The Full Averaging of Fuzzy Differential Inclusions
محورهای موضوعی : Operation Research
Natalia Skripnik
1
(Odessa National University named after I.I.Mechnikov, Odessa, Ukraine)
کلید واژه: FUZZY DIFFERENTIAL INCLUSIONS, AVERAGING,
چکیده مقاله :
In this paper the substantiation of the method of full averaging for fuzzy differential inclusions is considered. These results generalize the results of [17, 20] for differential inclusions with Hukuhara derivative and of [18] for fuzzy differential equations.
[1] Aubin J. P., Fuzzy differential inclusions, Probl. Control Inf. Theory, 19 (1), 55–67, 1990.
[2] Aumann R. J., Integrals of set-valued functions, J. Math. Anal. Appl., 12, 1–12, 1965.
[3] Baidosov V. A., Differential inclusions with fuzzy right-hand side, Soviet Mathematics, 40 (3), 567–569, 1990.
[4] Baidosov V. A., Fuzzy differential inclusions, J. of Appl. Math. and Mechan., 54 (1), 8–13, 1990.
[5] Hukuhara M., Integration des applications mesurables dont la valeur est un compact convexe, Func. Ekvacioj, 10, 205–223, 1967.
[6] Hullermeier E., An approach to modeling and simulation of uncertain dynamical system, Internat. J. Uncertain. Fuzziness Knowledge - Based Systems, 7, 117–137, 1997.
[7] Kaleva O., Fuzzy differential equations, Fuzzy Sets and Systems, 24 (3), 301–317, 1987.
[8] Kaleva O., The Cauchy problem for fuzzy differential equations, Fuzzy Sets and Systems, 35, 389–396, 1990.
[9] Kaleva O., The Peano theorem for fuzzy differential equations revisited, Fuzzy Sets and Systems, 98, 147–148, 1998.
[10] Kaleva O., A notes on fuzzy differential equations, Nonlinear Anal., 64, 895–900, 2006.
[11] Komleva T. A., Plotnikov V. A., Differential inclusions with the Hukuhara derivative, Nonlinear Oscil., 10(2), 229–245, 2007.
[12] Lakshmikantham V., Granna Bhaskar T., Vasundhara Devi J., Theory of set differential equations in metric spaces, Cambridge Scientific Publishers, Cambridge, 2006.
[13] Lakshmikantham V., Mohapatra R., Theory of fuzzy differential equations and inclusions, Taylor and Francis, 2003.
[14] Laksmikantham V., Tolstonogov A. A., Existence and interrelation between set and fuzzy differential equations, Nonlinear Anal., 55, 255–268, 2003.
[15] Park J. Y., Han H. K., Existence and uniqueness theorem for a solution of fuzzy differential equations, Internat. J. Math. and Math. Sci., 22 (2), 271–279, 1999.
[16] Park J. Y., Han H. K., Fuzzy differential equations. Fuzzy Sets and Systems, 110, 69–77, 2000.
[17] Plotnikov A. V., Averaging of differential inclusions with Hukuhara derivative. Ukr. Math. J., 41 (1), 121–125, 1989.
[18] Plotnikov A. V., Skripnik N. V., Differential equations with "clear" and fuzzy multivalued right-hand side: Asymptotical methods, Astroprint, Odessa, 2009.
[19] Plotnikov A. V., Skripnik N. V., The generalized solutions of the fuzzy differential inclusions, Int. J. Pure Appl. Math., 56 (2), 165–172, 2009.
[20] Plotnikov V. A., Plotnikov A. V., Vityuk A. N., Differential equations with a multivalued right-hand side: Asymptotic methods, Astroprint, Odessa, 1999.
[21] Puri M. L., Ralescu D. A., Differentielle d’une fonction floue, C.R. Acad. Sc. Paris, 293(I), 237–239, 1981.
[22] Puri M. L., Ralescu D. A., Fuzzy random variables, J. Math. Anal. Appl., 114 (2), 409–422, 1986.
[23] Seikkala S., On the fuzzy initial value problem, Fuzzy Sets and Systems, 24 , 319–330, 1987.
[24] Skripnik N. V., Existence of classic solutions of the fuzzy differential inclusions, Ukr. Math. Bull., 5, 244–257, 2008.
[25] Skripnik N. V., Kvazisolutions of the fuzzy differential inclusions, In Thesis of reports of IX Crimean intern. math. school "Method of Lyapunov functions and its applications", Alushta, 152, 2008.
[26] Song S. J., Wu C. X., Existence and uniqueness of solutions to Cauchy problem of fuzzy differential equations, Fuzzy Sets and Systems, 111, 55–67, 2000.
[27] Vorobiev D., Seikkala S., Towards the theory of fuzzy differential equations, Fuzzy Sets and Systems, 125, 231–237, 2002.
[28] Zadeh L. A., Fuzzy sets, Inform. Control, 8, 338–353, 1965.
