﻿ 基于犹豫模糊集的网络舆情突发事件应急群决策方法
 计算机系统应用  2019, Vol. 28 Issue (9): 9-17 PDF

Emergency Group Decision Making Method for Internet Public Opinion Outbreak Based on Hesitant Fuzzy Sets
TONG Yu-Zhen, WANG Ying-Ming
School of Economics and Management, Fuzhou University, Fuzhou 350108, China
Abstract: Considering that decision maker may hesitate to give the assessed value in the scenario of time urgency and incomplete information, the emergency group decision making method of internet public opinion outbreak based on hesitant fuzzy set is proposed. Firstly, the weight determination model of each evaluation index is established by hesitant fuzzy information entropy and cross entropy. Secondly, the HFWA and score function are used to calculate the evaluation score of each evaluation index. Then, using the weight value and evaluation score of each index to calculate comprehensive harmfulness score of internet public opinion emergency to assist emergency departments to determine the disposal order. Finally, the effectiveness of the proposed method is proved by a case study.
Key words: Internet public opinion outbreak     hesitant fuzzy sets     hesitant fuzzy entropy     score function     HFWA

1 引言

2 预备知识

2.1 犹豫模糊集

(1) ${h_1} \cap {h_2} = \bigcup\nolimits_{{\gamma _1} \in {h_1},{\gamma _2} \in {h_2}} {\{ \min ({\gamma _1},{\gamma _2})\} } ;$

(2) ${h_1} \cup {h_2} = \bigcup\nolimits_{{\gamma _1} \in {h_1},{\gamma _2} \in {h_2}} {\{ \max ({\gamma _1},{\gamma _2})\} } ;$

(3) ${h_1} \oplus {h_2} = \bigcup\nolimits_{{\gamma _1} \in {h_1},{\gamma _2} \in {h_2}} {\{ {\gamma _1} + {\gamma _2} - {\gamma _1}{\gamma _2}\} } ;$

(4) ${h_1} \otimes {h_2} = \bigcup\nolimits_{{\gamma _1} \in {h_1},{\gamma _2} \in {h_2}} {\{ {\gamma _1}{\gamma _2}\} }$ .

 $\begin{split} & HFWA({h_1},{h_2}, \cdots ,{h_n}) = \mathop \otimes \limits_{j = 1}^n ({w_j}{h_j})= \\ &\bigcup\nolimits_{{\gamma _1} \in {h_1},{\gamma _2} \in {h_2}, \cdots ,{\gamma _n} \in {h_n}} {\left\{ 1 - \prod\limits_{j = 1}^n {{{(1 - {\gamma _j})}^{{w_j}}}} \right\} } \end{split}$ (1)

 $s(h) = \frac{1}{{*h}}\sum\nolimits_{\gamma \in h} \gamma$ (2)

 $\begin{split} E\left( \beta \right) = &1 - \frac{2}{{lT}}\sum\limits_{i = 0}^l {(((1 + q} {\beta ^{\sigma (i)}})\ln (1 + q{\beta ^{\sigma (i)}}) + (1 \!+\! q(1 \!-\! q{\beta ^{\sigma (l - i + 1)}}))\ln (1 \!+\! q(1 \!-\! q(1 - {\beta ^{\sigma (l - i + 1)}})))/2 \\ & -(2 + q{\beta ^{\sigma (i)}}) + q(1 - q{\beta ^{\sigma (l - i + 1)}}))/2 \times \ln (2 + q{\beta ^{\sigma (i)}} + q(1 - q{\beta ^{\sigma (l - i + 1)}}))/2)) \end{split}$ (3)

 $E(\beta ) = 1.$

 $\begin{split} C(\alpha ,\beta )=& \frac{1}{{lT}}\sum\limits_{i = 1}^l {\Big(\frac{{(1 + q{\alpha _{\sigma (i)}})\ln (1\! +\! q{\alpha _{\sigma (i)}}) \!+\! (1 \!+\! q{\beta _{\sigma (i)}})\ln (1 \!+\! q{\beta _{\sigma (i)}})}}{2}} \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\! \\ & - \frac{{2 + q{\alpha _{\sigma (i)}} + q{\beta _{\sigma (i)}}}}{2}\ln \frac{{2 + q{\alpha _{\sigma (i)}} + q{\beta _{\sigma (i)}}}}{2} + \frac{{(1 + q(1 - {\alpha _{\sigma (l - i + 1)}})\ln (1 + q(1 - {\alpha _{\sigma (l - i + 1)}})}}{2}\\ & + \frac{{(1 + q(1 - {\beta _{\sigma (l - i + 1)}})\ln (1 + q(1 - {\beta _{\sigma (l - i + 1)}})}}{2} - \frac{{2 + q(1 - {\alpha _{\sigma (l - i + 1)}} + 1 - {\beta _{\sigma (l - i + 1)}})}}{2}\\ & \times \ln \frac{{2 + q(1 - {\alpha _{\sigma (l - i + 1)}} + 1 - {\beta _{\sigma (l - i + 1)}})}}{2}\Big),\;\;q > 0 \end{split}$ (4)

(1) $C(\alpha ,\beta ) \ge 0$ ;

(2) $C(\alpha ,\beta ) = 0 \Leftrightarrow {\alpha _{\sigma (i)}} = {\beta _{\sigma (i)}},\forall i = 1,2, \cdots ,l$ .

2.2 评估等级的划分

3 犹豫模糊环境下的网络舆情突发事件应急群决策模型构建 3.1 问题描述

3.2 指标的选择

3.3 指标权重的确定

Step 1. 第k个应急决策专家在网络舆情突发事件 ${X_i}$ 的评价指标 ${c_j}$ 下的评价值由犹豫模糊数 $h_{ij}^k$ 表示.

Step 2. 运用式(3), 计算各评价指标的信息熵 $E(h_{ij}^k)$ , 那么各决策专家在所有网络舆情突发事件中的评价指标 ${c_j}$ 下的综合信息熵可表示为 $\sum\limits_{k = 1}^l {\dfrac{1}{n}} (\sum\limits_{i = 1}^n {E(h_{ij}^k)} )$ , 其中, $\dfrac{1}{n}(\sum\limits_{i = 1}^n {E(h_{ij}^k)} )$ 为决策者 ${d_k}$ 认为所有网络舆情突发事件在应急决策指标 ${c_j}$ 下的平均信息熵.

Step 3. 运用式(4), 计算评价指标 ${c_j}$ 的全局犹豫模糊交叉熵, 将所有网络舆情突发事件在评价指标 ${c_j}$ 下的综合平均犹豫模糊交叉熵相加可以得到: $\sum\limits_{k = 1}^l {\dfrac{1}{n}} \Big[\dfrac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k)} \Big]$ . 它表示的是所有网络舆情事件在决策指标 ${c_j}$ 下的平均差异度,其中 $\dfrac{1}{{n - 1}}$ $\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k)}$ 表示第k个决策专家认为第 $i$ 个网络舆情突发事件与剩下所有网络舆情突发事件在评价指标 ${c_j}$ 下的平均犹豫模糊交叉熵.

Step 4. 由犹豫模糊信息熵及交叉熵理论可知, 评价指标 ${c_j}$ 平均犹豫模糊信息交叉熵越大, 该指标应赋予较大的权重值; 若评价指标 ${c_j}$ 的犹豫模糊信息熵越小, 则该指标应被赋予更大的权重值. 综合以上分析, 可以得到如下评价指标权重优化模型:

 $\left\{ \begin{array}{l} \max H(w) = \sum\limits_{j = 1}^m {\sum\limits_{k = 1}^l {\frac{1}{n}} } \sum\limits_{i = 1}^n {[(\frac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k) }}\\ \quad\quad\quad\quad\quad+{{ (1 - E(h_{ij}^k)){w_j})} ]} \\ \sum\limits_{j = 1}^m {w_j^2 = 1,\;\;0 \le {w_j} \le 1} \\ \end{array} \right.$ (5)

 ${w_j} = \frac{{\sum\limits_{k = 1}^l {\dfrac{1}{n}} \sum\limits_{i = 1}^n {[(\frac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k) + (1 - E(h_{ij}^k)){w_j})} ]} }}{{\sum\limits_{j = 1}^m {\sum\limits_{k = 1}^l {\frac{1}{n}} } \sum\limits_{i = 1}^n {[(\frac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k) + (1 - E(h_{ij}^k)){w_j})} ]} }}$ (6)

Step 5. 根据应急决策专家对决策影响大小的权重 $\lambda = \{ {\lambda _1},{\lambda _2}, \cdots ,{\lambda _l}\}$ , 对所得到的权重作进一步的修正:

 ${w_j} = \frac{{\sum\limits_{k = 1}^l {{\lambda _k}\frac{1}{n}} \sum\limits_{i = 1}^n {[(\frac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k) + (1 - E(h_{ij}^k)){w_j})} ]} }}{{\sum\limits_{j = 1}^m {\sum\limits_{k = 1}^l {{\lambda _k}\frac{1}{n}} } \sum\limits_{i = 1}^n {[(\frac{1}{{n - 1}}\sum\limits_{l = 1,l \ne i}^n {C(h_{ij}^k,h_{lj}^k) + (1 - E(h_{ij}^k)){w_j})} ]} }}$ (7)

Step 6. 最后得到各评价指标的权重集合 $W = \{ {w_1},$ ${w_2}, \cdots ,{w_m}\}$ .

3.4 计算各网络舆情突发事件的综合危害得分

Step 1. 运用式(1)得到各决策专家在网络舆情突发事件 ${X_i}$ 的评价指标 ${c_j}$ 下的犹豫模糊评价的加权平均算子, 即将各决策专家在同一网络突发舆情事件的同一评价指标下的犹豫模糊评估值进行集成. 令 $H_{ij}^k = \{ h_{ij}^1,h_{ij}^2, \cdots ,h_{ij}^l\} ,i = 1,2, \cdots ,n,j = 1,2, \cdots ,m$ 为所有决策专家在决策专家在第 $i$ 个突发事件的第 $j$ 个评价指标的犹豫模糊评估集, 则 $H_{ij}^k$ 的犹豫模糊加权平均算子可以表示为:

 $\begin{split} {H_{ij}}& = HFWA(h_{ij}^1,h_{ij}^2, \cdots ,h_{ij}^l) = \mathop \oplus \limits_{k = 1}^l ({\lambda _k}h_{ij}^k) \\ &= \bigcup\nolimits_{y_{ij}^1 \in h_{ij}^1,y_{ij}^2 \in h_{ij}^2, \cdots ,y_{ij}^l \in h_{ij}^l} {\left\{ {1 - \prod\limits_{k = 1}^l {{{(1 - y_{ij}^k)}^{{\lambda _k}}}} } \right\}} \\ \end{split}$

Step 2. 运用式(2)计算各网络舆情突发事件中的各评价指标的犹豫模糊评估分值 $S({H_{ij}}),i =1,2, \cdots ,n,$ $j = 1,2, \cdots ,m$ .

Step 3. 令 $Y = \{ {y_1},{y_2}, \cdots ,{y_m}\} = \{ S({H_{i1}}),S({H_{i2}}), \cdots ,$ $S({H_{im}})\}$ , $i = 1,2, \cdots ,n$ 为某一突发事件各评价指标的评估分值的集合, 结合2.2节中已求得的各评价指标的权重集合 $W = \{ {w_1},{w_2}, \cdots ,{w_m}\}$ 可计算各网络舆情突发事件的综合危害评估分值 $S({X_i}) = \{ S({X_n})\}S({X_1}),S({X_2}), \cdots$ , $i = 1,2, \cdots ,n$ :

 $S({X_i}){\rm{ = }}W*Y = ({w_1},{w_2}, \cdots ,{w_m})\left( \begin{gathered} {y_1} \\ {y_2} \\ \vdots \\ {y_m} \\ \end{gathered} \right)$ (8)

Step 4. 最后根据各网络舆情突发事件的综合评估分值对其综合危害性的高低进行排序, 进而为政府应急部门的确定处理顺序提供合理依据.

4 实证研究 4.1 问题描述

4.2 确定犹豫模糊评价矩阵

 ${R^1} = \left[{\begin{array}{*{20}{c}} \left\{ {0.7,0.7} \right\}\left\{ {0.3,0.4} \right\}\left\{ {0.9,0.9} \right\}\left\{ {0.6,0.6} \right\}\left\{ {0.1,0.2} \right\}\left\{ {0.7,0.7} \right\} \\ \left\{ {0.8,0.8} \right\}\left\{ {0.1,0.2} \right\}\left\{ {0.3,0.3} \right\}\left\{ {0.6,0.8} \right\}\left\{ {0.5,0.5} \right\}\left\{ {0.7,0.8} \right\} \\ \left\{ {0.3,0.4} \right\}\left\{ {08,0.8} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.8,0.8} \right\}\left\{ {0.4,0.5} \right\}\left\{ {0.2,0.2} \right\} \\ \left\{ {0.5,0.6} \right\}\left\{ {0.6,0.7} \right\}\left\{ {0.7,0.8} \right\}\left\{ {0.5,0.5} \right\}\left\{ {0.3,0.4} \right\}\left\{ {0.5,0.5} \right\} \\ \end{array}} \right]$
 ${R^2} = \left[ {\begin{array}{*{20}{c}} {\left\{ {0.8,0.8} \right\}\left\{ {0.3,0.3} \right\}\left\{ {0.7,0.8} \right\}\left\{ {0.1,0.1} \right\}\left\{ {0.5,0.7} \right\}\left\{ {0.7,0.7} \right\}} \\ {\left\{ {0.1,0.2} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.8,0.8} \right\}\left\{ {0.3,0.4} \right\}\left\{ {0.7,0.8} \right\}\left\{ {0.3,0.3} \right\}} \\ {\left\{ {0.3,0.3} \right\}\left\{ {0.6,0.6} \right\}\left\{ {0.8,0.8} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.3,0.4} \right\}\left\{ {0.4,0.5} \right\}} \\ {\left\{ {0.7,0.8} \right\}\left\{ {0.4,0.5} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.8,0.8} \right\}\left\{ {0.3,0.3} \right\}\left\{ {0.7,0.8} \right\}} \end{array}} \right]$
 ${R^3} = \left[ {\begin{array}{*{20}{c}} {\left\{ {0.1,0.2} \right\}\left\{ {0.7,0.7} \right\}\left\{ {0.1,0.2} \right\}\left\{ {0.5,0.5} \right\}\left\{ {0.9,0.9} \right\}\left\{ {0.3,0.3} \right\}} \\ {\left\{ {0.6,0.7} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.4,0.4} \right\}\left\{ {0.2,0.4} \right\}\left\{ {0.7,0.8} \right\}\left\{ {0.5,0.6} \right\}} \\ {\left\{ {0.8,0.8} \right\}\left\{ {0.4,0.5} \right\}\left\{ {0.6,0.6} \right\}\left\{ {0.1,0.2} \right\}\left\{ {0.6,0.7} \right\}\left\{ {0.6,0.6} \right\}} \\ {\left\{ {0.3,0.4} \right\}\left\{ {0.7,0.7} \right\}\left\{ {0.5,0.6} \right\}\left\{ {0.7,0.8} \right\}\left\{ {0.8,0.8} \right\}\left\{ {0.3,0.4} \right\}} \end{array}} \right]$
4.3 确定各评价指标权重

Step 1. 由4.2可得决策专家的犹豫模糊评价矩阵 ${R^1}$ ${R^2}$ ${R^3}$ .

Step 2. 运用式(3), 计算各应急决策指标的信息熵, 然后计算出各网络舆情突发事件在各评价指标下的平均信息熵, 计算结果如表5表6所示.

Step 3. 运用式(4), 计算各网络舆情突发事件关于各评价指标的全局犹豫模糊交叉熵, 然后计算出平均犹豫模糊交叉熵, 计算结果如表7所示.

Step 4. 运用式(6), 计算得到各评价指标的初始权W=(0.2311,0.1420,0.1761,0.1858,0.2010,0.1465).

Step 5. 根据决策专家对应急决策影响大小的权重 $\lambda = \{ {\lambda _1},{\lambda _2},{\lambda _3}\} = (0.3,0.35,0.35)$ , 运用式(7)对各评价指标的初始权重作进一步的修正.

Step 6. 最后得到各评价指标的权重集合W=(0.2050, 0.1171, 0.1931, 0.1822, 0.1974, 0.1052)

4.4 计算各网络舆情突发事件的综合危害得分

Step 1. 各决策专家对应急决策影响大小的权重 $\lambda = \{ {\lambda _1},{\lambda _2},{\lambda _3}\} = (0.3,0.35,0.35)$ 已知, 运用式(1), 对三位决策专家在同一舆情事件中的同一评价指标的犹豫模糊评估值进行集成. 以三位决策专家在第二个网络舆情事件中的第一个评价指标舆情广度为例

 $\begin{split} H_{21}^k & = HFWA(h_{21}^1,h_{21}^2,h_{21}^3) = HFWA(\{ 0.8,0.8\} ,\{ 0.1,0.2\} ,\{ 0.6,0.7\} ) = \mathop \oplus \limits_{k = 1}^2 ({\lambda _k}h_{21}^k) \\ &= \bigcup\nolimits_{y_{21}^1 \in h_{21}^1,y_{21}^2 \in h_{21}^2,y_{21}^3 \in h_{21}^3} {\left\{ {1 - \prod\limits_{k = 1}^3 {{{(1 - y_{21}^k)}^{{\lambda _k}}}} } \right\}}= \bigcup\nolimits_{y_{21}^1 \in h_{21}^1,y_{21}^2 \in h_{21}^2,y_{21}^3 \in h_{21}^3} {\left\{ {1 - {{(1 - h_{21}^1)}^{0.3}}{{(1 - h_{21}^2)}^{0.35}}{{(1 - h_{21}^3)}^{0.35}}} \right\}}\\ & = \{ 0.5685,0.6255,0.6098,0.5858,0.5684, 0.5858,0.6098,0.6255\} \\ \end{split}$

Step 2. 运用式(2), 计算得到各决策指标的评估分值, 结果如表8所示.

Step 3. 运用式(8), 计算得到各网络舆情突发事件的综合危害评估分值, 以网络舆情突发事件1为例, 其各评价指标的得分为{0.617 63, 0.491 39, 0.710 00, 0.425 56, 0.685 91, 0.606 76}, 那么网络舆情突发事件1的综合危害评估最终得分:

 $\begin{split} S\left( {{X_1}} \right) =& {\rm{0}}{\rm{.617\;63}} \times {\rm{0}}{\rm{.2050 + 0}}{\rm{.491\;39}} \times {\rm{0}}{\rm{.1171 }}\\ & + {\rm{0}}{\rm{.7100}} \times {\rm{0}}{\rm{.1931 + 0}}{\rm{.4256}} \times {\rm{0}}{\rm{.1822 + 0}}{\rm{.685\;91}} \\ & \times {\rm{0}}{\rm{.1974 + 0}}{\rm{.606\;76}} \times {\rm{0}}{\rm{.1052}}\;{\rm{ = }}\;{\rm{0}}{\rm{.598\;01}} \end{split}$

Step 4. 根据各网络舆情突发事件的综合危害评估分值, 对各网络舆情突发事件综合危害性的高低进行排序: S( ${X_4}$ )>S( ${X_1}$ )>S( ${X_2}$ )>S( ${X_3}$ ), 进而辅助应急部门确定处置网络舆情突发事件的顺序: ${X_4}\succ{X_1}\succ{X_2}\succ{X_3}$ .

4.5 比较分析

5 结语

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