﻿ 动力电池回收模式选择的多属性决策问题
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 同济大学学报(自然科学版)  2018, Vol. 46 Issue (9): 1312-1318.  DOI: 10.11908/j.issn.0253-374x.2018.09.020 0

### 引用本文

DING Xuefeng, MA Yu. Multiple Attribute Decision Making Problem in Power Battery Recycling Mode Selection[J]. Journal of Tongji University (Natural Science), 2018, 46(9): 1312-1318. DOI: 10.11908/j.issn.0253-374x.2018.09.020.

### 文章历史

Multiple Attribute Decision Making Problem in Power Battery Recycling Mode Selection
DING Xuefeng, MA Yu
School of Management, Shanghai University, Shanghai 200444, China
Abstract: The recycle of power batteries of electric vehicles not only protect the environment, but also has a positive impact on the sustainable development of electric vehicles. To solve the electric vehicle battery recycling mode decision-making problem, an improved method which combines the 2-dimensional uncertain linguistic variables (2-dimension uncertain linguistic variables, 2DULVs) and the VIKOR method (called 2DUL-VIKOR method) is proposed. First, 2DULVs is used to evaluate the power battery recycling mode in consideration of criteria. Then, experts' opinions are aggregated by using the 2DULVs aggregation operator. Next, the weights of criteria are calculated by the coefficient of the variation method. After that, the VIKOR method is used for selecting the best power battery recycling mode. Finally, an illustrative example is given to verify the effectiveness and practicability of the proposed method.
Key words: power battery    recycling mode    multiple attribute decision making    2-dimension uncertain linguistic variables    2DUL-VIKOR method

1 背景知识 1.1 二维不确定语言变量 1.1.1 不确定语言变量

(1) 若i>j，则sisj.

(2) 存在负算子neg(si)=sL-1-i.

(3) 若sisj，max(si, sj)=si.

(4) 若sisj，min(si, sj)=sisi, sjS.

1.1.2 二维不确定语言变量

1.1.3 2DULVs运算规则

 $\begin{array}{l} d({{\hat s}_1}, {{\hat s}_2}) = \frac{1}{{4\left( {l - 1} \right)}}(|{a_1}\frac{{{c_1}}}{{t - 1}} - {a_2}\frac{{{c_2}}}{{t - 1}}| + \\ \;\;\;\;\;|{a_1}\frac{{{d_1}}}{{t - 1}} - {a_2}\frac{{{d_2}}}{{t - 1}}| + \\ \;\;\;\;\;|{b_1}\frac{{{c_1}}}{{t - 1}} - {b_2}\frac{{{c_2}}}{{t - 1}}| + \\ \;\;\;\;\;|{b_1}\frac{{{d_1}}}{{t - 1}} - {b_2}\frac{{{d_2}}}{{t - 1}}| \end{array}$ (6)
1.1.5 期望值

 $E({{\hat s}_1}) = \left[ {\frac{{{a_1} + {b_1}}}{{2\left( {l - 1} \right)}}} \right]\left[ {\frac{{{c_1} + {d_1}}}{{2\left( {t - 1} \right)}}} \right]$ (7)

$E({\hat s_1}) \ge E({\hat s_2})$，则有${{\hat s}_1} \ge {{\hat s}_2}$，反之亦然.

1.2 聚合算子 1.2.1 GWA(geometric weighted aggregation)算子

 ${\rm{GWA}}({a_1}, {a_2}, \cdots , {a_n}) = {(\mathop \sum \limits_{i = 1}^n {w_i}a_i^\lambda )^{1/\lambda }}$ (8)

1.2.2 PA(power average)算子

 ${\rm{PA}}({a_1}, {a_2}, \cdots , {a_n}) = \frac{{\mathop \sum \limits_{i = 1}^n (1 + T({a_i})){a_i}}}{{\mathop \sum \limits_{i = 1}^n (1 + T({a_i}))}}$ (9)

1.2.3 2DULPGWA算子

Step 1.4   根据公式(19)，计算二维不确定语言变量${\hat s_{ij}^k}$相关权重.

ω111=0.200，ω121=0.188，ω131=0.199，ω141=0.204，ω151=0.192，ω161=0.195，ω211=0.192，ω221=0.205，ω231=0.197，ω241=0.204，ω251=0.200，ω261=0.201，ω311=0.198，ω321=0.197，ω331=0.204，ω341=0.199，ω351=0.204，ω361=0.201.

Step 1.5   根据公式(20)采用2DULPGWA算子对各专家评价进行聚合，结果如表 4所示.

Stage 2   采用变异系数法计算指标权重.

Step 2.1   采用公式(21)、(22)计算第j项指标的均值rj和标准差Dj.

r1=0.439，r2=0.440，r3=0.441，r4=0.267，r5=0.246，r6=0.450.

D1=0.194，D2=0.139，D3=0.121，D4=0.115，D5=0.122，D6=0.230.

Step 2.2   采用公式(23)计算第j项指标的变异系数Yj.

Y1=0.443，Y2=0.316，Y3=0.274，Y4=0.429，Y5=0.493，Y6=0.512.

Step 2.3   采用公式(24)计算指标权重wj.

w1=0.180，w2=0.128，w3=0.111，w4=0.174，w5=0.200，w6=0.207.

Stage 3   求解最优方案.

Step 3.1   根据公式(13)确定聚合专家意见后的信息集的理想解${{\hat S}^ + }$与负理想解${{\hat S}^ - }$.

${{\hat S}^ + } = \{ ([{{\hat s}_{4.487}^ + }, {{\hat s}_{5.314}^ + }][{{\hat s}_{2}^ + }, {{\hat s}_{4}^ + }])([{{\hat s}_{4.594}^ + }, $${{\hat s}_{5.610}^ + }][{{\hat s}_{2}^ + }, {{\hat s}_{3}^ + }])([{{\hat s}_{4.600}^ + }, {{\hat s}_{5.401}^ + }][{{\hat s}_{2}^ + },$${{\hat s}_{3}^ + }])([{{\hat s}_{2.802}^ + }, {{\hat s}_{3.805}^ + }][{{\hat s}_{2}^ + }, {{\hat s}_{3}^ + }])([{{\hat s}_{3.001}^ + }, $${{\hat s}_{3.800}^ + }][{{\hat s}_{2}^ + }, {{\hat s}_{3}^ + }])([{{\hat s}_{4.609}^ + }, {{\hat s}_{5.810}^ + }][{{\hat s}_{3}^ + }, {{\hat s}_{3}^ + }])\} . {{\hat S}^ - } = \{ ([{{\hat s}_{1.601}^ - }, {{\hat s}_{2.601}^ - }][{{\hat s}_{2}^ - }, {{\hat s}_{3}^ - }])([{{\hat s}_{2.191}^ - },$${{\hat s}_{3.190}^ - }][{{\hat s}_{2}^ - }, {{\hat s}_{3}^ - }])([{{\hat s}_{2.399}^ - }, {{\hat s}_{3.400}^ - }][{{\hat s}_{2}^ - }, $${{\hat s}_{3}^ - }])([{{\hat s}_{0.791}^ - }, {{\hat s}_{1.797}^ - }][{{\hat s}_{2}^ - }, {{\hat s}_{3}^ - }])([{{\hat s}_{0.391}^ - },$${{\hat s}_{1.810}^ - }][{{\hat s}_{2}^ - }, {{\hat s}_{3}^ - }])([{{\hat s}_{1.415}^ - }, {{\hat s}_{2.410}^ - }][{{\hat s}_{2}^ - }, {{\hat s}_{3}^ - }])\}$

Step 3.2   根据公式(14)~(16)，计算综合指标值Qi，并根据Qi值进行降序排序，确定最优解.

S1=1.058，S2=0.903，S3=1.050；R1=0.267，R2=0.215，R3=0.231；Q1=1，Q2=0，Q3=0.627，其排序结果为：Q2Q3Q1.Qi同时满足2.3节中Step4的条件1和条件2，故备选方案的排序为：A2A3A1.A2为最佳方案.

4 结语

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