[Podcast] Picture Fuzzy Set Machine Learning Model for Multi-Criteria Decision-Making of Bank credit scoring
6 January, 2025
Keywords: Consumer credit, credit scoring, Multi-Criteria decision, Picture Fuzzy Set
Credit is crucial to an economy. However, credit often accompanies the risk of bad debt. On a large scale, bad debt will have consequences for the economy and society in general. Therefore, from the lender’s perspective, determining which subjects should and should not be disbursed is of great importance. To do that, a credit scoring model is necessary. In the research project “Building a model combining Picture Fuzzy Set and Fuzzy Topsis for the for bank credit decisions”, the authors from University of Economics Ho Chi Minh City (UEH) proposed a credit scoring model using the theory of fuzzy sets in a multi-criteria environment which has a good effect on detecting bad debts.

Credit is an important activity of the national economy; Vietnam is no exception. Data from the State Bank of Vietnam (Credit balance for the economy, 2022) shows that the total credit balance of the economy from the beginning of the year to October 2022 reached 11,657 million billion, an increase of 11.62% compared to that of the end of 2021. Of which, outstanding consumer loans reached approximately 2,42 million billion VND, an increase of approximately 16% compared to that of the end of 2021, accounting for nearly 21% of the credit balance of the economy with 84 credit institutions involved in lending. Loans of consumer finance companies reached approximately 145 trillion VND, an increase of more than 20% compared to that of the end of 2021, accounting for nearly 6% of consumer loans of the system and nearly 1.3% of loans of the entire economy.
Regarding the credit card ownership rate in Vietnam, the updated data in 2017 from the World Bank’s data set (Credit Card Statistics, 2021) shows that the credit card ownership rate among adults is 4.12% – up from 1.93% in 2014 and 1.24% in 2011. Although the credit card ownership rate in Vietnam is not high, the general trend is increasing. Although the use of credit cards is not as popular as in other countries, the Vietnamese government is promoting credit card activities, especially domestic credit cards. In general, credit activities always go hand in hand with the risk of bad debt. If this risk is not well controlled, it will cause serious consequences for banks in particular and for the economy in general. For lenders, specifically banks or credit institutions, credit activities can cause financial damage, contributing to business losses. In a broader sense, banks and credit institutions suffering from bad debts can affect customers’ savings deposits as this is the main source of money for banks to lend. Once this situation occurs on a large scale, it is likely that a chain effect will occur, affecting the entire banking system. Economic and social instability is inevitable. The World Bank report (August 2022, 2022 Review) reported that in the first quarter of 2022, the adjusted bad debt ratio is estimated to be up to 5.76%. In particular, the consumer credit segment seems to have deteriorated significantly, in which the bad debt ratio in this sector at non-bank consumer finance companies skyrocketing from 5.5% in 2020 to 9.4% in 2021.
With the above analysis and comments, it is not difficult to understand why bad credit control has always received attention from both researchers and practitioners. Within the framework of this article, the UEH author group has proposed a consumer credit scoring model to help detect bad credit applications early in order to limit bad credit, contributing to maintaining economic and social security.

Figure 1: General framework for consumer credit scoring
Figure 1 describes in detail the proposed model for the consumer credit scoring, including input factors, providing information and data; the analysis of credit scoring uses the picture fuzzy set theory, and the output is a list of credit applications sorted by credit score. The following section describes in detail the components of the proposed model.
The input of the model includes:
- Data on credit applications previously filled out by consumers in need of credit. This data is extracted from the credit institution’s storage system.
- The weights of the criteria are provided by experts.
- The function to calculate the picture fuzzy number synthesized from each criterion is selected by the model builder and user.
- The credit scoring function is selected by the model builder and user.
- The form of the membership function and the appropriate functions to calculate its parameters are selected by the model builder and user.
Model processing:
- Step 1: The model builder selects the appropriate membership function form and parameter calculation function for the membership, neutral and non-membership functions for each criterion. Normally, we can use the same function form and parameter calculation function for the criteria. However, depending on the case, the model builder can use different function forms and parameter calculation functions for different criteria.
- Step 2: Put the actual data of credit applications stored in the organization’s system into the function and parameter calculation functions selected in Step 1 to create the membership, neutral and non-membership functions of each criterion
- Step 3: Data from the storage system is put into the membership, neutral and non-membership functions of each criterion to produce the picture fuzzy numbers of each criterion
- Step 4: These picture fuzzy numbers are combined with the weights of the criteria according to the picture fuzzy weighted average method to obtain the overall picture fuzzy number, calculated for all criteria
- Step 5: From the overall picture fuzzy number, use the scoring function to score the consumer credit for each consumer credit application
- Step 6: From the score of each consumer credit application, arrange in order from the largest to the smallest
Model output:
After the process, the model consists of 6 steps, the final result from the proposed model is a list of credit applications arranged in order of credit score from high to low.
The data used to test the proposed model is actual data of a commercial bank in Vietnam including 8182 rows recorded in the period from May 2015 to December 2020. The data is collected during the process of consumers filling out consumer credit applications. The data set used for this study has been filtered out to 07 data fields related to the problem with the criteria mentioned in the previous section. After the data preprocessing, the original data set has 3367 rows and continues to be entered into the proposed model.
Experimental results: Using the credit score equaling 0.5 to classify good or bad credit applications. In practice, when it is applied, credit institutions or individuals using the model can choose different threshold scores to test the results depending on the risk. The output of the credit scoring is equivalent to the classification; therefore, the author uses the confusion matrix to evaluate the results of the proposed model with this specific dataset.
Table 1: Confusion matrix results of the proposed model
Total observations | Forecast | ||
100% | non-bad debts | bad debts | |
In practice | non-bad debts | 65.30% | 34.70% |
bad debts | 7.50% | 92.50% |
For credit scoring, the goal is to identify credit applications that are likely to become bad debts, therefore, the authors choose the true positive index in the confusion matrix to evaluate the models. Table 2 below compares the results between the proposed model and two machine learning techniques, logistic regression and decision tree.
Table 2: Results of comparison for models based on true positive score criteria
The proposed model using the picture fuzzy set theory shows the most positive results among the tested models in detecting consumer credit applications that become bad debts. The Decision Tree model shows positive results with a close True Positive score and finally the Logistic Regression model.
Credit is an important component of the economy, however, the development of credit activities always comes with the risk of bad debts and uncollectible debts. Without active measures to minimize and to limit the risks of bad debt, credit activities will easily cause harm to the economy and disrupt social order and security. One measure to minimize bad debt is to tighten the credit lending process, through careful consideration of the borrower’s ability to repay. In this reality, the problem of credit scoring was born and received much attention from academics as well as administrators. In this article, the UEH author proposes a new model to help score credit, specifically in the field of consumer credit lending, using the theory of picture fuzzy sets, taking advantage of expert opinions to calculate scores for consumer credit loan applications. The proposed model is tested on an actual data set, with more than 3,000 data rows of a commercial bank in Vietnam. The results of the proposed model on the sample data set show its effectiveness in detecting cases of bad debt. The proposed model fills a research gap in the academic environment on the topic of credit scoring and fuzzy theory application. In addition, banks and lenders, in general, can test the proposed model for credit scoring. The output of the model is a list of credit applications from the input sorted from largest to smallest according to credit score. Based on this result, the lender can have two directions to exploit the results of the model. First, the lender can choose an appropriate score threshold to convert the results into a classification form, as conducted above. Second, the output is a list sorted from the highest to the lowest based on credit score, the lender can disburse according to the available budget from top to bottom until the budget is exhausted.
In terms of academics, the proposed model has helped fill a research gap in the topic of credit scoring, especially consumer credit scoring. In addition, studies related to the application of fuzzy set theory and picture fuzzy set theory can refer to this report. In practice, the proposed model can be applied to support the consumer lending decision-making activities of commercial banks and credit institutions in general, contributing to promoting consumer credit lending activities, avoiding the situation where people in need have to resort to black credit and contributing to limiting bad debt, helping to stabilize security and social order.
The full-text research article on Building a model combining Picture Fuzzy Set and Fuzzy Topsis for bank credit decisions can be accessed HERE.
Author: Dr. Nguyen Quoc Hung – University of Economics Ho Chi Minh City.
This article is part of the series spreading research and applied knowledge from UEH with the message “Research Contribution For All”. UEH cordially invites readers to wait for the next UEH Research Insights newsletter.
News, photos: The Author, UEH Department of Communications and Partnership

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