Platform type fuzzy number and separability of fuzzy number space

摘要

In this paper, we introduce the notions of the rectangular fuzzy set and step ape fuzzy number. It is shown that the family of all platform type fuzzy numbers E~1_T 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~1_QG(E~1_QG is contained in E~1_QG and E~1_QG is a countable set) is dense in (E~1_T, D_P). Further, as corollaries, we obtain that (E~1, D_P) is a separable metric space and several separable metric spaces about p-mean symmetric difference metric d_△p.