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On the validity of the Peano theorem for fuzzy differential equations

✍ Scribed by Menahem Friedman; Ma Ming; Abraham Kandel

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
201 KB
Volume
86
Category
Article
ISSN
0165-0114

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In Kaleva [Fuzzy Sets and Systems 35 (1990) 389] we proved a Peano theorem for fuzzy differential equations. Recently, Friedman et al. [Fuzzy Sets and Systems 86 (1997) 331] provided a counterexample for the theorem. Here we refute this counterexample.

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We prove a version of the classical Peano's theorem for the initial value problem for a fuzzy differential equation in the metric space of normal fuzzy convex sets with distance given by the maximum of the Hausdorff distances between level sets.