Platform type fuzzy number and separability of fuzzy number space

In this paper, we introduce the notions of the rectangular fuzzy set and st ep type fuzzy number. It is shown that the family of all platform type fuzz y numbers E-T(1) is dense in fuzzy numbers space E-1 about L-p-metric D-p, and the family of all rational type step fuzzy numbers E-QG(1)(E-QG(1) subs et of E-T(1) and E-QG(1) is a countable set) is dense in (E-T(1), D-p) Furt her, as corollaries, we obtain that (E-1,D-p) is a separable metric space a nd several separable metric spaces about p-mean symmetric difference metric d(Deltap). (C) 2001 Elsevier Science B.V. All rights reserved.