﻿ 基于综合赋权和可拓理论的协作企业优选
 计算机系统应用  2019, Vol. 28 Issue (4): 18-24 PDF

Cooperative Enterprise Optimization Based on Comprehensive Weighting and Extension Theory
YANG Jing-Ya, SUN Lin-Fu, WU Qi-Shi
School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
Foundation item: National Key Research and Development Program of China (2017YFB1400303)
Abstract: Different core companies have different requirements and standards for the collaborative enterprises associated with the cloud platform, and the collaborative enterprises to be evaluated have different objective features. In order to select the best collaboration companies for the core enterprises of the after-sales automotive service supply chain cloud platform, the weight coefficient of the evaluation index of each cooperative enterprise is determined by the comprehensive weighting method based on the combination of the analytic hierarchy process method and the fuzzy rough set method. The subjective weight is determined by the analytic hierarchy process, and the objective weight is determined by the fuzzy rough set method. The comprehensive weight coefficient is achieved by reintegrating the main and objective weights. Finally, based on the extension discriminant method, the evaluation object is evaluated by the degree of goodness. The result is the ranking of each appraisal object and the order of the advantages and disadvantages. The actual service data of the after-sales service supply chain cloud service platform for the after-sales service is used as an example for comparative analysis. The results demonstrate the effectiveness and feasibility of the method, which are superior to other evaluation methods.
Key words: automotive service     cooperative enterprise optimization     comprehensive weighting     analytic hierarchy process     fuzzy rough set     extension judgment method

 图 1 协作企业评价模型结构图

1 本课题研究的协作企业优选的特点

2 基于综合集成赋权法和可拓理论的评价模型

2.1 评价指标体系

2.2 综合集成赋权 2.2.1 层次分析法确定主观权重

Step 1. 建立层次结构模型.

Step 2. 根据常用标度法[18,19]对各层元素进行两两比较, 构造比较判断矩阵. 对于 $n$ 个元素, 得到的两两比较判断矩阵为:

$B = {\left( {{B_{ij}}} \right)_{m \times n}}$ , 其中 ${B_{ij}}$ 表示因素和因素相对于目标重要值, 根据其重要性等级给予赋值.

Step 3. 判断矩阵B一致性检验.

Step 4. 若判断矩阵B一致性检验通过, 则B的特征向量 $x$ 归一化后即为权重向量; 若检验不通过, 则重新构造判断矩阵.

2.2.2 基于模糊粗糙集理论确定客观权重

$S = \left( {U,A,V,f} \right)$ 为一信息系统, $U$ 为非空有限的对象集合, $A = \left\{ {{a_1},{a_2},\cdots,{a_n}} \right\}$ 为非空有限的属性集合, $V$ 表示属性值, $f:U \times A \to V$ 为信息函数, 表示对每个 $f:U \times$ $A \to V$ , $a \in A$ $f\left( {u,a} \right) \in V$ .

 ${u_i}R{u_j} = \left\{ {\left( {{u_i},{u_j}} \right) \in U \times U\left| {\frac{1}{n}\sum\nolimits_{m = 1}^n {\left| {V_{im}^{'} - V_{jm}^{'}} \right|} \le \alpha } \right.} \right\}$ (1)

 $FR\left( {{u_i}} \right) = \left\{ {\left( {{u_j}} \right) \in U\left| {\frac{1}{n}\sum\nolimits_{m = 1}^n {\left| {V_{im}^{'} - V_{jm}^{'}} \right|} \le \alpha } \right.} \right\}$ (2)

 ${\overline R _\delta }\left( X \right) = \cup \left\{ {u \in U\left| {\frac{{\left| {X \cap FR\left( u \right)} \right|}}{{\left| {FR\left( u \right)} \right|}} > 1 - \delta } \right.} \right\}$ (3)

 ${\underline R _\delta }\left( X \right) = \cup \left\{ {u \in U\left| {\frac{{\left| {X \cap FR\left( u \right)} \right|}}{{\left| {FR\left( u \right)} \right|}} \ge \delta } \right.} \right\}$ (4)

 ${\gamma _R}\left( X \right){\rm{ = }}\frac{{\displaystyle\sum\nolimits_{s = 1}^t {\left| {{{\underline R }_\delta }\left( {{X_s}} \right)} \right|} }}{{\left| U \right|}}$ (5)

 $imp\left( {{a_m}} \right) = 1 - {\gamma _{A - \left\{ {{a_m}} \right\}}}\left( X \right)$ (6)

 $w\left( {{a_m}} \right) = \frac{{imp\left( {{a_m}} \right)}}{{\displaystyle\sum\limits_{m = 1}^n {imp\left( {{a_m}} \right)} }}$ (7)
2.2.3 计算综合权重

$w_m^{\left( {sub} \right)}$ 表示层次分析法得到的第 $m$ 个指标的主观权重, $w_m^{\left( {sub} \right)}$ 表示运用模糊粗糙集理论得到的第 $m$ 个指标的客观权重, 则第 $m$ 个指标的综合权重为:

 ${w_m} = \dfrac{{{{\left( {w_m^{\left( {sub} \right)}} \right)}^\eta }{{\left( {w_m^{\left( {obj} \right)}} \right)}^\mu }}}{{\displaystyle\sum\limits_{m = 1}^n {{{\left( {w_m^{\left( {sub} \right)}} \right)}^\eta }{{\left( {w_m^{\left( {obj} \right)}} \right)}^\mu }} }}$ (8)

2.3 基于可拓判别法进行优度评价

 $\rho \left( {y,{Y_0}} \right){\rm{ = }}\left| {y - \frac{{a + b}}{2}} \right| - \frac{{b - a}}{2}$ (9)

Step 1. 确定评价指标及评价指标的权重系数, 3.1和3.2节中已确定.

Step 2. 确定经典域和节域. 可拓理论中经典域 ${R_i}$ 定义为:

 ${R_i} = \left\{ {\begin{array}{*{20}{c}} {{N_i}}&A&{{V_{mi}}} \end{array}} \right\} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{N_i}}\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{a_1}}\\ {{a_2}}\\ {\vdots}\\ {{a_n}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {{a_{1i}},{b_{1i}}} \right\rangle }\\ {\left\langle {{a_{2i}},{b_{2i}}} \right\rangle }\\ {\vdots}\\ {\left\langle {{a_{ni}},{b_{ni}}} \right\rangle } \end{array}} \end{array}} \right]$ (10)

 ${R_p} = \left\{ {\begin{array}{*{20}{c}} P&A&{{V_{mp}}} \end{array}} \right\} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} P\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{a_1}}\\ {{a_2}}\\ {\vdots}\\ {{a_n}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {{a_{1p}},{b_{1p}}} \right\rangle }\\ {\left\langle {{a_{2p}},{b_{2p}}} \right\rangle }\\ {\vdots}\\ {\left\langle {{a_{np}},{b_{np}}} \right\rangle } \end{array}} \end{array}} \right]$ (11)

Step 3. 确定待评价的物元. 将收集到的待评对象各评价指标的数据用物元表示, 即:

 $R = \left\{ {\begin{array}{*{20}{c}} u&A&v \end{array}} \right\} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} u\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{a_1}}\\ {{a_2}}\\ {\vdots}\\ {{a_n}} \end{array}}&{\begin{array}{*{20}{c}} {{v_1}}\\ {{v_2}}\\ {\vdots}\\ {{v_n}} \end{array}} \end{array}} \right]$ (12)

Step 4. 计算物元各评价指标 ${v_m}$ 关于各等级 $i$ 的关联度 ${K_i}\left( {{v_m}} \right)$ .

 ${K_i}\left( {{v_m}} \right){\rm{ = }}\left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} \!\!\!\!\!\!\!\!\!{\dfrac{{\rho \left( {{v_m},{V_{mi}}} \right)}}{{\rho \left( {{v_m},{V_{mp}}} \right) - \rho \left( {{v_m},{V_{mi}}} \right)}}},&\!\!\!\!\!\!\!{\rho \left( {{v_m},{V_{mp}}} \right) \ne \rho \left( {{v_m},{V_{mi}}} \right)} \end{array}}\\ {\begin{array}{*{20}{c}} { - \rho \left( {{v_m},{V_{mi}}} \right)},&\;\;\;{\rho \left( {{v_m},{V_{mp}}} \right) = \rho \left( {{v_m},{V_{mi}}} \right)} \end{array}} \end{array}} \right.$ (13)

Step 5. 根据已确定的各评价指标的权重系数, 计算待评价对象关于各评价等级的归属程度, 即多因素综合关联度.

 ${K_i}\left( u \right) = \sum\limits_{m = 1}^n {{w_m}{K_i}\left( {{v_m}} \right)}$ (14)

Step 6. 根据综合关联度确定售后服务商的优先序.

3 实例及结果分析

3.1 评价指标权重确定

(1) 确定主观权重系数

$B = \left[ {\begin{array}{*{20}{c}} 1&1&7&4&5&3&7\\ 1&1&7&4&5&3&7\\ {{1 \mathord{\left/ {\vphantom {1 7}} \right.} 7}}&{{1 \mathord{\left/ {\vphantom {1 7}} \right.} 7}}&1&{{4 \mathord{\left/ {\vphantom {4 7}} \right.} 7}}&{{5 \mathord{\left/ {\vphantom {5 7}} \right.} 7}}&{{3 \mathord{\left/ {\vphantom {3 7}} \right.} 7}}&1\\ {{1 \mathord{\left/ {\vphantom {1 4}} \right.} 4}}&{{1 \mathord{\left/ {\vphantom {1 4}} \right.} 4}}&{{7 \mathord{\left/ {\vphantom {7 4}} \right.} 4}}&1&{{5 \mathord{\left/ {\vphantom {5 4}} \right.} 4}}&{{3 \mathord{\left/ {\vphantom {3 4}} \right.} 4}}&{{7 \mathord{\left/ {\vphantom {7 4}} \right.} 4}}\\ {{1 \mathord{\left/ {\vphantom {1 5}} \right.} 5}}&{{1 \mathord{\left/ {\vphantom {1 5}} \right.} 5}}&{{7 \mathord{\left/ {\vphantom {7 5}} \right.} 5}}&{{4 \mathord{\left/ {\vphantom {4 5}} \right.} 5}}&1&{{3 \mathord{\left/ {\vphantom {3 5}} \right.} 5}}&{{7 \mathord{\left/ {\vphantom {7 5}} \right.} 5}}\\ {{1 \mathord{\left/ {\vphantom {1 3}} \right.} 3}}&{{1 \mathord{\left/ {\vphantom {1 3}} \right.} 3}}&{{7 \mathord{\left/ {\vphantom {7 3}} \right.} 3}}&{{4 \mathord{\left/ {\vphantom {4 3}} \right.} 3}}&{{5 \mathord{\left/ {\vphantom {5 3}} \right.} 3}}&1&{{7 \mathord{\left/ {\vphantom {7 3}} \right.} 3}}\\ {{1 \mathord{\left/ {\vphantom {1 7}} \right.} 7}}&{{1 \mathord{\left/ {\vphantom {1 7}} \right.} 7}}&1&{{4 \mathord{\left/ {\vphantom {4 7}} \right.} 7}}&{{5 \mathord{\left/ {\vphantom {5 7}} \right.} 7}}&{{3 \mathord{\left/ {\vphantom {3 7}} \right.} 7}}&1 \end{array}} \right]$ 由判断矩阵计算出:

 $\left\{ \begin{array}{l} CI = 4.4409e - 016\\ CR = {\rm{3}}{\rm{.3643}}e - {\rm{016}} \end{array}\right.$

$CI$ $CR$ 验证判断矩阵B通过一致性检验, 进一步计算出主观权重向量为: [0.3258 0.3258 0.0465 0.0815 0.0652 0.1086 0.0465].

(2) 确定客观权重系数

 $\left\{ \begin{array}{l} FR\left( {{u_1}} \right) = \left\{ {{u_1}} \right\},\;\;\;\;\;\;\\FR\left( {{u_2}} \right) = \left\{ {{u_2},{u_8}} \right\},\\ FR\left( {{u_3}} \right) = \left\{ {{u_3},{u_4},{u_5},{u_7},{u_8}} \right\},\\ \;\;\;\;\;\;\;\;\;\;\;\;\vdots \\ FR\left( {{u_8}} \right) = \left\{ {{u_2},{u_3},{u_4},{u_8}} \right\} \end{array}\right.$

 $\begin{array}{l} X = \left\{ {{X_1},{X_2},{X_3}} \right\} = \left\{ {\left\{ {{u_1}} \right\},\left\{ {{u_2},} \right\},\left\{ {{u_3}} \right\},\left\{ {{u_4}} \right\},\left\{ {{u_5},{u_7}} \right\},\left\{ {{u_6}} \right\},\left\{ {{u_8}} \right\}} \right\} \end{array}$

(3) 求综合权重

3.2 评价结果及分析

 $\begin{array}{l} {R_1} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{N_1}}\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{\text{客户满意度}}}\\ {\vdots}\\ {{\text{旧件处理规范性}}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {0,2.5} \right\rangle }\\ {\left\langle {0,2.5} \right\rangle }\\ {\vdots}\\ {\left\langle {0,2.5} \right\rangle } \end{array}} \end{array}} \right]\\ {R_2} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{N_2}}\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{\text{客户满意度}}}\\ {{\text{保单真实性}}}\\ {\vdots}\\ {{\text{旧件处理规范性}}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {2.5,4} \right\rangle }\\ {\left\langle {2.5,4} \right\rangle }\\ {\vdots}\\ {\left\langle {2.5,4} \right\rangle } \end{array}} \end{array}} \right]\\ \end{array}$
 $\begin{array}{l} {R_3} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{N_3}}\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{\text{客户满意度}}}\\ {{\text{保单真实性}}}\\ {\vdots}\\ {{\text{旧件处理规范性}}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {4,5} \right\rangle }\\ {\left\langle {4,5} \right\rangle }\\ {\vdots}\\ {\left\langle {4,5} \right\rangle } \end{array}} \end{array}} \right] \end{array}$

 ${R_P} = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {{N_P}}\\ {}\\ {}\\ {} \end{array}}&{\begin{array}{*{20}{c}} {{\text{客户满意度}}}\\ {{\text{保单真实性}}}\\ {\vdots}\\ {{\text{旧件处理规范性}}} \end{array}}&{\begin{array}{*{20}{c}} {\left\langle {0,5} \right\rangle }\\ {\left\langle {0,5} \right\rangle }\\ {\vdots}\\ {\left\langle {0,5} \right\rangle } \end{array}} \end{array}} \right]$

 $\begin{array}{c} K\left( {{\rm{U}}1} \right) = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} { - 0.2}\\ {{\rm{ - 0}}{\rm{.4 }}}\\ { - 0.2}\\ { - 0.6}\\ 1\\ {{\rm{ - 0}}{\rm{.4}}}\\ {0.33} \end{array}}&{\begin{array}{*{20}{c}} {0.33}\\ {{\rm{0}}{\rm{.5}}}\\ {0.33}\\ 0\\ { - 0.6}\\ {{\rm{0}}{\rm{.5}}}\\ { - 0.2} \end{array}}&{\begin{array}{*{20}{c}} { - 0.33}\\ {{\rm{ - 0}}{\rm{.25}}}\\ { - 0.33}\\ 0\\ { - 0.75}\\ {{\rm{ - 0}}{\rm{.25}}}\\ { - 0.5} \end{array}} \end{array}} \right],\\ K\left( {{\rm{U}}2} \right) = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 0\\ { - 0.6}\\ { - 0.2}\\ {0.33}\\ {0.33}\\ { - 0.2}\\ 1 \end{array}}&{\begin{array}{*{20}{c}} 0\\ 0\\ {0.33}\\ { - 0.2}\\ { - 0.2}\\ {0.33}\\ { - 0.6} \end{array}}&{\begin{array}{*{20}{c}} { - 0.375}\\ 0\\ { - 0.33}\\ { - 0.5}\\ { - 0.5}\\ { - 0.33}\\ { - 0.75} \end{array}} \end{array}} \right],\\ \vdots\\ K\left( {{\rm{U}}8} \right) = \left[ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} 2\\ {{\rm{ - }}0.4}\\ {{\rm{ - }}0.2}\\ {0.33}\\ {{\rm{ - }}0.8}\\ 0\\ 0 \end{array}}&{\begin{array}{*{20}{c}} {{\rm{ - }}0.4}\\ {0.5}\\ {0.33}\\ {{\rm{ - }}0.2}\\ {0.5}\\ 0\\ 0 \end{array}}&{\begin{array}{*{20}{c}} {{\rm{ - }}0.625}\\ {{\rm{ - }}0.25}\\ {{\rm{ - }}0.33}\\ {{\rm{ - }}0.5}\\ {0.5}\\ {{\rm{ - }}0.375}\\ {{\rm{ - }}0.375} \end{array}} \end{array}} \right] \end{array}$

 $\begin{array}{l} {\rm{U}}1 \succ {\rm{U}}4 \succ {\rm{U}}6 \succ {\rm{U}}2 \succ {\rm{U}}7 \succ {\rm{U}}3 \succ {\rm{U}}8 \succ {\rm{U}}5 \end{array}$

 $\begin{array}{l} {\rm{U}}1 \succ {\rm{U}}4 \succ {\rm{U}}6 \succ {\rm{U}}3 \succ {\rm{U}}7 \succ {\rm{U}}8 \succ {\rm{U}}2 \succ {\rm{U}}5 \end{array}$

 $\begin{array}{l} {\rm{U}}1 \succ {\rm{U}}4 \succ {\rm{U}}6 \succ {\rm{U}}2 \succ {\rm{U}}3 \succ {\rm{U}}7 \succ {\rm{U}}8 \succ {\rm{U}}5 \end{array}$

4 结论与展望

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