QQ群聊

• CN 62-1112/TF
• ISSN 1005-2518
• 创刊于1988年

## 基于博弈论和模糊综合评判的锌冶炼企业清洁生产评价

1 中南大学资源与安全工程学院，湖南 长沙 410083

2 湖北省沙市中学，湖北 荆州 434000

## Cleaner Production Assessments of Zinc Smelting Enterprise Based on Game Theory and Fuzzy Comprehensive Evaluation

LI Huan,1, MING Junhua1, SHI Xiaofeng2

1 School of Resources and Safety Engineering，Central South University，Changsha 410083，Hunan， China

2 Hubei Shashi Middle School,Jingzhou 434000，Hubei， China

 基金资助: 国家自然科学基金青年基金项目“基于人工智能的矿山技术经济指标动态优化”.  51404305

Abstract

In order to promote cleaner production and promote the sustainable development of zinc smelting enterprises,the evaluation model based on game theory and fuzzy comprehensive evaluation was put forward on the basis of smelting process and mathematical method.Firstly,the weight values were calculated by the analytic hierarchy process and entropy weight method.Secondly， the final weight was determined by the game theory. Finally,the fuzzy comprehensive evaluation method was used to get the evaluation results.The results of the application examples showed that the cleaner production level of the enterprise is in the second level,which has great potential for cleaner production,among the six first level indicators in the index system,two indicators are in third levels,three indicators are in second grades, and one indicator is in the first level.And the evaluation model based on game theory and fuzzy comprehensive evaluation had a strong applicability in the cleaner production evaluation of zinc smelting enterprises and it would effectively promote the development of cleaner production.

Keywords： zinc smelting enterprise ; cleaner production assessments ; game theory ; combined weight ; fuzzy comprehensive evaluation

LI Huan, MING Junhua, SHI Xiaofeng. Cleaner Production Assessments of Zinc Smelting Enterprise Based on Game Theory and Fuzzy Comprehensive Evaluation[J]. Gold Science and Technology, 2018, 26(5): 635-646 doi:10.11872/j.issn.1005-2518.2018.05.635

### 1.2 熵值法

（1）数据标准化。按照定性与定量相结合的原则，以原始数据信息构建评价矩阵：$R1=(aij)m×n$；再根据式（1）和式（2）对量纲不统一的原始数据进行标准化处理，得到标准矩阵$R2=(fij)m×n$

$fij=aij-miniaijmaxiaij-miniaij,j∈1,n,i∈B$
$fij=maxiaij-aijmaxiaij-miniaij,j∈1,n,i∈C$

（2）第i项指标的信息熵计算。根据传统的熵概念，第i项评价指标的信息熵为

$Hi=-k∑j=1npijlnpij,i=1,2,⋅⋅⋅,m;j=1,2,⋅⋅⋅,n$

$pij=fij∑j=1nfij,i=1,2,⋅⋅⋅,m;j=1,2,⋅⋅⋅,n$

（3）第i项指标的差异系数

$gi=1-Hi,i=1,2,3,⋯,m$

（4）第i项指标的熵权。根据熵理论的定义，第i项评价指标的熵权Wi可表示为

$Wi=gi∑i=1mgi,i=1,2,⋅⋅⋅,m$

### 1.3基于博弈论的组合赋权模型

（1）构造基本权重向量集。假设用了H种赋权方法得到了H种权重数值，那么H种方法的基本权重向量集为

$wk=(wk1,wk2,⋯,wkn),k=1,2,⋯,H$

H种权重向量的任意线性组合为

$w=∑k=1HakwkT,ak>0$

（2）最优组合权重。本文利用博弈论的核心思想，在不同的权重中找到均衡，以求得最优效果的权重向量W。在计算过程中，可以转化成对权重系数$ak$的优化，使得$w$和不同的$wk$之间的离差最小化，计算公式如下：

$min∑j=1HajWjT-WiT,i=1,2,⋅⋅⋅,H$

$∑j=1HajWiWjT=WiWiT$

### 图1

Fig. 1   Comprehensive evaluation flowchart of game

theory-fuzzy mathematics

### 图2

Fig. 2   Evaluation index system of cleaner production in zinc smelting industry

### 3.2 层次分析法计算指标权重

Table 1  Judgment matrix and weights of target layer

AB1B2B3B4B5B6Wi
B11226230.3231
B21/2114220.1996
B31/2114220.1996
B41/61/41/411/31/20.0484
B51/21/21/23120.1364
B61/31/21/221/210.0930

Table 2  Judgment matrix and weights of production process and device index

B1B11B12B13B14Wi
B1111220.3334
B1211220.3334
B131/21/2110.1666
B141/21/2110.1666

Table 3  Judgment matrix and weights of resource

B2B21B22B23B24Wi
B21111/21/20.1666
B22111/21/20.1666
B2322110.3334
B2422110.3334

Table 4  Judgment matrix and weights of resource

B3B31B32B33B34B35Wi
B31132310.3133
B321/311/211/30.0986
B331/22121/20.1763
B341/311/211/30.0986
B35132310.3133

Table 5  Judgment matrix and weights of product

B4B41B42Wi
B41110.5000
B42110.5000

Table 6  Judgment matrix and weights of pollutant generation and emission index

B5B51B52B53B54Wi
B5114410.4000
B521/4111/40.1000
B531/4111/40.1000
B5414410.4000

Table 7  Judgment matrix and weights of cleaner production management index

B6B61B62B63B64B65B66B67B68B69Wi
B6111/211111110.1000
B622122222220.2000
B6311/211111110.1000
B6411/211111110.1000
B6511/211111110.1000
B6611/211111110.1000
B6711/211111110.1000
B6811/211111110.1000
B6911/211111110.1000

Table 8  Weights value of cleaner production potential assessment index in zinc smelting industry

1生产工艺与装置要求0.3231冶炼工艺0.3334
2阴极板0.3334
3物流运输系统0.1666
4自动控制系统0.1666
5资源能源消耗指标0.1996电锌电流效率0.1666
6单位产品新鲜水用量0.1666
7电锌直流电耗0.3334
8电锌单位产品综合能耗（折标煤）0.3334
9资源综合利用指标0.1996工业用水循环利用率0.3133
10镉利用率0.0986
11总硫利用率0.1763
12有价元素利用率0.0986
13锌总回收率0.3133
14产品指标0.0484安全性0.5000
15锌产品成分限制要求0.5000
16污染物产生与排放指标0.1364废水产生量0.4000
17排空烟尘固体物含量0.1000
18允许废渣排放量0.1000
19单位产品二氧化硫产生量0.4000
20清洁生产管理指标0.0930环境法律法规标准0.1000
21产业政策执行情况0.2000
22环境应急预案0.1000
23组织机构0.1000
24危险化学品管理0.1000
25环境审核0.1000
26生产过程管理0.1000
27污染物排放监测0.1000
28环境管理制度0.1000

### 3.3 熵值法计算指标权重

Table 9  Expert scoring table of qualitative indicators

12345678910
B118010080100901009010010010094
B133030303030303030303030
B143030303030303030303030
B4110090808595100100100809092
B61100100100100100100100100100100100
B628070756085707060656070.5
B632030301530303030152025
B647080658570606575806071
B656060607065505050556058
B665060707060606060606061
B673030201010302020203022
B6800105105105505
B6900050500501.5

Table 10  Evaluation Indicator Data Sheet

B11-100703094
B12m23.22.62.02.2
B13-100703030
B14-100703030
B21-90%89%88%90%
B22t/tZn10152031.33
B23kW*h/t350400450380
B24kgce/t700800900780
B31-95%85%75%90%
B32-90%80%70%76%
B33-98%97%96%0
B34-80%75%70%73%
B35-97%96.5%96%96.45%
B41-100703092
B42-99.995%99.99%99.95%99.998%
B51t/t2.557.54
B52mg/ m3501001505.3
B53t/tZn0.50.71.01.2
B54kg/t8102015
B61-1007030100
B62-100703070.5
B63-100703025
B64-100703071
B65-100703058
B66-100703061
B67-100703022
B68-10070305
B69-10070301.5

Table 11  Calculation data of information entropy（<span class="formulaText"><inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>H</mi></mrow><mrow><mi>i</mi></mrow></msub></math></inline-formula></span>），difference coefficient（<span class="formulaText"><inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>g</mi></mrow><mrow><mi>i</mi></mrow></msub></math></inline-formula></span>）and entropy weight(<span class="formulaText"><inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><msub><mrow><mi>W</mi></mrow><mrow><mi>i</mi></mrow></msub></math></inline-formula></span><span class="formulaNumber">)</span>

B110.95720.04280.1542B420.97710.02290.1477
B120.95450.04550.1765B510.97910.02090.1613
B130.94760.05240.1795B520.97730.02270.1657
B140.94760.05240.1795B530.97590.02410.2143
B210.97500.02500.1538B540.97670.02330.1600
B220.97900.02100.2402B610.99090.00910.1522
B230.97910.02090.1613B620.98990.01010.1626
B240.97960.02040.1639B630.99100.00900.1882
B310.97870.02130.1600B640.98980.01020.1624
B320.97760.02240.1724B650.98990.01010.1675
B330.97540.02460.2840B660.98930.01070.1663
B340.97760.02240.1724B670.99060.00940.1928
B350.97930.02070.1681B680.99080.00920.2124
B410.97760.02240.1549B690.98920.01080.2154

Table 12  Weight value of cleaner production potential assessment index and cleaner production assessment index in zinc smelting industry

1生产工艺与装置要求0.3132/0.3203冶炼工艺0.2216/0.3033
2阴极板0.2356/0.3071
3物流运输系统0.2714/0.1948
4自动控制系统0.2714/0.1948
5资源能源消耗指标0.1414/0.1835电锌电流效率0.2863/0.1922
6单位产品新鲜水用量0.2406/0.1825
7电锌直流电耗0.2393/0.3132
8电锌单位产品综合能耗（折标煤）0.2337/0.3120
9资源综合利用指标0.1807/0.1944工业用水循环利用率0.1911/0.2818
10镉利用率0.2014/0.1250
11总硫利用率0.2206/0.1877
12有价元素利用率0.2014/0.1250
13锌总回收率0.1855/0.2804
14产品指标0.0735/0.0553安全性0.4939/0.4978
15锌产品成分限制要求0.5061/0.5022
16污染物产生与排放指标0.1475/0.1394废水产生量0.2295/0.3505
17排空烟尘固体物含量0.2493/0.1434
18允许废渣排放量0.2652/0.1479
19单位产品二氧化硫产生量0.2560/0.3582
20清洁生产管理指标0.1437/0.1070环境法律法规标准0.1027/0.1011
21产业政策执行情况0.1140/0.1682
22环境应急预案0.1016/0.1006
23组织机构0.1151/0.1055
24危险化学品管理0.1140/0.1052
25环境审核0.1208/0.1078
26生产过程管理0.1061/0.1021
27污染物排放监测0.1038/0.1014
28环境管理制度0.1219/0.1081

### 3.4 组合权重的计算

$a1W1W1T+a2W1W2T=W1W1Ta1W2W1T+a2W2W2T=W2W2T$

$Wi=0.0971,0.0984,0.0624,0.0624(B11~B14)0.0353,0.0353,0.0575,0.0573(B21~B24)0.0548,0.0243,0.0365,0.0243,0.0545(B31~B35)0.0275,0.0278(B41~B42)0.0489,0.0200,0.0206,0.0499(B51~B54)0.0108,0.0180,0.0108,0.0113,0.0113,0.0115,0.0109,0.0108,0.0116(B61~B69)$

### 3.5综合评价指数计算

$R1=0.60.40000.30.7000100010$$R2=100000010.40.6000.20.800$
$R3=100000.60.40000100.60.4000.90.10$$R4=0.40.6001000$
$R5=0.40.6001000000100.50.50$$R6=100000.60.40000.60.400.60.4000.10.9000.20.80000.40.600010001$
$R=0.18200.21350.60460.00000.37990.43750.00000.18250.28180.40240.12800.18770.70130.29870.00000.00000.28360.38940.17910.14790.10110.19630.39160.3110$

（1）二级指标评价指数的计算。生产工艺与装置、资源能源消耗指标、资源综合利用指标、产品指标、污染物产生与排放标准、清洁生产管理指标等6个二级指标的评价指数分别为：

$YB1=W1×R1=0.18200.21350.60460.0000$
$YB2=W2×R2=0.37990.43750.00000.1825$
$YB3=W3×R3=0.28180.40240.12800.1877$
$YB4=W4×R4=0.70130.29870.00000.0000$
$YB5=W5×R5=0.28360.38940.17910.1479$
$YB6=W6×R6=0.10110.19630.39160.3110$

（2）一级指标评价指数的计算。将二级指标评价指数计算所得到的结果作为已知条件，计算一级指标评价指数，结果为

$Y=W×R=0.27190.31870.28540.1239$

### 3.6 清洁生产潜力分析

（1）生产工艺与装置要求。由第3.5小节可知，$YB1=0.18200.21350.60460.0000$，生产工艺与装置要求在第三等级的隶属度最高，说明该二级指标处于清洁生产第三等级。该企业在生产工艺与装置要求方面还有很大的改进空间，特别是物流运输系统和自动控制系统亟需完善，具有很大的清洁生产潜力。

（2）资源能源消耗指标。由第3.5小节可知，$YB2=0.37990.43750.00000.1825$，资源能源消耗指标在第二等级的隶属度最高，说明该二级指标处于清洁生产第二等级。该企业在电锌电流效率方面虽然做得很好，但是在其他3个方面都有改进的空间，特别是在单位产品新鲜用水量方面需要加大力度去完善。因此，该公司在资源能源消耗方面具有较大的清洁生产潜力。

（3）资源综合利用指标。由第3.5小节可知，$YB3=0.28180.40240.12800.1877$，资源综合利用指标在第二等级的隶属度最高，说明该二级指标处于清洁生产第二等级。该企业的工业用水几乎实现全循环使用，但是总硫的利用率却为0，因此在硫的利用方面急需改善，以减少资源的浪费，达到最大程度上的资源利用率。因此，该公司在资源综合利用方面具有较大的清洁生产潜力。

（4）产品指标。由第3.5小节可知，$YB4=0.70130.29870.00000.0000$，产品指标在第一等级的隶属度最高，说明该二级指标处于清洁生产第一等级。该企业在产品的安全性和成分限制要求方面都做得比较好，因此该企业在产品方面具有较小的清洁生产潜力。

（5）污染物产生与排放指标。由第3.5小节可知，$YB5=0.28360.38940.17910.1479$，污染物产生与排放指标在第二等级的隶属度最高，说明该二级指标处于清洁生产第二等级。该企业在废水产生量和排空烟尘固体物含量方面采取的控制措施比较有效，但是废渣和二氧化硫的产生量较大，仍有改进的空间。因此，该公司在污染物产生与排放方面具有较大的清洁生产潜力。

（6）清洁生产管理指标。由第3.5小节可知，$YB6=0.10110.19630.39160.3110$，清洁生产管理指标在第三等级的隶属度最高，说明该二级指标处于清洁生产第三等级。虽然该企业遵守环境法律法规，符合产业政策执行情况，也有专门的组织机构，但是还远远不够，在其他方面仍有很大的提升空间，比如未设置污染物排放检测系统和未制定环境管理制度。因此该公司在清洁生产管理方面具有很大的清洁生产潜力。

（7）一级指标。由第3.5小节可知，$Y=0.27190.31870.28540.1239$，一级指标在第二等级的隶属度最高，说明该企业的整体生产水平处于清洁生产第二等级。但是在第三等级和第四等级也有相当大的权重比例，说明该公司在清洁生产方面依旧任重道远，具有较大的清洁生产潜力。

## 4 结论

（1）以层次分析法和熵权法为基础，利用博弈论的思想，确定最优权重，并结合模糊综合评判方法，最终建立基于博弈论和模糊综合评判的评价模型。

（2）将模型应用于某锌冶炼企业清洁生产评价实践中，评价结果表明，该企业的清洁生产等级处于第二等级，具有较大的清洁生产潜力。评价指标体系包含6个一级指标，其中有2个指标处于第三等级，3个指标处于第二等级，1个指标处于第一等级。该评估结果对清洁生产的整改措施的确定具有重要的指导作用。

（3）基于博弈论和模糊综合评判的评价模型在锌冶炼企业的清洁生产评价方面具有很强的适用性，能够有效促进清洁生产的发展。

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