Supply Chain Finance Credit Risk Evaluation Based on Trapezoid Fuzzy Number
Xing Bi 1, Xin Dong 2, Yu-tong Liu 3
1
School of Management, Tianjin University, Tianjin 300072 , China
School of Management, Tianjin University, Tianjin 300072 , China
3
International Business College, Shandong Institute Of Business and Technology,Yantai 264005,China
(dxcynthia@163.com)
2
Abstract - Supply chain finance has tremendous
development potential as a new type of bank financing
product. However, its risk is also developing gradually
towards the direction of complexity. The paper has
established an evaluation system for the credit risk of supply
chain finance, which evaluates all the indices of the index
system with the method of trapezoid fuzzy number
combined with the entropy weight theory, hence increasing
the accuracy of the evaluation. This combined evaluation
method can surmount the deficiency of the method evaluated
by triangular fuzzy numbers and other methods, and lower
the errors in judgement of the credit risk in supply chain
finance, so it is relatively a scientific evaluation method.
Keywords - Supply chain finance, Credit risk, Trapezoid
fuzzy number, Entropy weight
I. INTRODUCTION
In recent years, as a new bank financial product,
supply chain finance has gained rapid development. This
new model promotes fund integration effectively. It can
not only meet the finance requirements of small- and
medium-sized enterprises (SMES) in the supply chain, but
also help these enterprises get loan. Supply chain finance
has been promoted as more and more banks began to
conduct SMES credit in a more fierce competition
situation[1]. Especially since the financial crisis in 2008,
supply chain finance has undergone rapid development
and large logistics companies and banks devote major
efforts to the business to make profit. In these days, banks
do business in supply chain finance in varied forms which
include credit and factoring in the form of capital
guarantee, L/C, and honour in the form of bank credit;
and services like account management, account settlement
and corporate finance[2][3]. After joining in the supply
chain finance, banks evaluate the payment capacity and
credit support of core enterprises and design for SMES
the credit by the use of inventory pledge or receivables,
which can also solve the problems of credit imbalances
and fill the finance gap of SMES, finally realizing a threeside winning situation in which banks, enterprises and
logistics companies all get profit.
For a long time, SMES credit has been taking a only
small proportion in the business conducted by banks,
which have not found an index system of credit-risk
evaluation for SMES and have no complete SMES creditrisk evaluation system for a special finance product either.
With the development of supply chain finance, credit risk
incidents between banks and SMES also occur one after
another endlessly, which can be classified into four
categories. Firstly, enterprise breaches the contract and
changes the use of capital without the permission of the
bank[4]. Secondly, the enterprise conceals the revenue to
shirk the duty of paying back the debt, or cheat the bank
with the excuse of investment failure to make the bank
suffer from the loss[5]. Thirdly, after getting the loan,
enterprises sustain capital loss for the reason that they
don’t manage the money well or that the employees don’t
work hard[6]. Fourthly, malicious loans of the enterprise
with no intention of repaying them make the bank suffer a
lot from dead loans[7].
So, on currently existing foundation of credit risk
analysis of SMES, this articles make a credit risk
evaluation model of SMES in supply chain finance with
the basis of Trapezoid fuzzy number.
II. CREDIT ANALYSIS OF SUPPLY CHAIN
FINANCE
Credit risk of supply chain finance mainly indicates the
risk that the bank suffers when the enterprise cannot
totally or partly repay the loan because of the reasons
above. So evaluation and discernment of enterprise’s
repayment capacity is a key part of credit loan. In the
operating activities of a bank, evaluating credit risk
rationally can decrease credit risk effectively. In the
process of evaluation, a set of rational credit evaluation
system, which can get the credit information of an
enterprise by tracking, analyzing and summarizing the
credit indices in a certain operation period, should be
established. Study on credit risk of supply chain finance
has seen some achievements in China. The evaluation of
using FAHP, mainly by Zhao Zhong[8], is a relatively
simple evaluation method. Bai Shaobu[9] takes the method
of the value of fuzzy evaluation, membership vector fuzzy
evaluation, and typical fuzzy comprehensive evaluation
method to do credit risk analysis of supply chain finance.
Xiong Xiong[10] and others come up with a credit risk
evaluation system which concerns main rating and debt
rating, and applies PCA and Logist probit in setting up a
credit risk evaluation model. From the research
achievements above, it can be seen that credit risk of
supply chain finance can be affected by many factors.
There are a lot of risk evaluation methods, among which
the frequently used ones are fuzzy comprehensive
evaluation method, gray comprehensive evaluation
method, GAHP and neural network evaluation method.
Though these methods are simple, the evaluation effects
can be influenced as they are not likely to get all the
necessary information. On the other hand, supply chain
finance is related to many factors. It is hard to give
accurate judgments to every criterion. So the uncertainty
of credit risk was not fully considered by these research
achievements and methods, which cannot provide enough
decision-making information for a decision maker.
The using of fuzzy number to quantify the entire
evaluation index can put the information into full use. In
the past, the evaluation method of Triangular Fuzzy
Number was adopted[11][12]. However, it can’t reflect the
decision-making information effectively as Triangular
Fuzzy Number belongs to a simple function. Trapezoidal
fuzzy number is a better choice and has an edge in the
evaluation of credit risk in supply chain finance as it
doesn’t have such defect and can reflect a decisionmaker’s subjectivity better. Considering that the
comprehension or emphasis of evaluation indices is varied
among experts, which leads to a different survey result,
the idea of entropy weight is introduced to revise the
weight of every index and make the evaluation result
more rational.
III. A CREDIT RISK EVALUATION MODEL OF
SMES IN SUPPLY CHAIN FINANCE WITH THE
BASIS OF TRAPEZOID FUZZY NUMBER
A. The establishment of credit risk evaluation system in
supply chain finance
The factors that affect credit risk level in supply chain
finance are rather complicate and they mainly include
credit risk from enterprises themselves and the supply
chain. From the aspect of the enterprises, their credit risks
are mainly affected by themselves. From the aspect of the
supply chain, it plays an important role in affecting the
credit risk level the enterprise. As a whole, industry
conditions, enterprise’s conditions, core enterprises’
conditions and supply conditions should be considered
when analyzing the factors that affect credit risk of
enterprises in a supply chain. As a result, according to the
four conditions above, the evaluation index system is
established as follows (Fig. 1).
The evaluation index system of credit risk in supply chain finance
Financial enterprise’s
conditions
Industry conditions
Supply chain
relationship conditions
Core enterprise’s conditions
Status of financing
enterprise
Relationship quality
Relationship duration
Relationship strength
Credit history
Short-term liquidity
Profitability
Credit history
Quality of enterprise
Tie strength
Profitability
Growth ability
Profitability
Operating capacity
Quality of enterprise
Industry development goals
Macro environment
Fig.1 The index system of credit risk evaluation in supply chain finance
When evaluating the credit risk of supply chain
finance, the main task is to decide the weight of these
indices above. This article makes use of the evaluation
model based on trapezoidal fuzzy number to decide the
weight of these indices and then provide scientific basis
for banks to evaluate credit risk in supply chain finance.
B. Credit risk evaluation of supply chain finance
1. The fuzzy numbers used in this article are
trapezoidal fuzzy numbers with specific definition[13] as
follows:
We use M  (m1 , m2 , m3 , m4 ) to represent
trapezoidal fuzzy number, and then its membership
function is :
0,

 xm
1

,
 m2  m1

 M ( x)  
1,
 xm
4

,
 m3  m4

0,

x  m1
m1  x  m2
(1)
m2  x  m3
m3  x  m4
x  m4
m1  0 , then M is positive
trapezoidal fuzzy number. And m1  m2  m3  m 4 , if
m2  m3 , trapezoidal fuzzy number degenerates into a
Among them, if
triangular
if m1  m2
fuzzy
 m3
number.
Specially,
 m 4 , then M, as a trapezoidal fuzzy
number, degenerates into an ordinary real number.

M
( x)
1
x
0
m1
m2
m3
m4
Fig.2 Figure of trapezoidal fuzzy number
2. The determination of the index weight.
(1) Determination of the trapezoidal fuzzy weight[14][15]
1) The establishment of the trapezoidal fuzzy matrix.
Suppose that there are n experts to evaluate the m indices,
and the four evaluations of index i by expert j
are [ aij , bij , cij , d ij ] , with aij  bij  cij  dij . Experts
give each index a mark in the interval from 0 to 100, and
then form the initial evaluation matrix as follows:
  a11 b11 c11 d11   a12 b12 c12 d12 

 a b c d  a22 b22 c22 d 22 
M   21 21 21 21


 am1 bm1 cm1 d m1   am 2 bm 2 cm 2 d m 2 
a1n
 a2 n
amn
b1n c1n d1n  

b2 n c2 n d 2 n  


bmn cmn d mn 
(2)
2)
To
obtain
the
evaluations V  [v1 , v2 ,
weight
set
of
expert
, vm ] , in which v j means the
proportion of the evaluation expert j gives to each index
of the whole.
3) Fuzzy synthesis. We use weighted average fuzzy
operator to synthesize V and M, i.e. V M . A is in
representative of the synthetic fuzzy matrix, so
namely A  [[a1 b1 c1 d1 ] [am bm cm dm ]] .
4) To get the fuzzy weight. According to the
characteristics of the trapezoidal fuzzy numbers, the fuzzy
weight
of
index
j
can
be
set
with pi  (ai  2bi  2ci  di ) 6 , then dealt with the
normalized processing, so we can get the fuzzy weight set
W p  [ p1 , p2 ,
, pm ]
(2) Determination of entropy weight
Many supply chain finance credit risk evaluation
indices belong to the class of qualitative indexes. With
individual subjective opinion, to the same index, experts
may have different evaluation results, so we can use the
method of entropy weight to make appropriate
adjustments. Entropy reflects the degree of the chaos of
the system, the smaller the entropy value of the index,
then the greater the variation, the more information it can
provide, the greater the role that the index plays in the
comprehensive evaluation, also the bigger the weight.
Through the degree of variation, we can calculate the
weight of each index. And the calculation process is as
follows:
1) Calculate the total entropy of each index. First, we
should establish the trapezoidal fuzzy matrix, and then
calculate the total entropy of index i according to M:
n
1
Hi  
( xij


4 ln n x a ,b,c ,d j 1
m
x
i 1
ij
m
) ln( xij
x
i 1
ij
)
(3)
2) Compute the entropy weight of index i. The entropy
weight of index i is:
m
i  (1  H i ) (m   H i )
(4)
i 1
Thus, we can get the entropy weight set of m indexes:
W  [1 ,2 ,
,m ]
(5)
3) Calculate the combination weight.
With analytic hierarchy process (ahp) as the
example, the level weight set of supply chain finance
credit risk evaluation system is w  [1 ,  2 , ,  m ] ,
then the final weight of index i after the fuzzy entropy
adjustment is:
wi  ( pii i )
Thus,
we
W  [w1 , w2 ,
can
m
 p 
i 1
get
i i
the
(6)
i
final
evaluation
set:
wm ] .
IV. CASE ANALYSIS
In the supply chain finance, when using trapezoidal
fuzzy numbers to evaluate the credit factor of the core
supplier in the supply chain, the bank mainly evaluates
from the following four angles: the industry status,
financing enterprises’ status, core enterprises’ status, and
the supply chain status. Under the circumstances, the
weight of the evaluations from 5 experts is
V  [0.24，
0.20，
0.17，
0.23，
0.16]
Experts work out four groups of possible data about
the possibility of the above 17 Level-3 indices that may
arise. The results are shown in TABLE I.
TABLE I
Experts’ score of the weight of level-2 indices in the credit risk evaluation
system of supply chain finance
Index
Expert 1
Expert 2
Expert 3
Macro0.22,0.23,0.25,0.27 0.24,0.25,0.27,0.28 0.22,0.23,0.23,0.27
environment
（C1）
Industry
0.24,0.25,0.25,0.26 0.27,0.28,0.28,0.29 0.23,0.25,0.26,0.28
development
prospects（
C2）
Enterprise0.39,0.41,0.41,0.42 0.36,0.37,0.37,0.39 0.34,0.36,0.36,0.37
basic quality
（C3）
Profitability
0.36,0.38,0.39,0.42 0.33,0.36,0.36,0.39 0.32,0.33,0.33,0.35
（C4）
Operating
0.37,0.39,0.39,0.44 0.34,0.36,0.38,0.39 0.33,0.37,0.37,0.40
capacity（
C5）
Growing
0.35,0.38,0.38,0.43 0.33,0.35,0.35,0.37 0.32,0.33,0.33,0.38
capacity（
C6）
Short-term
0.39,0.41,0.41,0.43 0.37,0.39,0.41,0.45 0.32,0.36,0.37,0.38
liquidity（
C7）
Expe
0.19,
0.21,
0.30,
0.30,
0.30,
0.31,
0.35,
Long-term
liquidity（
C 8）
Credit
record
（C9）
Enterprisebasic
quality（
C10）
Profitability
（C11）
Short-term
liquidity（
C12）
Credit
record
（C13）
Relationship
strength（
C14）
Relationship
quality（
C15）
Relationship
long
degree（C16
）
Financing
enterprise
status（C17
）
be seen from the
sequence of
0.35,0.37,0.37,0.42 It can
0.33,0.34,0.36,0.41
0.28,0.29,0.35,0.36
the 17 indices, that
among all the factors affecting the credit risk, the
enterprise’s profitability matters the most, and macro
0.34,0.37,0.37,0.39
0.33,0.38,0.38,0.39
0.35,0.37,0.38,0.39
environment,
growth capacity,
and short-term liquidity
are also important factors. While examining the credit risk
of the
supply chain finance,
commercial banks should
0.13,0.15,0.17,0.19
0.15,0.17,0.18,0.19
0.16,0.18,0.19,0.20
focus on the factors with large weight.
0.38,0.39,0.41,0.43
0.36,0.38,0.38,0.40
0.37,0.38,0.38,0.42
0.35,0.37,0.38,0.40
0.12,0.15,0.15,0.17
0.11,0.13,0.15,0.16
0.13,0.15,0.16,0.18
0.12,0.15,0.15,0.18
0.14,0.17,0.19,0.20
0.11,0.15,0.16,0.18
0.11,0.13,0.15,0.16
0.14,0.15,0.16,0.17
0.13,0.15,0.17,0.18
0.14,0.16,0.17,0.19
0.13,0.15,0.16,0.17
0.11,0.13,0.14,0.17
0.20,0.23,0.24,0.26
0.19,0.22,0.22,0.26
0.24,0.26,0.26,0.30
0.24,0.28,0.28,0.31
0.22,0.25,0.25,0.27
0.24,0.26,0.27,0.29
0.28,0.29,0.29,0.31
0.22,0.24,0.25,0.27
IV. 0.13,0.15,0.15,0.19
CONCLUSION
0.13,0.16,0.18,0.19
This paper transfers the language information
evaluation given by experts into trapezoidal fuzzy
0.12,0.15,0.16,0.18
0.16,0.17,0.18,0.20
numbers,
and use the0.14,0.16,0.18,0.19
method of the trapezoidal fuzzy
number combined with the theory of entropy weight to
sort the weight of the 17 evaluation indexes of the supply
0.23,0.25,0.25,0.27 0.24,0.26,0.26,0.28 0.23,0.25,0.28,0.29
chain finance. Through the case analysis, it can be seen
that bringing in the trapezoidal fuzzy number and the
theory
of entropy weight
can not only absorb individual
0.22,0.24,0.26,0.29
0.23,0.26,0.29,0.30
0.21,0.23,0.25,0.26
expert’s opinion, but also have the effect of balancing the
evaluation results of all experts, which greatly reduces the
0.20,0.22,0.24,0.25 0.21,0.24,0.25,0.28 0.24,0.26,0.28,0.31
loss of the decision information. By the comprehensive
utilization of trapezoidal fuzzy numbers and entropy
weight method to get the combination weight, the article
not 0.21,0.25,0.27,0.28
only retains much
useful information in the
0.23,0.26,0.27,0.29
0.24,0.26,0.26,0.28
quantification process of evaluating qualitative indexes,
but also takes into full consideration the influence to the
weight of index of discrete degree of the data, which
makes the final index weight both subjective and
objective, thus having greater practical significance.
REFERENCES
The fuzzy weight, and entropy weight, also the weight
of hierarchical authority can be confirmed by the method
of the calculation of the entropy weight and triangular
fuzzy synthesis method, as is shown in TABLEⅡ.
TABLE Ⅱ
The fuzzy weight, entropy weight, hierarchical authority weight
The fuzzy
0.0508 0.0550 0.0774 0.0745 0.0756 0.0742
weight
0.0817 0.0788 0.0801 0.0340 0.0334 0.0332
0.0336 0.0521 0.0559 0.0535 0.0563
The
0.0631 0.0599 0.0465 0.0481 0.0476 0.0480
entropy
0.0439 0.0454 0.0445 0.0769 0.0775 0.0776
weight
0.0774 0.0622 0.0600 0.0613 0.0597
Hierarchical 0.0760 0.0470 0.0590 0.0710 0.0540 0.0660
authority
0.0500 0.0460 0.0410 0.0670 0.0890 0.0840
weight
0.0630 0.0590 0.0460 0.0490 0.0350
Finally, we can calculate the weight of these 17 indices as
[0.0763, 0.0485, 0.0665, 0.0797, 0.0608, 0.0736, 0.0561,
0.0515, 0.0458, 0.0548, 0.0721, 0.0678, 0.0513, 0.0599,
0.0483, 0.0503,0.0368].
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