The problem of completeness for p-mean symmetric difference metric

In this paper, by applying Lebesgue's measure on the symmetric difference o f sets, the p-mean symmetric difference metric d(Deltap) is established to measure the difference between fuzzy numbers. The basic properties of Cauch y sequences of (E-1, d(Deltap)) are discussed, and we show (E-1(K), d(Delta p)) is complete (where E-1(K) = {(A) under tilde\(A) under tilde is an elem ent of E-1 and A(0) subset of K}, K is a closed interval, A(0) is the closu re of support set of (A) under tilde), further, an example where the space (E-1, d(Deltap)) is not complete is given. (C) 2000 Elsevier Science B.V. A ll rights reserved.