A Fairness Model Based on Interval Type-2 Fuzzy Set for Islamic Financing Scoring in Indonesia

Conventional credit scoring model could lead to serious and unfair problems because in certain case it would incriminate one party in financing. Islamic financing scoring model complies with Sharia rules and ensures fairness among parties. Currently, there are no certain rules on Islamic financing scoring model which lead to subjective judgments. In the subjective judgments, words could mean different things to different people. Thus, this paper proposed and deployed models for scoring of default risk level by using Interval Type-2 Fuzzy Set model to support the subjective judgments in maintaining Sharia rules. Installment amount and the sum of delay period has used as variables for that scoring. Interval Type-2 Fuzzy Set model was proposed to support the subjective judgments in maintaining Sharia rules. Beginning delay period also used as a weight to the risk scoring results. Besides that, this paper also proposed the method for computing real loss value. It has used as a basis for fines computation according to default risk level, bad debt expense, and installment weighted average.


Introduction
Credit scoring is a classic problem which is still interesting to study. Fisher's publication in 1936 is known as the first publication that introduces credit scoring system (Lu et al. 2013). Recent Yu et al. (2008). It is interesting to study because of the complexity of processes and data behavior that changes dynamically. The more interesting is most of the scholars only discuss credit scoring as feasibility analysis. Moreover, we can see from existing definitions that tend to equalize credit scoring as a credit feasibility analysis such as in Jentzch (2007), Yu et al. (2008), and Abdou and Pointon (2011).
The conventional credit scoring could lead to serious and unfair problems because in certain case it would incriminate one party in financing. It has seen from several indications: in the scoring of default status based solely on the sum of delay, installments would not be fair because it cannot depict the actual credit risk; while in fines computation, there is no rule of the maximum fines allowed. Under certain conditions, this method can inflict a financial loss on the customer.  The rest of this paper has organized as follows: Section 2 presents our proposed method in the scoring of default status, IT2FS model in scoring for default status, and fines computation. Section 3 presents the trial results and discussion. Section 4 concludes.

Methods
In according to meet the fairness condition, we will explain the steps and the methods which have used in this research.

Research Workflow
This research workflow was designed to ensure the validity of the proposed model by modifying prototyping techniques (see the detail of prototyping techniques in Laudon and Laudon (2012)).
Research workflow has seen in Fig. 1. knowledge that had been gained to be IT2FS models. Implementation stage was conducted to deploy the program application. Validation stage has conducted by asking experts to review and ensure the validity of the models and program application built.

Scoring for Default Status
According to our explanation in introduction part, scoring for default status is aimed to classify the customers (debtor) based on their risk (credit). The existing process is only according to the sum of late day. Therefore in case of fairness guarantee, we propose two parameters for scoring default status that has based on the sum of late day and installment value which are expected more illustrate the credit risk for each customer rather than just based on the sum of late day.
In this research, default status (default) has calculated by using an IT2FS algorithm based on the sum of the late day (late) and installment value (amount) for each customer-i (see equation (1)).
We design the default status value as interval value [0,100]. Lower credit risk has characterized by the closer value to zero (0) and vice versa.
In fact, Islamic bank use annuity method for calculating margin (MUI 2012; BI 2013). This treatment will affect the recognition of margin and principal. On annuity method, installment amount for each period will be constant, while margin value has calculated by the remainder of the principal amount (MUI 2012). This treatment will cause the margin value on period-t is higher than period t+1, while principal value on period-t is smaller than period t+1. This condition will cause the default risk level of financing in Islamic bank is higher on the beginning periods of contract than the end periods of contract. Thus, this research also uses the period as the weight of the scoring result (default). This weight can be obtained by equation (2) while N is a total period of the contract. So that, risk level (risk) will be obtained by this formula:

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The rules have been seeing in Table 3.

Result and Discussion
The series of the evaluation conducted by using proposed method to compute the risk of default value and fines amount. The dataset was a hypothetical data from two customers who have different values of installments, i.e., customers who have installment value of 1 million and 3.8 million. The data were computed for each end of month period of delay for 0 days to 12 months.
This evaluation assumed that both of customer had been arrears since June 30th, 2013 until May 31st, 2014. In case of fines computation, this evaluation assumed that bad debt expense value was 20% to total installment. Thus, bad debt expense value was 960 thousand rupiahs (20 %*(1 million + 3.8 million) rupiahs). Evaluation results can be seen in Fig. 2 Fig. 3. According to our explanation in introduction part, in the conventional method, the fines amount will continue to increase with the sum of delay periods without any maximum limit. While the proposed method (see Fig. 4), the fines amount will achieve the maximum value in a delay period of 9 months, so that the next period will be constant.
Based on these results, we claim that our methods are fair and compliance with sharia.

Conclusion
This paper proposed models for scoring of default risk level. Installment amount and the sum of delay period have used as variables for that scoring. Interval Type-2 Fuzzy Set model was proposed to support the subjective judgments in maintaining Islamic rules. Beginning delay period also used as weight to the risk scoring results. Besides that, this paper also proposed the method for computing real loss value. It was used as a basis in fines computation according to default risk level, bad debt expense, and installment weighted average. It has shown that our proposed method is fair and compliance with Sharia.