2) is continuous on each
3) For any constant weight vector, , there is a variable state vector
Assuming that there are N indicators, , whose values changing over time. The values of M indicators in M time points are , where is the closest state value from the current time. Given the constant weight vector , the variable state vector can be defined as
It can be proved that the variable state vectors satisfy the defined conditions of excited variable state vectors. So the value of all variable state vectors in different time points can be defined
Calculate the values of the comprehensive function of all indicators in different time points which are the Hadamard product of variable vectors and state values,
Finally, the state values of all evaluation indicators can be defined as
3.2. A Variable Weight Model with Multiple Indicators
The state value of indicator is different, as well as the importance of different indicator. In traditional, constant weight variable is usually used to determine the importance of indicator. In this paper, the weight of indicator is also adopted to the variable weight theory in order to study the influence of the state value on the indicator. Satisfaction Principle is introduced  .
For a multi criteria decision making problem, assuming a decision set U, an indicator set related decision making problem and a constant weight vector of the indicators, . The value of the indicator f is and is the number of satisfaction. For any choice , the choice u is the satisfaction choice if there are more than indicators who are satisfactory. Indicator is satisfactory if where is the basic number whose values is the standard given by decision makers. Assuming that there are many small and medium sized enterprises and N indicators that measure the credit risk of small and medium sized enterprises. For any in , assuming that the value of N indicators is and the number of satisfaction is . In order to determine the constant weight vector more objectively, this paper uses the analytic hierarchy process to determine the value of the constant weight vector . The state value of all indicators are standardized by Z-score method and then the basic number can be . According to Liu Chang (2014,  ), variable state vector can be defined as
where is the excited factor, , is the number of satisfaction indicators that the number of satisfied condition and
It can be proved easily that satisfies all conditions of the definition excited variable state vectors and then the value of the variable weight vector of all suppliers can be calculated
Finally, calculating the values of the comprehensive function of all small and medium sized enterprises in different indicators which are the Hadamard product of variable vectors and state values,
Equation (8) gives the final scores of all small and medium sized enterprises.
4. Case Analysis
4.1. Index Design and Data Description
Based on the characteristics of the supply chain on the electronic platform and the literature of supply chain, the credit risk assessment index is constructed as Table 1.
According to the credit risk assessment indexes, this paper collects the data through the questionnaire to the merchant and the electronic business platform. Qualitative indexes take 5 points system score, and quantitative indexes are from the electronic business platform history records. There were 13 valid questionnaires returned. Therefore, a Multi-criteria decision-making model can be constructed with 13 financing enterprises and8 credit risk assessment indexes . Some indexes have three months of data .
Table 1. The credit risk evaluation index of internet supply chain finance.
4.2. A Variable Weight Model with Multiple Time Points of Any Indicator
In the collected data, some of them change with time. Sales profit margin X3, Purchasing data X4, Sales data X5 and Returned merchandise data X6 need to be calculated the values of the comprehensive function with three months record. Given a constant weight vector , the comprehensive function value of any indicator in three months can be calculated by Equation (5).
Besides, this paper uses the analytic hierarchy process to determine the value of the constant weight vector . According to the relative importance of each index, the judgment matrix of the hierarchical structure is determined. The relative importance between each other of the First-grade index can be expressed as a matrix A and the Second-grade index one can be expressed as a matrix B, C, D
The relative weight and combined weight of index can be determined by MATLAB according the judgment matrix. The relative weight and combination weight are shown as Table 2.
4.3. A Variable Weight Model with Multiple Indicators
According to variable weight theory, when an index meets the requirements of financial institutions, increase the weight of the index to indicate the impact of the index, or to reduce its weight. Constant weight vector , can be obtained from Table 2 by analytic hierarchy process. By Equation (6), the variable weight vectors of each index of the 13 financing enterprises can be obtained. Variable weight vector of each index of sample financing enterprise are shown as Table 3.
Table 2. The relative weight and combination weight of index by AHP.
Table 3. Variable weight vector of each index of sample financing enterprise.
Table 4. The final score boundary value and risk degree.
By Equation (8), the final scores of 13 small and medium sized enterprises are calculated. Take P as a boundary value. When P is larger, the credit risk degree of the financing enterprise is lower; when P is smaller, the credit risk of the financing enterprise is higher. The values are given as Table 4.
The final score values and risk assessment degrees of the 13 financing enterprises based on Multi-criteria decision-making(MID) model with the principle of variable weight and Analytic hierarchy process(AHP) model are shown as Table 5.
The credit risk of small- and medium-sized financing enterprises is relatively high due to shortage of its own funds and weak comprehensive ability. In traditional supply chain finance, when evaluating the credit level of small- and medium-sized enterprises, banks often take the analysis of the financial data of small- and medium-sized enterprises, and so on. In this paper, from the perspective of electronic business enterprise, we build the credit risk assessment indicators combined with the characteristics of internet supply chain financing mode and its platform data. In this paper, the credit risk assessment index is constructed through analysis of the characteristics of the financing model and the change of the model when the electronic commerce enterprise participates in the supply chain finance. At the same time, the index state value will change with time due to the real-time nature of internet data. Then a multi-criteria decision-
Table 5. The final score values and risk assessment degrees of the 13 financing enterprises.
making model based on the principle of variable weight was established combined with the characteristics of internet supply chain financing model, complexity and dynamic of data and the credit risk assessment index. Finally, based on the case validation, through comparing with the results of the traditional analytic hierarchy process, it is proved that the multi-criteria decision-making model has higher accuracy rate of credit risk assessment for financing enterprises.
This research was supported by “the Fundamental Research Funds for the Central Universities” (2015ZKYJZX02) and Guangzhou Financial Services Innovation and Risk Management Research Base.
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