REMARKS ON PEANO-LIKE THEOREMS FOR FUZZY DIFFERENTIAL-EQUATIONS

The validity of the classical Peano theorem is noted for differential equations on the metric space (E(n), d(p)) of normal fuzzy convex sets in R(n), where d(p) is the p-th mean of the Hausdorff distances between corresponding level sets. This contrasts with differential equations on the space (E(n), D) where D is the max metric, which is not locally compact so more than just continuity is required to ensure the existence of solutions. Some additional properties, differing from that given by Kaleva, are mentioned.