LG_(pd)-度量及其收敛问题

LG_(pd)-Metric Space and Its Convergence

以平面Ｒ２ 上的距离ｄ 为基础，结合水平λ的重要性函数ｇ（λ），在Ｆｕｚｚｙ 数空间Ｅ１ 上建立了ＬＧｐｄ－度量Ｄ［ｐｇ］，证明了（Ｅ１，Ｄ［ｐｇ］）为度量空间的充分必要条件是ｇ（λ）在［０，１］上几乎处处不为零。进而讨论了当ｄ 是由Ｒ２ 上的范数确定的距离时，（Ｅ１，Ｄ［ｐｇ］）的基本性质及Ｄ［ｐｇ］的完备性问题。

In this paper,by applying the distance of plane R 2 and level importance function g(λ),we establish the LG pd metric D [pg] on fuzzy number space E 1,and show that (E 1,D [pg] ) is a metric space if and only if g(λ)≠0 almost everywhere on [0,1].In addition,the basic properties and the completeness of D [pg] are discussed when the distance is determined by the norm of plane.