiladze, Fuzzy dynamic programming problem for extremal fuzzy dynamic system, in: Fuzzy Optimization: Recent Developments and Applications, W. A. Lodwick and J. Kacprzyk (Eds.), Studies in Fuzziness and Soft Computing, 254 (2010), 231-270.
[38] G. Sirbiladze, New fuzzy aggregation operators based on the finite Choquet integral - Application in the MADM problem, International Journal of Information Technology and Decision Making, 15(3) (2016), 517-55.
[39] G. Sirbiladze, Associated probabilities’ aggregations in interactive multi-attribute decision making for q-rung orthopair fuzzy discrimination environment, International Journal of Intelligent Systems, 35(3) (2020), 335-372.
[40] G. Sirbiladze, T. Gachechiladze, Restored fuzzy measures in expert decision-making, Information Sciences, 169(1/2) (2005), 71-95.
[41] G. Sirbiladze, A. Sikharulidze, B. Ghvaberidze, B. Matsaberidze, Fuzzy-probabilistic aggregations in the discrete covering problem, International Journal of General Systems, 40(2) (2011), 169-196.
[42] M. Sugeno, Theory of fuzzy integrals and its applications, Ph.D. Thesis of Tokyo Insitute of Technology, 1974.
[43] H. Tanaka, H. Ishibuchi, S. Yoshikawa, Exponential possibility regression analysis, Fuzzy Sets and Systems, 69(3) (1995), 305-318.
[44] H. N. Teodorescu, A. Kandel, M. Schneider, Fuzzy modeling and dynamics (preface), Fuzzy Sets and Systems, 106(1) (1999).
[45] T. Terano, K. Asai, M. Sugeno, Fuzzy systems theory and its applications, Translated from the Japanese, Academic Press, Inc., Boston, MA, 1992.
[46] S. Tomasiello, J. E. Macías-Díaz, A. Khastan, Z. Alijani, New sinusoidal basis functions and a neural network approach to solve nonlinear Volterra-Fredholm integral equations, Neural Computing and Applications, 31 (2019), 4865-4878.
[47] G. Vachkov, T. Fukuda, Simplified fuzzy model based identification of dynamical systems, International Journal of Fuzzy Systems (Taiwan), 2(4) (2000), 229-235.
[48] Y. Yoshida, Markov chains with a transition possibility measure and fuzzy dynamic programming, Fuzzy Sets and Systems, 66 (1994), 39-57.
[49] Y. Yoshida, Duality in dynamic fuzzy systems, Fuzzy Sets and Systems, 95(1) (1998), 53-65.
[50] Y. Yoshida (ed.), Dynamical aspects in fuzzy decision making, Studies in Fuzziness and Soft Computing, 73, Physica-Verlag, Wurzburg, 2001.
[51] S. Ziari, I. Perfilieva, S. Abbasbandy, Block-pulse functions in the method of successive approximations for nonlinear fuzzy Fredholm integral equations, Differential Equations and Dynamical Systems, 29(1) (2019), 1-5. | ||
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