Evaluation on Financing Environment of Attracting Private Capital into Government Projects

Quan Zhou, Weilai Huang Scholl of Management,

Huazhong University of Science and Technology Wuhan, China

027zhouquan@163.com

Abstract—Through the investigation in Ruian City of Zhejiang Province, the authors found that there is an increasing demand of a scientific evaluation system of financing environment of attracting private capital into government projects. But constructing this comprehensive evaluation system is a multi-criteria problem which involves a number of interrelated factors. This paper develops an evaluation model based on the analytic hierarchy process (AHP) and triangular fuzzy number. AHP is used to analyze the structure of the financing environment and to determine weights of various criteria. And triangular fuzzy number is used to obtain final ranking to make comparisons. In the end, an application evaluating the financing environment in Ruian City is conducted to illustrate the utilization of the model constructed in this paper.

Keywords-evaluation; AHP; triangular fuzzy number

I. INTRODUCTION Attracting private capital to participate in government

projects is a good way to use private capital for social construction and ease the economic pressure of the government projects. It can enable the government to have a wider source of funds to ensure the implementation of government projects. However, there are still many problems exiting in the financing environment of attracting private capital into government projects. Moreover, whether private capital can effectively invest in government projects is impacted by a wide range of different factors, such as economy and finance, society and public opinion, and so on. And to evaluate each different factor, we need different indicators, many of which are difficult to get exact data. During the project of Ruian City, we found that China still lacks a scientific and comprehensive evaluation system of the financing environment of attracting private capital in government projects. So, in order to make objective evaluation on the financing environment of a certain region, it is necessary and urgent to build a scientific and comprehensive evaluation system.

Based on the investigation of Ruian City, this paper analyses the environment and related influencing factors and builds a comprehensive evaluation system. AHP, analytic hierarchy process, is used to construct a comprehensive evaluation system of financing environment of attracting private capital in the operation of government projects. And triangular fuzzy number is used to convert the evaluation of

vague language into quantitative data so as to make quantitative evaluation on a certain object.

II. METHODOLOGY

A. Analytic Hierarchy Process In practice, there always are a variety of interrelated factors

influencing a system. So in order to address a multi-criteria problem, we can build a multi-level analysis model based on the impacts and affiliations among various factors. Then the analysis of this complicated system can be disassembled to determine the relative weight of the lowest level to the highest level. And this is the basic idea of AHP. In fact, AHP has been widely used in solving complicated decision-making problems.

To implement AHP, first of all, a complex system is structured as hierarchy. We need to analyze different criteria, and break down the system into a hierarchy according to their interrelationship.

Next step is to determine the relative importance of the criteria within each level. This prioritization procedure starts from the second level and finishes in the lowest level. In each level, the criteria are compared in pairs according to their relative degree of the influence on the higher level [1]. The result of the comparison on n criteria can be summarized in a

)( nn× judgment matrix A , where aij is the relative

importance of criteria Ci to criteria C j , as shown in (1).

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

aaa

aaaaaa

nnnn

n

n

A

21

22221

11211

1=aii ,a ji

aij1= , 0≠a ij (1)

Then these judgment matrixes undergo a synthesis process in order to calculate a priority weight vector for the criteria. The relative weights in each level are given by the normalized

The research is supported by Soft Science Research Projects of Ruian City (No. 20062017).

The 1st International Conference on Information Science and Engineering (ICISE2009)

978-0-7695-3887-7/09/$26.00 ©2009 IEEE 3781

vector W corresponding to the maximum eigenvalue λmax of A , as

WAW λmax= (2)

It should be noted that the quality of the output of AHP is strictly related to the consistency of the in-pair comparison judgments. The consistency is defined by the relation between the entries of A : aika jkaij =× .The consistency index is

1max

−−

=n

nCI λ (3)

RICICR = (4)

And the final consistency ratio ( CR ) which helps decision maker to determine whether the evaluation is sufficiently consistent, can be calculated as (4), in which RI is the random index and can be found in a standard table. Generally, the evaluation outcome is acceptable, if CR does not exceed 1.0 . If it exceeds this value, the judgment matrix is inconsistent, and the procedure has to be repeated to improve consistency until the outcome is satisfactory. The measurement of consistency should be used to evaluate the consistency of both judgment matrixes and the overall hierarchy [2].

At last, aggregate the relative weights of elements in each level to arrive a set of rating of all the decision criteria, and then we get that the overall weight of criteria Ci to the highest level is wi .

B. Triangular Fuzzy Numbers It is widely accepted that the evaluation on qualitative

criteria of a certain object is based on judgments given by experts or decision makers. But human’s judgments are naturally expressed in lingual expressions, such as good, bad, fair, and so on. And such linguistic satisfaction degree and importance degree are vague, which makes the analysis outcome hard to compute. So, fuzzy set theory can be implemented to measure these ambiguous concepts that are associated with human being’s subjective judgments [3]. We can turn the ambiguous judgments into triangular fuzzy numbers according to TABLEⅠ.

TABLE I. CORESPONDING RELATIONSHIP BETWEEN LANGUAGE AND FUZZY NUMBER

Linguistic judgments Corresponding triangular fuzzy number absolutely bad （0，0，0.1） bad （0，0.1，0.3） relatively bad （0.1，0.3，0.5） fair （0.3，0.5，0.7） relatively good （0.5，0.7，0.9） good （0.7，0.9，1） absolutely good (0.9，1，1)

A triangular fuzzy number B can be denoted by a triplet ),,( nml where nml ≤≤ . The membership function

)(xAμ is defined below as (5).

[ ]

[ ]⎪⎪

⎩

⎪⎪

⎨

⎧

∈−−

∈−−

=

.otherwise 0

,,

,,

)( nmxmnxn

mlxlmlx

xAμ

(5)

Then the judgments about criteria in the lowest level of AHP can be transformed into triangular fuzzy numbers. Let

),,( nimiliT i = be a triangular fuzzy number corresponded

to the criteria Ci . In consideration of the weight wi derived in AHP, we can deduce that the comprehensive evaluation index of the object is ),,( cbaTW = which can be computed by (6).

∑=

=n

iT iwiTW

1 (6)

We compare the performance of two triangular fuzzy numbers using f j defined as (7). As f j is the defuzzication

form of fuzzy number ),,( c jb ja j , we can rank evaluation

objects according to their defuzzication forms.

4*2 c jb ja jf j

++= (7)

III. EVALUATION SYSTEM CONSTRUCTING AND AN APPLICATION

A. Identification of Criteria for the Evaluation System On the basis of the investigation and analysis about the

financing environment of attracting personal capital to government projects in Ruian city, this paper constructs the comprehensive evaluation system using AHP methods. Based on the principles of building hierarchy in AHP, we determine 4 sub-goals for the overall financing environment, and then, 19 criteria are identified under these four sub-goals. These criteria and their membership to sub-goals are displayed in TABLEⅡ.

B. Calculate the Weights of Criteria According to the data derived from the investigation,

judgment matrixes of each level are built based on the standard comparison scale of nine levels. And then the weights of criteria are calculated. We will display the calculation process of the first level as a representation.

So, in the first level there are four elements which are economic and financial environment, operational environment, policy environment, and social environment. Then the judgment matrix is built as followed.

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⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=

13/12231322/13/112/12/12/121

A

We can calculate out that the maximum eigenvalue of A is

4.14313, and the corresponding normalized eigenvector

is Tw )2404.0,4582.0,1163.0,1851.0(= . And then,

according to (3), the consistency ratio ( CR ) can be computed as 1.0053011.0 ≤=CR .

Then implement the above process for each level, we will get the weights of all criteria which are displayed in TABLEⅢ. If the consistencies of both judgment matrixes and the overall hierarchy meet the requirement, aggregate the relative weights of elements in each level to arrive a set of overall weights of all the decision criteria, and then we get wi which is the overall weight of criteria Ci to the highest level. The overall weight of each criteria and the ranking list can be seen in TABLEⅡ.

TABLE II. CRITERIA FOR EVALUATION SYSTEM OF ATTRACTING PERSONAL CAPITAL INTO GOVERNMENT PROJECTS

Sub-goals Criteria Ci Overall weight wi Ranking

Economic and

financial environment

B1

professional degree of financial institutions（C1） 0.020457 15 diversity of financing methods（C2 ） 0.065926 6 the scale and intensity of private capital（C3） 0.014537 16 liquidity of private capital（C4 ） 0.034343 11 financial institutions’ support to private capital（C5） 0.049837 7

Operational environment

B 2

ratio of private capital in funds of government projects ( C6 ) 0.008169 18 shortage of funds in government projects ( C7 ) 0.009749 17 publicity of government projects ( C8 ) 0.004950 19 matching degree of private capital to projects( C9 ) 0.021813 14 the level of participation of government( C10 ) 0.045107 8 status of completion of accomplished projects( C11) 0.026512 12

Policy environment

B3

market openness of capital operation ( C12 ) 0.094906 4 mechanism of choosing partners of government projects ( C13) 0.036547 10 protection on the rights of private capital ( C14 ) 0.222663 1 supporting incentives( C15 ) 0.104083 3

Social environment

B 4

private capital’s willingness to participate( C16 ) 0.025460 13 attitude of public( C17 ) 0.039336 9 monitoring mechanism ( C18 ) 0.068011 5 expected social effects ( C19 ) 0.107593 2

TABLE III. WEIGHTS AND CR INDEX OF EACH LEVEL

level maximum eigenvalue weights CR BA ~ 4.143130 0.1851，0.1163，0.4582，0.2404 0.053011 CB i

~1

5.146269 0.1105，0.3562，0.0785，0.1855，0.2692 0.032649 CB i

~2

6.270525 0.0702，0.0838，0.0426，0.1876，0.3879，0.228 0.043633 CB i

~3

4.034137 0.2071，0.0797，0.486，0.2272 0.012643 CB i

~4

4.071013 0.1059，0.1636，0.2829，0.2267 0.026301

Overall weights（ ww 191 ~ ） 0.0205，0.066，0.0145，0.0343，0.0498，0.0082，0.0097，0.005，0.0218，0.0451，0.0265，0.0949，0.0365，

0.2227，0.1041，0.0255，0.0393，0.068，0.1076 0.02447

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C. Evaluation Example Based on Triangular Fuzzy Numbers In the process of constructing the evaluation system of

financing environment of attracting private capital into government projects, most of the criteria are qualitative indicators which are difficult to gain accurate data. So the value of these criteria should be determined by experts. As to criteria CC 19~1 of which the evaluations are ambiguous, we can convert them into triangular fuzzy numbers. Thus, there are 19 triangular fuzzy numbers corresponding to the value of these 19 indicators.

Through sending questionnaires to experts and a series of investigations about the financing environment in Ruian City, we get original evaluation data as follows: C1(bad), C2（bad

）、 C3 （good）, C4 （relatively good）, C5 （relatively bad）, C6（absolutely bad）, C7（bad）, C8 （bad）, C9（fair）, C10 （fair）, C11（relatively good）, C12 （fair

）, C13（relatively good）, C14 （relatively good）, C15 （

fair） , C16 （ absolutely good） , C17 （ good） , C18 （

relatively bad）, C19 （absolutely good）. Then convert them into triangular fuzzy numbers according to TABLEⅠ . Use these triangular fuzzy numbers in (6). And in combination with the overall weights derived from AHP, we can get that the comprehensive evaluation of financing environment of attracting private capital into government projects is =TW （

0.4091，0.5840，0.7512）.

At the same time, in order to make a reference, we obtain from the experts the expected data which is thought more reasonable for the development of Ruian City. Repeat the above process and we can get that the expected outcome is

=T （0.5793，0.7793，0.9313）.

Using (7) to gain defuzzication form of vector TW andT , we get the evaluation value of Ruian is 0.5821, while the expected value is 0.7673. These two figures suggest the following statements. To attract private capital into government projects, the financing environment of Ruian City is a little better than the average degree. But obviously, the existing financing mechanism and environment does not meet the increasing requirement of attracting private capital to

participate in government projects, and it do not take full advantage of the local private capital.

IV. CONCLUSION On the basis of investigation in Ruian City, this paper

construct an effective evaluation system of the financing environment of attracting private capital in government projects, and make a case study combined with the actual situation of Ruian City. The analysis suggests that policy factors are most important for government to attract private capital, which is consistent with the fact that our country lacks policy supports and legal protection. What’s more, the evaluation of Ruian City reflects that the government’s inadequate efforts to provide protection and support on the financial industry and the rights of private capital. Therefore, the government needs to build and improve the scientific evaluation system to make appraisal about the current financing environment, and provide more incentives to ensure the private capital to participate in government projects.

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