p-平均对称差度量的Cauchy问题(Ⅱ)

The Cauchy Problem for p-mean Symmetric Difference Metric (Ⅱ)

从集合的对称差集合的 L ebesgue测度出发 ,建立了衡量 Fuzzy数之间差异的p-平均对称差度量 dΔp,证明了 dΔp在空间 E1(K) ={ A～ |A～ ∈ E1,A0 K,K∈ I(R) }上是完备的拟度量 ,并举例说明 (E1,dΔ p)不是完备的拟度量空间。

By applying Lebesgue s measure on the symmetric difference of sets,the p mean symmetric difference metric d Δp is established to measure the difference between Fuzzy numbers,and it is proved that d Δ p is a complete pseudo metric on space E(K)={A~｜A~∈E 1,A 0K,K∈I(R)},and it is illustrated by examples that (E 1,d Δp ) is not complete pseudo metric space.