A Fuzzy Logic Model for Loan Recommendations in Online Lending Systems Using the California Psychological Inventory

2.1 The proposed system

Based on Figure 1, the activities involved in the borrowing process are outlined. The first stage involves the borrower submitting a loan application to the online lending system along with the necessary supporting documents. The documents will then be screened, and after the selection process, the system will make a Stage 1 decision on whether to approve or reject the documents. If the documents are rejected, the process will end; however, if the application is approved, the borrower will receive a link to complete the CPI questions. After completing the test, the results will be processed using a fuzzy system, which will generate a loan amount recommendation based on the calculations. The recommended loan amount will be confirmed to the borrower, and if they agree, the process will proceed with approval and the disbursement of funds to the designated account or third party, in accordance with the initial agreement.

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Figure 1. Proposed system using CPI with Mamdani fuzzy logic

2.2 Personality assessment using the CPI

The selection of ten traits from the CPI for recommending loan amounts in online lending is justified by their relevance to financial behavior, comprehensive nature, high psychometric validity, and flexibility in data integration. These traits enhance objective decision-making and capture the complexity of individual financial management skills, ultimately improving predictive accuracy in lending assessments [17, 18].

The questionnaire utilized in this study was developed based on the CPI methodology, which is a recognized tool for assessing personality traits [17, 19]. It consists of 10 distinct components, each of which is represented by three specific questions designed to gauge the respective trait accurately. The 10 components included in the questionnaire are Control, which measures an individual's ability to manage impulses; Ego Strength, assessing resilience; Warmth, reflecting interpersonal engagement; Social Presence, evaluating charisma; Self-Acceptance, focusing on self-esteem; Empathy, measuring sensitivity to others; Achievement via Conformance, relating to adherence to social norms; Responsibility, assessing reliability; Flexibility, evaluating adaptability; and Realistic, which measures practicality in decision-making [3, 18].

Table 1 presents a list of CPI questions designed to assess various psychological aspects such as ego strength, warmth, social presence, self-acceptance, empathy, responsibility, flexibility, and realism. Each question offers response options on a scale ranging from 20 (Never) to 100 (Always).

Table 1. CPI questions

2.3 Input variables

As input for the processing, data is obtained from borrowers who have been approved in Stage 1 selection, which involves documentation, to facilitate the completion of questions using the CPI. The recorded data from the 10 question components will be processed using a fuzzy system to produce output in the form of loan recommendations expressed as a percentage of the base loan amount on the platform [20, 21]. The input and output variables are presented in Figure 2.

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Figure 2. Proposed input and output flow

2.3.1 Fuzzification function

Control measures an individual's ability to manage impulses and act in an orderly and disciplined manner. Individuals with high scores tend to effectively regulate their emotions and behaviours, often maintaining calm under pressure [22]. They are organized, reliable, and consistent in their actions. Conversely, individuals with low scores may be more impulsive, less organized, and more easily influenced by their immediate emotions [23].

Ego Strength measures how strongly an individual tends to influence or control social situations. Individuals with high scores on this scale are usually very assertive, willing to take initiative, and capable of leading others. They are often regarded as natural leaders by their peers. Conversely, a low score may indicate someone who prefers to follow or avoid conflict [24].

Warmth measures an individual’s preference for social interaction and tendency to seek the company of others. Individuals with high scores on this scale are typically friendly, open, and enjoy being part of social groups. They often blend in easily and build relationships quickly. Conversely, individuals with low scores may be more introverted, enjoy spending time alone, and have smaller social circles.

Social Presence assesses an individual's ability to attract attention and make a good impression in social situations. Individuals with high scores typically possess charisma, confidence in self-expression, and are skilled in non-verbal communication. They often make others feel comfortable and engaged with what they say. A low score may indicate someone who is quieter or less comfortable in public attention.

Self-Acceptance measures how satisfied an individual feels with themselves and their acceptance of their strengths and weaknesses. Individuals with high scores tend to have high self-esteem and are rarely plagued by self-doubt. They accept themselves as they are and feel comfortable with their personality. Low scores may indicate self-dissatisfaction and struggles with self-acceptance [25, 26].

Empathy measures an individual's ability to understand and share the feelings of others. Individuals with high scores tend to be sensitive to the needs and emotions of others, making them effective in providing support and care [27, 28]. They can view situations from others' perspectives and are often regarded as understanding friends. Low scores may indicate difficulty in recognizing or responding to others' feelings.

Achievement via Conformance evaluates an individual's tendency to think and act independently rather than conforming to the group. People with high scores on this scale tend to make decisions based on their own beliefs and are often innovative in their approaches. They value autonomy and are frequently unaffected by peer pressure. Individuals with low scores may prioritize group consensus and seek guidance from others in decision-making.

Table 2 presents the magnitude of the limits for the calculation conditions. These calculation conditions serve as the basis for determining the recommendation computations.

Based on Figure 3, it explains the gradual transition between the "poor" and "high" membership values in the fuzzy logic system. This figure illustrates fuzzy logic membership functions with two categories: "poor" and "high." The blue line represents the "poor" category, which holds a value of 1 from 0 to 30, then decreases to 0 at 70. The red line represents the "high" category, which remains at 0 until 30, then increases to 1 at 70, intersecting around the value of 50 on the x-axis.

Table 2. Fuzzification function of the variable “control, warmth, social presence, social presence, self-acceptance, empathy, achievement via conformance, responsibility, flexibility”

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Figure 3. Membership function of the “control, warmth, social presence, social presence, self-acceptance, empathy, achievement via conformance, responsibility, flexibility” component

Responsibility assesses the extent to which individuals feel bound by ethical norms and social commitments. Individuals with high scores on this scale take their responsibilities toward others and society seriously. They are reliable and often seen as pillars of strength within their groups or families. Low scores may indicate a more relaxed attitude toward obligations and a lack of consistency in fulfilling commitments.

Flexibility assesses how open and accepting an individual is towards opinions, behaviors, and backgrounds that differ from their own. Individuals with high scores tend to be open to new and diverse ideas, demonstrating the ability to adapt to various social and cultural situations. They are not quick to judge and appreciate diversity. Conversely, individuals with low scores may be more resistant to change and less comfortable with differences.

2.3.2 Realistic

Realistic evaluates the extent of a person's desire and ability to gain recognition, social status, or professional standing. Individuals with high scores often have strong ambitions and work hard to achieve respected positions in society or their jobs. They are also likely to be very aware of their image and how they are perceived by others. Low scores may indicate a lack of concern for social status or satisfaction with simpler roles. Realistic is divided into two components, namely 'poor' and 'high', as described in detail in Table 3.

$\mu$ Poor $[x]=\left\{\begin{array}{cc}1 ; & x \leq 30 \\ \frac{70-x}{70-30} & 30 \leq x \leq 70 \\ 0 ; & x \geq 70\end{array}\right.$               (1)

$\mu$ High $[x]=\left\{\begin{array}{cc}0 ; & x \leq 30 \\ \frac{x-30}{70-30} & 30 \leq x \leq 70 \\ 1 ; & x \geq 70\end{array}\right.$     (2)

Table 3 presents the magnitude of the limits for the calculation conditions of the "high" and "poor" boundaries. These calculation conditions serve as the basis for determining the recommendation computations, which have values inverse to those in Table 2.

Table 3. Fuzzification function of the “realistic” variable

Figure 4 illustrates fuzzy logic membership functions with two categories: "high" and "poor." The blue line represents the "high" category, which holds a value of 1 from 0 to 30, then decreases to 0 at 70. The red line represents the "poor" category, which remains at 0 until 30, then increases to 1 from 70 to 100. Both lines intersect around the value of 50 on the x-axis.

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Figure 4. Membership function of the “realistic” component

$\mu$High$[x]=\left\{\begin{array}{cc}1 ; & x \leq 30 \\ \frac{70-x}{70-30} & 30 \leq x \leq 70 \\ 0 ; & x \geq 70\end{array}\right.$          (3)

$\mu \operatorname{Poor}[x]=\left\{\begin{array}{cc}0 ; & x \leq 30 \\ \frac{x-30}{70-30} & 30 \leq x \leq 70 \\ 1 ; & x \geq 70\end{array}\right.$                (4)

2.4 Output variable

2.4.1 Loan recommendation (%)

The output of the CPI is in the form of loan amount recommendations expressed as a percentage, derived from the recommended value multiplied by the base loan platform.

Numeric values play a crucial role in determining the suggested loan limits, including minimum and maximum thresholds based on factors such as experience, caution, extroversion, compatibility, and the level of neuroticism of the loan applicants, all of which serve as inputs for the Fuzzy Evaluation System (FES). When the loan value does not exceed 35, there is a high likelihood that the applicant will receive a loan amount within the minimum range. Conversely, a value reaching or exceeding 65 indicates that the applicant is likely to obtain the maximum loan allocation. The output of this loan is categorized into two fuzzy categories, namely "minimum" and "maximum," employing trapezoidal curves to determine the output membership functions. Table 4 and Figure 5 provide illustrations of the fuzzy sets and membership functions related to the loan output.

Table 4. Fuzzification of the “loan” recommendation variable

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Figure 5. Output variable in the form of recommendations (%)

$\mu$ Minimum $[\mathrm{x}]=\left\{\begin{array}{cc}1 ; & \mathrm{x} \leq 35 \\ \frac{65-\mathrm{x}}{65-35} & 35 \leq \mathrm{x} \leq 65 \\ 0 ; & \mathrm{x} \geq 65\end{array}\right.$            (5)

$\mu$ Maximum $[x]=\left\{\begin{array}{cc}0 ; & x \leq 35 \\ \frac{x-35}{65-35} & 35 \leq x \leq 65 \\ 1 ; & x \geq 65\end{array}\right.$          (6)

2.4.2 Fuzzy rule base

In the system we developed, there are 10 input variables, each with 2 conditions, namely 'Poor' and 'High,' resulting in a calculation base of 2^10=1,024 possibilities. The rule base is constructed using the IF-Then formula to generate outputs in the form of percentages. We conducted an analysis to determine the weights for each output domain variable. We sought the weights for each variable that influence the output results. The highest weights are 0.467 for the Control variable, 0.214 for Ego Strength, 0.328 for Warmth, 0.247 for Social Presence, 0.451 for Self-Acceptance, 0.325 for Empathy, 0.472 for Achievement via Conformance, 0.325 for Responsibility, 0.712 for Flexibility, and 0.635 for Realistic. Based on the weight values, we established the conditional rules as follows:

2.4.3 Defuzzification and Mamdani inference

Defuzzification is executed to convert fuzzy values into crisp values that can be easily understood and applied in a non-fuzzy context. This process is used in fuzzy control systems, where decisions must be made based on fuzzy logic involving linguistic variables and fuzzy rules. After the fuzzy logic system evaluates the conditions and applies the relevant rules, the results obtained are in the form of fuzzy values. Defuzzification is necessary to transform these fuzzy values into real values or specific actions that can be implemented in physical systems or practical decisions. In FES, we utilize the centroid method to implement the defuzzification process (23).

$z=\frac{\int \mu C(z) \cdot z d z}{\int \mu C(z) \cdot d z}$              (7)

In a data capture showing the aggregation results with the following conditions: Control=68, Ego Strength=72, Warmth=83, Social Presence=74, Self-Acceptance=60, Empathy=84, Achievement via Conformance=76, Responsibility=78, Flexibility=42, and Realistic=38. The next step will be to calculate the membership degrees for each variable. The truth degree (i) is a component of the Mamdani FIS rules by taking the minimum value from several displayed membership degrees. Subsequently, the largest value will be selected from the smallest values compared. After that, through calculations using the centroid method, the crisp value for the loan output is obtained. The steps below illustrate the input data as stated above:

(1) Control $=68, \mu(Poor)=0$, and $\mu$ High $=0.70$

(2) Ego Strength $=72, \mu(Poor)=0$, and $\mu$ High $=1$

(3) Warmth $=83, \mu(Poor)=0$, and $\mu$ High $=1$

(4) Social Presence $74, \mu(Poor)=0$, and $\mu$ High $=0.88$

(5) Self - Acceptance $=60, \mu(Poor)=0$, and $\mu$ High $=0.70$

(6) Empathy $=84, \mu (Poor) =0$, and $\mu$ High $=1$

(7) $\begin{aligned} & \text { Achievement via Conformance }=76, \mu \text { (Poor) } =0 \text {, and } \mu \text { High }=1\end{aligned}$

(8) Responsibility $=78, \mu(Poor) =0$, and $\mu$ High $=1$

(9) Flexibility $=42, \quad \mu(Poor)=0$, and $\mu$ High $=1$

(10) Realistic $=34, \quad \mu(Poor)=0$, and $\mu$ High $=1$

Based on the collected data, it can be conditioned using the above formulation through the 8 rule approaches that have been described, resulting in the outcomes displayed below:

(1) $\alpha_{092}=\min (0.21 ; 1 ; 0.14 ; 0.31 ; 1)=0.14$

(2) $\alpha_{115}=\min (0.22 ; 1 ; 0.16 ; 0.81 ; 1)=0.16$

(3) $\alpha_{172}=\min (0.18 ; 1 ; 0.19 ; 0.48 ; 1)=0.18$

(4) $\alpha_{248}=\min (0.17 ; 1 ; 0.16 ; 0.92 ; 1)=0.16$

(5) $\alpha_{320}=\min (0.98 ; 1 ; 0.42 ; 0.38 ; 1)=0.38$

(6) $\alpha_{329}=\min (0.72 ; 1 ; 0.63 ; 0.82 ; 1)=0.63$

(7) $\alpha_{351}=\min (0.98 ; 1 ; 0.62 ; 0.82 ; 1)=0.62$

(8) $\alpha_{388}=\min (0.78 ; 1 ; 0.61 ; 0.72 ; 1)=0.61$

Based on the calculations, the results will be as follows:

$\begin{gathered}\alpha= \max \left(\alpha_{092}, \alpha_{115}, \alpha_{172}, \alpha_{248}, \alpha_{320}, \alpha_{329}, \alpha_{351}, \alpha_{388}\right) \\ \alpha=\max (0.14,0.16,0.18,0.16,0.38,0.63,0.62,0.61) \\ \alpha=0.63\end{gathered}$             (8)

Using the centroid method, the recommendation given is 63%, which indicates that this recommendation is lower than the recommendation provided by the admin system, which is 70%. In this regard, we recommend that the suggested loan percentage be 36%, considering the psychological influence of borrowers that will impact the repayment process for the loan.

Table 6. Comparison data of credit recommendations based on admin assessments and improvements to the CPI principles using fuzzy methods

Name	City	Province	Loan (IDR)	Loan (%) by Admin	Loan (%) by CPI
Costumer 1	Sleman	Yogyakarta	60.000.000	80	66
Costumer 2	Bandung	West Java	55.000.000	75	61
Costumer 3	Gresik	East Java	40.000.000	80	64
Costumer 4	Badung	Bali	80.000.000	70	63
Costumer 5	Cimahi	West Java	20.000.000	80	63
Costumer 6	Semarang	Central Java	50.000.000	100	63
Costumer 7	Sidoarjo	East Java	25.000.000	80	65
Costumer 8	Karawang	West Java	40.000.000	75	63
Costumer 9	Jember	East Java	40.000.000	80	64
Costumer 10	Buleleng	Bali	50.000.000	80	63
Costumer 11	Sampang	East Java	80.000.000	75	61
Costumer 12	Pasuruan	East Java	75.000.000	80	68
Costumer 13	Bantul	Yogyakarta	30.000.000	75	64
Costumer 14	Tulungagung	East Java	50.000.000	100	69
Costumer 15	Banyuwangi	East Java	60.000.000	80	65
Costumer 16	Cirebon	West Java	40.000.000	90	68
Costumer 17	Malang	East Java	40.000.000	80	69
Costumer 18	Magelang	Central Java	50.000.000	75	59
Costumer 19	Purwakarta	West Java	40.000.000	75	69
Costumer 20	Nganjuk	East Java	80.000.000	80	65
Costumer 21	Indramayu	West Java	20.000.000	70	67
Costumer 22	Pati	Central Java	50.000.000	75	69
Costumer 23	Klaten	Central Java	25.000.000	80	64
Costumer 24	Palembang	South Sumatra	40.000.000	80	67
Costumer 25	Sumba Barat	East Nusa Tenggara	40.000.000	70	68
Average				79.4	65.1

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Figure 6. Comparison chart of recommendations based on admin assessments and CPI

The data also reveals that the variable weights within the fuzzy model play a crucial role in determining loan recommendations. The analysis indicates that the Empathy variable holds the highest weight at 0.572, followed closely by Achievement via Conformance at 0.524, while the Flexibility variable has the lowest weight at 0.085. By utilizing these weights, this study successfully established 1,024 fuzzy rule bases, which contribute to more accurate loan recommendations.

By integrating psychometric analysis with financial data, this research provides evidence supporting the application of the CPI in credit assessments, potentially reducing the risk of problematic loans by up to 20%. Through this approach, financial institutions are expected to make more informed decisions regarding loan provisions, ultimately enhancing financial stability within the online lending sector in Indonesia. Furthermore, the findings highlight the need to further explore additional factors that may influence the evaluation of prospective borrowers, such as their financial conditions and loan history.

The potential reduction of problematic loan risk by up to 20% is achieved through the accumulation process of model performance metrics. Model performance metrics are essential tools for evaluating the effectiveness of models in prediction and classification, particularly in online lending. Key metrics include accuracy, precision, recall, and F1 score, which measure the reliability of detecting bad loans. Additionally, AUC-ROC assesses the ability to distinguish between positive and negative classes, while the confusion matrix provides detailed insights into classification errors. Mean Absolute Error (MAE) and Mean Squared Error (MSE) are utilized in regression to measure prediction errors. The use of these metrics aids in comprehensively understanding model performance and identifying areas for improvement.

This table presents a comparison of credit recommendation data based on administrative assessments and improvements using the California Psychological Inventory (CPI) principles with fuzzy methods. It includes customer details, loan amounts, and loan percentages by both admin and CPI, highlighting differences and averages across 25 customers. This is shown in Table 6.

The comparison of loan percentages by Admin and CPI over 25 periods reveals distinct patterns of fluctuation and stability. Loans managed by Admin (blue line) exhibit high variability, with significant peaks occurring in periods 7 and 14. In contrast, loans managed by CPI (orange line) remain relatively stable and consistent within the 60–70 percent range throughout the entire period. Although Admin’s loan percentages are generally higher, they are notably unstable, reflecting significant volatility. On the other hand, CPI demonstrates a lower but steady loan percentage, indicating greater consistency in loan management. This suggests that CPI tends to adopt a more conservative or structured approach compared to Admin, as illustrated in Figure 6.

The author wishes to express gratitude to Universitas Trisakti for their support in providing funding for this research. Additionally, thanks are extended to the Online Loan Service for their assistance in supplying loan data for this study, as well as to all related parties who have contributed help and support throughout the completion of this research.