1960~2005年中国蒸发皿蒸发量变化趋势及其影响因素分析

祁添垚, 张强, 王月, 肖名忠, 刘剑宇, 孙鹏

Spatiotemporal Patterns of Pan Evaporation in 1960-2005 in China: Changing Properties and Possible Causes

Tian-yao QI, Qiang ZHANG, Yue WANG, Ming-zhong XIAO, Jian-yu LIU, Peng SUN

表1 评价模糊聚类分析分区的7种指标

Table 1 Definitions of 7 indices which describe the goodness of clustering by FCM algorithm

指标	定义
Partition Coefficient（PC）	$\begin{matrix} PC (c) = \frac{1}{N} \overset{c}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} u_{ij} \end{matrix}$
Classification Entropy（CE）	$\begin{matrix} CE (c) = \frac{1}{N} \overset{c}{\sum_{i = 1}} \overset{N}{\sum_{j = 1}} u_{ij} \log (u_{ij}) \end{matrix}$
Partition Index（SC）	$\begin{matrix} SC (c) = \overset{c}{\sum_{i=1 1}} \frac{\sum_{k=1}^{N} (u_{ij})^{m} \|\| x_{j} - v_{i} \| \|^{2}}{N_{i} \sum_{k}^{=} \| v_{k} - v_{i} \| \|^{2}} \end{matrix}$
Separation Index（S）	$\begin{matrix} S (c) = \frac{\sum_{i}^{=} \sum_{k}^{=} (u_{ij})^{2} \|\| x_{j} - v_{i} \| \|^{2}}{Nmi n_{i, j} \|\| v_{k} - v_{i} \| \|^{2}} \end{matrix}$
Xie and Beni's Index（XB）	$\begin{matrix} XB (c) = \frac{\sum_{i=1}^{N} \sum_{k=1}^{N} (u_{ij})^{m} \|\| x_{j} - v_{i} \| \|^{2}}{Nmi n_{i, j} \|\| v_{k} - v_{i} \| \|^{2}} \end{matrix}$
Dunn's Index（DI）	$\begin{matrix} DI (c) = mi n_{i \in c} {mi n_{j \in c, i \neq j} {\frac{mi n_{x \in C_{i,} y \in C_{i}} d (x, y)}{ma x_{k \in c} {ma x_{x, y \in C} d (x, y)}}}} \end{matrix}$
Alternative Dunn Index（ADI）	$\begin{matrix} ADI (c) = mi n_{i \in c} {mi n_{j \in c, i \neq j} {\frac{mi n_{x \in C_{i,} y \in C_{i}} \| d (y_{i}, v_{i}) - d (x_{i}, v_{i}) \|}{ma x_{k \in c} {ma x_{x, y \in C} d (x, y)}}}} \end{matrix}$