Interval type-2 Fuzzy set model for sharia financing scoring: analysis and design

Abstract

Credit scoring system is a classic problem containing uncertainty in measuring default status. Current existing studies tend to assume credit scoring as credit feasibility analysis. Based on Sharia rules, credit scoring system (in Syariah called as financing) should be able to accommodate all processes on financing contract, mainly in scoring performance fulfillment. As a different to the conventional banks, in practice Islamic banks must comply with the Sharia rules. According to the principle in ushul fiqh, the basic law of muamalah is allowed as long as no argument against it. Therefore, in the implementation of financing scoring system, Islamic Bank is enforced to adopt the model that used by conventional banks that have been modified according to Sharia rules based on relevant verses and hadiths. This study has two main objectives: (1) to build the business processes models of Sharia financing scoring in scoring process of default status and fines calculation, and (2) to develop a mechanism and algorithm for scoring of default status and fines calculation on Sharia financing scoring by using Interval Type-2 Fuzzy Sets models. Currently, there are no crisp rules in Sharia financing scoring model which lead to subjective judgments. In the subjective judgements, words could mean different things to different people. Thus this study deployed the Interval Type-2 Fuzzy Set model to support the subjective judgments in maintaining Sharia rules. In this study, the business processes were modeled in BPMN version 2.0. Interval Type-2 Fuzzy Set model was used for scoring default status computation. This study used sum of delay time and installment value as variables for that scoring. Those variables were mapped in linguistic value. This study built the membership function for each variable by aggregating expert’s judgments in overlapping interval value. Then this membership function was used to activate a subset of rules by computing the firing interval. After that the type of firing interval results was reduced by using Karnik and Mendel algorithm. Then the defuzzification procedure was done to obtain the score in interval of [0,100]. In obtaining the risk value, this study used the first period of late as a weight to the scoring result. Finally, this risk value was used for real lost computation which is fair and compliance to Sharia rules for computing the fines value. In this study, the real lost value was obtained by computing based on the risk value, the value of bad debt expense, and the weighted average of each customer’s installment. Beside that this research proposed fairnesss computation by comparing the fines value to the installment value. In the conventional method, the fairness value will be in the interval [- ∞, 0, 1], while in the Islamic method the fairnesss value should be in the interval of [0, 1]. Based on the evaluation results, the proposed method produced the fairness values in the interval of [0, 1]. The results showed that the proposed method was fair and compliance to Sharia rules.