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Fuzzy differential equations and the extension principle. (English) Zbl 1147.34311
In this paper, the authors study the Cauchy problem for differential equations, considering its parameters and initial conditions given by fuzzy sets. They prove that a solution for fuzzy differential equations can be obtained through Zadeh’s extension principle and they also prove the existence of a fuzzy solution which is strongly dependent on the choice of both fuzzy initial condition and parameter. But the authors conclude that this fuzzy solution coincides with the solution obtained by using Hullermeier’s interpretation, via differential inclusions. Moreover, they provide some illustrative examples.

MSC:
34A60Differential inclusions
03E72Fuzzy set theory