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For pt.1 see ibid., vol.117, p.347-353 (2001). We show that the family of all platform type fuzzy numbers is separable with respect to the uniform Hausdorff metric, thus deducing that this family is also separable with respect to the uniform symmetric difference metric. Subsequently, the family of all rational step type fuzzy numbers, which is a countable set, is claimed to be dense in the previous two spaces with rational platform heights, and the family of all step type fuzzy numbers be dense in fuzzy number space with respect to the previous two metrics. Finally, we investigate the separability of weak fuzzy number space with respect to the two metrics. All these results offer a good path to process general fuzzy numbers by using simple fuzzy numbers sequence.