Advances in Dynamical Systems and Applications ISSN 0973-5321, Volume 6, Number 2, pp. 199–207 (2011) http://campus.mst.edu/adsa Partial Averaging of Fuzzy Differential Equations with Maxima Olga Kichmarenko and Natalia Skripnik Odessa National University named after I.I. Mechnikov Department of Optimal Control and Economic Cybernetics Odessa, Ukraina olga.kichmarenko@gmail.com and talie@ukr.net Abstract In this paper, a scheme of partial averaging of fuzzy differential equations with maxima is considered. AMS Subject Classifications: 03E72, 34C29, 34K05. Keywords: Averaging method, fuzzy differential equation with maxima. 1 Introduction The study of fuzzy differential equations (FDEs) forms a suitable setting for the mathe- matical modelling of real world problems in which uncertainty or vagueness pervades. Fuzzy differential equations were first formulated by Kaleva [4,5]. He used the concept of H-differentiability which was introduced by Puri and Ralescu [13], and obtained the existence and uniqueness theorem for a solution of FDE under the Lipschitz condition. Since then there appeared a lot of papers concerning the theory and applications of fuzzy differential equations, fuzzy dynamics and fuzzy differential inclusions [2, 9, 10, 12]. In this paper, a scheme of partial averaging of fuzzy differential equations with max- ima is considered that continues researches devoted to the fuzzy differential equations with delay [7, 8]. 2 Main Definitions Let conv(R n ) be a family of all nonempty compact convex subsets of R n with Hausdorff metric h(A,B) = max{max a∈A min b∈B ‖a − b‖, max b∈B min a∈A ‖a − b‖}, Received December 1, 2010; Accepted June 1, 2011 Communicated by Martin Bohner