算术平均

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

On the aspect of error compensation, the system using the geometric average sound pressure instead of the arithmetic average sound pressure to get the sound pressure of the measurement point. This method not only reduces the high frequency error in the sound intensity measurement, which compensates the finite difference approximation error, but also greatly reduces the computation of the sound pressure spectrum.

误差补偿方面，课题采用几何平均声压代替通常的算术平均声压来计算双传声器法的声场声压值，这样不仅可以有效的减少声强测量中的高频误差，对有限差分误差起到了补偿作用，而且还大大减小了声压谱计算中的计算量。

There are two means to measure the average prices of the assets in an Asian option theoretically:with the arithmetic average and with the geometric average.

亚式期权有两种理论上的表示方式，即采用算术平均法计算资产价格的平均值和采用几何平均法计算资产价格的平均值。

The main results are as follows:We review the existing Monte Carlo control variates estimators of the price of Asian options and propose a new one. According to pratical needs, we define efficiency as the inverse of the product of the variance of an estimator and its computational time and make it a standard for comparisons to draw the following conclusions: Firstly, the more control variates correlate with arithmetic average Asian options, the larger is the efficiency of an estimator with these control variates, but among which the geometric average option plays the most important role; Secondly, an estimator with more control variates is better than one with less ones only when the time to maturity is long and the volatility is high.

在综合已有研究工作的基础上，本论文的主要创新成果如下：（1）我们回顾了已有的亚洲期权价格的蒙特卡罗控制变量估计，并提出了一个新的控制变量估计，且从客观实际出发，将估计值的方差和计算时间的乘积的倒数定义为效率并以它为标准比较各估计，得到以下结论：与算术平均亚洲期权相关程度越大的控制变量构成的估计的效率越大，而其中起主要作用的控制变量为几何平均亚洲期权的价格；只有在到期时间较长且标的资产的波动率较大时，元素多的多元控制变量估计比元素少的效率大。

Two amelioration operators were developed, such as the triangular intuitionistic fuzzy numbers weighted arithmetic average operator, and the f interval-valued intuitionistic fuzzy numbers weighted geometric average operator.

定义了三角和区间直觉模糊集的一些运算法则，给出了直觉模糊集两个改进算子，即三角模糊数加权算术平均算子和区间直觉模糊数加权几何平均算子。

The algorithms are respectively to compute arithmetic mean of the probabilities and normalized geometric mean of the probabilities.

采用公理化方法给出了相应的算法，这两个算法算法分别是对概率进行算术平均和几何平均，再进行归一化处理。

The research for the means has a long history, the classical means include algebraic mean, geometric mean and harmonic mean etc.

平均数理论研究的历史久远，经典的平均数包括算术平均，几何平均，调和平均等。

Average flow within the prescribed time in flood calculations is worked out tising curve integral instead of arithmetic mean.

用曲线积分代替算术平均法来计算洪水流量演算中的时段平均流量，减小了时段△t对流量值的影响，使计算流量更接近实测值。

Eight hierarchical clustering methods including single linkage method, complete linkage method, median linkage method, centroid method, unweighted pair-group average method, Wards method, flexible-beta method and weighted pair-group average method were combined with three sampling strategies, random, preferred and deviation sampling to develop 24-core collections.

川最短距离法、最长距离法、中间距离法、重心法、不加权类平均法、离差平方和法、可变法和加权配对算术平均法等8种系统聚类方法，结合随机取样法、优先取样法和变异度取样法等3种取样方法，发展了24个水稻核心种质库。

However, the weighted geometric mean method is simpler than the weighted arithmetic mean method, and the former can keep the reciprocity of the improved judgement matrix without transformation.

理论分析表明：虽然这2种方法都具有收敛性，且均可对一致性较差的判断矩阵进行修正，但加权几何平均法比加权算术平均法简洁，且前者无需通过转换，直接保持了修正后的判断矩阵的互反性。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。