1) p mean Symmetric Difference Metric
p-平均对称差度量
1.
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 0K,K∈I(R)},and it is illustrated by examples that (E 1,d Δp ) is not complete pseudo metric space.
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。
2) p mean symmetric difference distance
p-平均对称差度量d_(Δp)
3) pmean symmetric distance difference
p-平均对称差距离
4) Symmetric mean
对称平均
1.
A symmetric mean and its basic property;
一类对称平均及其基本性质
2.
In this paper,the authors established a chain of inequalities involving first symmertic mean of k degree ∑~k_n(a)=nk~(-1)∑1≤i_1<…<i_k≤n∏kj=1a_(i_j)~(1/k),and second symmetric mean of k degree σ~k_n(a)=nk~(-1)∑1≤i_1<…<i_k≤n(a_(i_1)a_(i_2)…a_(i_k))~(1/k) and third symmetric mean of k degree ∏~k_n(a)=∏1≤i_1<…<i_k≤na_(i_1)+a_(i_2)+…+a_(i_k)k~(nk~(-1)) as follows.
用降维法建立了含n个正实数a1,a2,…,an的第一k次对称平均∑kn(a)=nnk-1∑1≤i1<…
3.
A condition of equivalence for the convex sequence is established by means of the theory of majorizotion, moreover a class of inequality for weighted symmetric mean is generalized by the above condition of equivalence.
利用控制不等式理论建立了凸数列的一个等价条件 ,并应用其推广了一类加权对称平均不等
5) uniform Hausdorff metric
一致对称差度量
1.
Discuss further the relation between uniform symmetric difference metric d Δ and uniform Hausdorff metric D H about convergence Prove that the array of Fuzzy unmbers { A ～ (n) } convergent to a non real type Fuzzy number A ～ about d Δ if and only if { A ～ (n) } convegent about D H to A ～ or convergent to a Fuzzy number B ～ that has same platform as A ～ (n) .
讨论了一致对称差度量 ｄ Δ 与一致 Ｈａｕｓｄｏｒｆｆ 度量 Ｄ Ｈ 收敛性之间的联系，证明了 Ｆｕｚｚｙ 数序列｛ Ａ～ （ｎ）｝按 ｄ Δ收敛于非实型 Ｆｕｚｚｙ 数 Ａ～ 的充分必要条件是｛ Ａ～ （ｎ）｝按 Ｄ Ｈ 收敛于 Ａ～，或收敛于一个与 Ａ～同台的 Ｆｕｚｚｙ 数 Ｂ～ 。
6) symmetric diffrence distance d Δ
对称差度量d_Δ
补充资料：可公度量和不可公度量
可公度量和不可公度量
ommensulble and incommensuable magnitudes (quantities)
可公度t和不可公度t【~e璐u由lea目in~men-su.ble magultodes(quanti柱es);“洲口Mel娜M毗“”“”-113Mep目M曰e肠eJ皿，一皿曰』 如果两个同类量(例如两个长度或两个面积)具有或不具有公度(common measure，即另一个同类量，所考虑的两个量都是这个量的整数倍)，则相应地称这两个量为可公度量或不可公度量.正方形的边长和对角线，或圆的面积和丫的半径的平方，都是不可公度量的例尹.如果两个量是可公度的，则‘l艺们的比是有理数;相反，不可公度量忿比是无理数、
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条