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In this paper we use pointwise modulus of smoothness to study approximation direct theorem and equivalent theorem for some linear operators and quasi-interpolant operators; Using pointwise modulus we discuss the strong converse inequality on K-functional; and using a modified weighted K-functional and weighted modulus of smoothness we study approximation with Jacobi weight on operator with non-zero first order moments.

本文利用点态光滑模ω_~(2r)来研究某些线性算子及逆中插式逼近正定理和等价定理；利用点态光滑模讨论其关于K-泛函的强逆不等式；同时利用一种改变的带权K-泛函和带权光滑模研究一阶矩不为零的算子的点态带Jacobi权逼近。

The concept of the weighted logarithmic power mean is introduced; its relation with two-parameter mean is given; the inequality for weighted logarithmic power mean is derived; the magnitude relation among upper bounds of geometric mean and arithmetic mean of geometrically convex functions are made certain.

建立了几何凸函数的对称拟算术平均不等式，对文献[1]提出的不等式进行了推广统一；引进加权对数幂平均的概念，建立起其与双参数平均之间的关系，得到加权对数平均不等式，从而确定了几何凸函数的几何平均、算术平均的上界的大小关系；最后，提出了几何凸函数的对称拟算术平均不等式的推广问题。

And use frequency formula or weighted harmonic mean formula of weighted arithmetic mean formula to get its mean value.

利用加权算数平均数的频数公式或加权调和平均数公式求其平均值。

The numerical results also indicate that the weighted geometric mean method needs less number of iteration than the weighted arithmetic mean method.

数值结果也显示：加权几何平均法所需的迭代次数比加权算术平均法所需迭代次数少。

The average weighted programming method was generalized, and the minimun average weighted deviation method was established.

对决策者部分偏好信息不确知的多目标决策问题进行研究，拓展了加权平均规划方法，并提出和建立了最小加权平均偏差法。

The interval estimation information given by estimators is classfied. The bargaining interval and bargaining value is also determined for each class information. Then, the information of the bargaining interval and bargaining value is integrated by utilizing the induced ordered weighted averaging operator. The problem to choice the weighted vector of the IOWA operator is also discussed.

首先对评价者给出的区间赋值信息进行分类，确定各类信息的协商区间和协商值；然后利用所导出的有序加权平均算子对各类信息的协商区间和协商值进行集成，并对如何选取IOWA算子加权向量的问题进行了讨论。

The method utilizes fuzzy ordered weighted averaging operator to aggregate the fuzzy linguistic evaluation information given by experts, and then uses the expected values formula of triangular fuzzy numbers to obtain the weighted vector of factors determining the scale of logistics park.

结合模糊集理论和多属性群决策理论，提出基于模糊语言多属性群决策的物流因区规模确定模型。

Based on these operational laws, some aggregation operators, including pure interval-valued intuitionistic fuzzy weighted arithmetric averaging operator and pure interval-valued intuitionistic fuzzy ordered weighted averaging operator, are proposed.

论文摘要：对纯区间直觉模糊信息的集结算子进行了进一步研究，引入了区间直觉模糊数的一些运算法则、区间直觉模糊数的得分函数和精确函数，并基于这些运算法则，提出了一些新算子：纯区间直觉模糊数加权算术平均算子和纯区间直觉模糊数有序加权平均算子。

Interval-valued intuitionistic fuzzy numbers; operation laws; pure interval-valued intuitionistic fuzzy weighted arithmetric averagingoperator; pure interval-valued intuitionistic fuzzy ordered weighted averaging operator

区间直觉模糊数；运算法则；纯区间直觉模糊数加权算术平均算子；纯区间直觉模糊数有序加权平均算子

Density weighted harmonic averaging middle operator; argument clustering; density weighted vector; aggregation

从密度加权平均中间算子（文中式（3））和密度加权几何平均中间算子的（文中式（4））的形式与平均数的形式进行对比，很容易得到密度加权调和平均中间算子（文中式（7））。

The teacher likes the honeymouthed little girl very much.

老师很喜欢这个嘴甜的小姑娘。

Mr. Notker Bien's interests are traveling, spending quality time with the family and long-distance-running.

诺特卡·柏恩先生热爱旅游，长跑，以及和家人一起共度美好时光。