On the structure of solutions for fuzzy initial value problem

Authors:
Xue Xiaoping;Fu Yongqiang
Affiliations:
Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China;Department of Mathematics, Harbin Institute of Technology, Harbin 150001, PR China
Venue:
Fuzzy Sets and Systems
Year:
2006

Citing 10
Cited 10

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Abstract

In this paper, by means of Banach Fixed-point Theorem we establish the existence and uniqueness of solutions for set differential equations, the continuous dependence of solutions on initial values, and the structural stability of solutions. On the basis of these results, we define level sets of solutions to fuzzy differential equations by the solutions of set differential equations, and then we obtain the corresponding results for the large solutions of the fuzzy initial value problem (FIVP). Finally, discuss the relationship between small solutions and large solutions of FIVP.