﻿ 基于模糊层次评价法的PPP项目风险评价研究

# 基于模糊层次评价法的PPP项目风险评价研究Research on PPP Project Risk Evaluation Based on Fuzzy Hierarchical Evaluation Process

Abstract: This paper analyses the risk factor system of PPP projects, establishes evaluation criteria and de-cision-making criteria, and combines fuzzy mathematical evaluation method with analytic hier-archy process to form the fuzzy hierarchical evaluation method (F-AHP). This paper uses the method of Fuzzy Hierarchical Assessment to make qualitative analysis and quantitative analysis of risk factors such as political policy risk, economic risk, environmental risk, project construction risk and management risk of PPP project. It accurately calculates the evaluation score of each risk factor evaluation index and the overall risk evaluation score in the case, and determines the size of the PPP project risk, provides the basis for risk decision-making of PPP project. Therefore, Fuzzy Hierarchical Evaluation method is an effective method for risk evaluation of PPP projects.

1. 引言

2. 风险评价方法

2.1. 层次分析法

2.2. 模糊数学评价法

1) 建立影响评价对象因素集：

$U=\left\{{u}_{1},{u}_{2},\cdots ,{u}_{n}\right\}$ (1)

2) 建立评价集

$Y=\left\{{Y}_{1},{Y}_{2},\cdots ,{Y}_{m}\right\}$ (2)

$f=U\to F\left(Y\right)$ (3)

${\left({R}_{ij}\right)}_{n×m}=\left[\begin{array}{cccc}{R}_{11}& {R}_{12}& \cdots & {R}_{1m}\\ {R}_{21}& {R}_{22}& \cdots & {R}_{2m}\\ ⋮& ⋮& & ⋮\\ {R}_{n1}& {R}_{n2}& \cdots & {R}_{nm}\end{array}\right]$ (4)

Rij表示第i个因素对第j判断的隶属度。

3) 建立权重集

$A=\left\{{a}_{1},{a}_{2},\cdots ,{a}_{n}\right\}$ (5)

$\underset{i=1}{\overset{n}{\sum }}{a}_{i}=1$ (6)

4) 综合评价

$B=A×R=\left({a}_{1},{a}_{2},\cdots ,{a}_{n}\right)×\left[\begin{array}{cccc}{R}_{11}& {R}_{12}& \cdots & {R}_{1m}\\ {R}_{21}& {R}_{22}& \cdots & {R}_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ {R}_{n1}& {R}_{n2}& \cdots & {R}_{nm}\end{array}\right]=\left({b}_{1},{b}_{2},\cdots ,{b}_{m}\right)$ (7)

2.3. 模糊层次评价法

3. 模糊层次评价法层级要素权重计算

3.1. 建立比较判断矩阵

${\left({Q}_{ij}\right)}_{n×m}=\left[\begin{array}{cccc}{Q}_{11}& {Q}_{12}& \cdots & {Q}_{1m}\\ {Q}_{21}& {Q}_{22}& \cdots & {Q}_{2m}\\ ⋮& ⋮& \ddots & ⋮\\ {Q}_{n1}& {Q}_{n2}& \cdots & {Q}_{nm}\end{array}\right]$ (8)

Table 1. The relative importance of judgement matrix and its meaning

3.2. 计算各层因素权重值

1) 和法

${W}_{i}=\frac{1}{n}\underset{j=1}{\overset{n}{\sum }}\frac{{Q}_{ij}}{\underset{k=1}{\overset{n}{\sum }}{Q}_{kj}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2,3,\cdots ,n\right)$ (9)

2) 根法

${\stackrel{¯}{W}}_{i}=n\sqrt{\underset{j=1}{\overset{n}{\prod }}{Q}_{ij}}$ (10)

${W}_{i}=\frac{{\stackrel{¯}{W}}_{i}}{\underset{i=1}{\overset{n}{\sum }}{\stackrel{¯}{W}}_{i}}$ (11)

3) 最优传递矩阵法

${\stackrel{¯}{W}}_{1},{\stackrel{¯}{W}}_{2},{\stackrel{¯}{W}}_{3},{\stackrel{¯}{W}}_{4},{\stackrel{¯}{W}}_{5}$ (12)

$W=\frac{{\stackrel{¯}{W}}_{i}}{\underset{i=1}{\overset{5}{\sum }}{\stackrel{¯}{W}}_{i}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(i=1,2,3,4,5\right)$ (13)

3.3. 判断矩阵的一致性检验

$CR=\frac{CI}{RI}<0.1$ (14)

$CI=\frac{{\lambda }_{\mathrm{max}}-n}{n-1}$ (15)

Table 2. The value of average stochastic consistency index corresponding to the order of matrix

4. 因素评价尺度集

4.1. 一级模糊综合评价

$Y=\left\{很小,较小,中等,较大,较大,很大\right\}=\left\{0.1,0.3,0.5,0.7,0.9\right\}$

${\left({R}_{ij}\right)}_{n×m}=\left[\begin{array}{cccc}{R}_{11}& {R}_{12}& \cdots & {R}_{1m}\\ {R}_{21}& {R}_{22}& \cdots & {R}_{2m}\\ ⋮& ⋮& & ⋮\\ {R}_{n1}& {R}_{n2}& \cdots & {R}_{nm}\end{array}\right]$ (16)

4.2. 二级模糊综合评价

4.3. 三级模糊综合评价

5. 案例应用

5.1. 项目概况

5.2. 风险评价过程

1) 构建风险要素指标集

$U=\left\{{U}_{1},{U}_{2},{U}_{3},{U}_{4},{U}_{5}\right\}=\left\{政治政策风险,经济风险,环境风险,项目建设风险,管理风险\right\}$

${U}_{1}=\left\{{u}_{11},{u}_{12},{u}_{13}\right\}$${U}_{2}=\left\{{u}_{21},{u}_{22},{u}_{23},{u}_{24}\right\}$${U}_{3}=\left\{{u}_{31},{u}_{32},{u}_{33}\right\}$

${U}_{4}=\left\{{u}_{41},{u}_{42},{u}_{43},{u}_{44},{u}_{45},{u}_{46},{u}_{47}\right\}$${U}_{5}=\left\{{u}_{51},{u}_{52},{u}_{53}\right\}$

2) 建立各层级风险因素两两对比的判断矩阵

Table 3. Risk factor judgement matrix

Table 4. RI value table

Table 5. Calculator for political policy risk indicator A1

Table 6. Calculating table for economic risk indicator A2

Table 7. Calculation table for environmental risk indicator A3

Table 8. A4 Calculation form of project construction risk index

Table 9. Management risk indicator A5 worksheet

3) 风险模糊综合评价及建立评语集

① 建立评价因素及评语集合

Table 10. Risk assessment form

② 确定评价隶属矩阵

${R}_{1}=\left[\begin{array}{ccccc}0& 0.41& 0.49& 0.1& 0\\ 0& 0.14& 0.19& 0.31& 0.36\\ 0& 0.14& 0.19& 0.31& 0.36\end{array}\right]$${R}_{2}=\left[\begin{array}{ccccc}0& 0.12& 0.49& 0.20& 0.19\\ 0.20& 0.20& 0.20& 0.30& 0.10\\ 0.16& 0.29& 0.20& 0.23& 0.12\\ 0& 0& 0.40& 0.60& 0\end{array}\right]$

${R}_{3}=\left[\begin{array}{ccccc}0& 0& 0& 0.50& 0.50\\ 0.20& 0.31& 0.32& 0.17& 0\\ 0.16& 0.35& 0.29& 0.20& 0\end{array}\right]$${R}_{4}=\left[\begin{array}{ccccc}0.29& 0.30& 0.22& 0.10& 0.09\\ 0& 0.21& 0.47& 0.32& 0\\ 0& 0.20& 0.40& 0.30& 0.10\\ 0& 0.10& 0.21& 0.28& 0.41\\ 0& 0& 0.29& 0.24& 0.47\\ 0& 0.10& 0.20& 0.30& 0.40\\ 0& 0.11& 0.22& 0.30& 0.36\end{array}\right]$

${R}_{5}=\left[\begin{array}{ccccc}0.40& 0.40& 0.20& 0& 0\\ 0.40& 0.30& 0.30& 0& 0\\ 0.20& 0.40& 0.13& 0.27& 0\end{array}\right]$

③ 各二级指标因素权重集为

${A}_{i}=\left\{{a}_{i1},{a}_{i2},\cdots ,{a}_{in}\right\},{a}_{ij}\left(j=1,2,3,\cdots ,n\right)$ 是第二层次中决定因素Xi中第j个因素Xij的权数，且满足： $\underset{j=1}{\overset{n}{\sum }}{a}_{ij}=1$

${C}_{1}={A}_{1}\ast {R}_{1}=\left(0.2,0.2,0.6\right)\ast {R}_{1}=\left(0,0.194,0.25,0.268,0.288\right)$

${C}_{2}={A}_{2}\ast {R}_{2}=\left(0.154,0.064,0.154,0.628\right)\ast {R}_{2}=\left(0.03744,0.07594,0.37026,0.46222,0.05414\right)$

${C}_{3}={A}_{3}\ast {R}_{3}=\left(0.539,0.297,0.164\right)\ast {R}_{3}=\left(0.08564,0.14947,0.1426,0.35279,0.2695\right)$

$\begin{array}{c}{C}_{4}={A}_{4}\ast {R}_{4}=\left(0.107,0.235,0.138,0.034,0.380,0.043,0.064\right)\ast {R}_{4}\\ =\left(0.03103,0.12379,0.32921,0.26012,0.25621\right)\end{array}$

${C}_{5}={A}_{5}\ast {R}_{5}=\left(0.230,0.648,0.122\right)\ast {R}_{5}=\left(0.3756,0.3352,0.25626,0.03294,0\right)$

④ 确定三级模糊矩阵

$C={\left({C}_{1},{C}_{2},{C}_{3},{C}_{4},{C}_{5}\right)}^{\text{T}}=\left[\begin{array}{ccccc}0& 0.194& 0.25& 0.268& 0.288\\ 0.03744& 0.07549& 0.37026& 0.46222& 0.05414\\ 0.08564& 0.14947& 0.1426& 0.35279& 0.2695\\ 0.03103& 0.12379& 0.32921& 0.26012& 0.25621\\ 0.3756& 0.3352& 0.25626& 0.03294& 0\end{array}\right]$

$W=\left(0.265,0.418,0.167,0.041,0.108\right)$。因此

$P=W\ast C=\left(0.03799,0.1492,0.286,0.36938,0.15446\right)$

$Y=\left\{很小,较小,中等,较大,较大,很大\right\}=\left\{0.1,0.3,0.5,0.7,0.9\right\}$

$Q=P\ast {Y}^{\text{T}}=\left(0.03799,0.1492,0.286,0.36938,0.15446\right)\left(\begin{array}{c}0.1\\ 0.3\\ 0.5\\ 0.7\\ 0.9\end{array}\right)=0.5891$

5.3. 结果分析

6. 结论

1) 模糊层次评价法结合了层次分析法与模糊数学评价法，将定性分析与定量分析相结合是PPP模式下基础设施项目投资方进行风险管理的一种风险评价方法。

2) PPP项目风险评价贯穿于项目的全生命周期，在项目的不同阶段都会遇到不同种类的风险，而且项目主要风险会随之项目进度的变化而发生改变，模糊数学综合评价法是从定性到定量的研究思路，保证了PPP项目的风险评估结果的可靠性。

NOTES

*通讯作者。

[1] 孙振正. PPP模式下基础设施项目融资风险管理研究[D]: [硕士学位论文]. 上海: 华东理工大学, 2010: 35-38.

[2] 张晨. PPP项目风险分担: 发达国家与发展中国家的比较分析[D]: [硕士学位论文]. 天津: 天津大学, 2013: 60-63.

[3] 欧宗奇. PPP模式下城市基础设施项目投资方风险评价研究[D]: [硕士学位论文]. 合肥: 安徽建筑大学, 2016: 43-47.

[4] Chapman, C.B. and Cooper, D.F. (1987) Risk Analysis for Large Projects: Models, Methods and Cases. John Wiley & Sons.

[5] Hastak, M. and Shaked, A. (2000) ICRAM-1: Model for International Construction Risk Assessment. Journal of Management in Engineering, 16, 59-69.
https://doi.org/10.1061/(ASCE)0742-597X(2000)16:1(59)

[6] PPIAF (2016) The APMG Public-Private Part-nership (PPP) Certification Guide. The World Bank Group, 74-80.

[7] Fischer, K., Leidel, K., Riemann, A. and Alfen, H.W. (2010) An Integrated Risk Management System (IRMS) for PPP Projects. Journal of Financial Management of Property and Construction, 45-47.

[8] Jin, X.H., Zhang, G.M. and Yang, R.J. (2012) Factor Analysis of Partners’ Commitment to Risk Management in Public-Private Partnership Projects. Construction Innovation: Information, Process, Management, 43-46.

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