Academic Report
Title: Some Advances in Fuzzy Differential Equations
Reporter: Prof. CHEN Minghao (Harbin Institute of Technology)
Time: March 28, 2019 (Thursday) AM 8:30-9:30
Location: A1101# room, Innovation Park Building
Contact: Prof. LEI Fengchun (tel:84708360)
Abstract: As we all know, fuzzy differential equation is a powerful tool for describing uncertain systems. After more than 30 years of development, three completely different types have been formed: the first one is based on Hukuhara derivative and its extended Bede generalized derivative, which is an ordinary differential equation in some kind of fuzzy number space, abbreviated as (H) type; the second one is based on differential inclusion theory. Fuzzy differential equations form a family of differential inclusions by taking the level set of the fuzzy vector field. The solution set of this differential inclusion forms the level set of the solution of the fuzzy differential equation, which is called DI type for short. The third kind is the fuzzy differential equation based on Zadeh expansion principle. By applying the Zadeh expansion primitive to the solution of the differential equation with uncertain parameters or initial values. The solution of the fuzzy differential equation is obtained, which is called ZEP type. Fuzzy differential equations are usually divided into initial value problems, two-point boundary value problems and periodic problems. In this paper, we will briefly introduce the research progress and current situation of definite solutions of (H) type and (DI) type fuzzy differential equations in our team and colleagues at home and abroad in the past ten years.
The brief introduction to the reporter: Chen Minghao, male, born on February 13, 1964, Doctor of Science, graduated from the Department of Mathematics, Harbin University of Technology in 1983. He is currently a professor in the Department of Mathematics, Harbin University of Technology, a doctoral tutor in mathematics and a doctoral tutor in statistics. He has participated in the International Conference of Mathematicians (ICM) twice at the formal invitation of the Chairman of the Organizing Committee. He has served as a member of the Procedure Committee and Chairman of the Sub-Committee of the International Academic Conference. He is currently Senior Member of the International Conference of Mathematicians (ICM), International Journal of Applied & Experimental Mathematics, Scientiae Mathematicae Japonicae and other magazines. His research interests include uncertain dynamical systems, fuzzy differential equations, topological entropy of discrete dynamical systems, discrete optimization, fuzzy optimization, fuzzy statistics and computation, and applications in AI, rough sets and applications. He has published more than 40 papers in high-level international SCI magazines such as Fuzzy Sets and Systems , Information Sciences, Neurocomputing and Applied Soft Computing in recent ten years.
