Evaluating Reputation of Internet Financial Platform: An Improved Fuzzy Evaluation Approach

Recent frequent “thunderstorm incidents” of the internet financial platforms (IFPs) have caused the panic of investors. In order to measure and reduce the investment risk of IFPs, the focus of this study is to evaluate the reputation of IFPs regarding investment risk. First, the reputation evaluation indicator system of IFPs is constructed from two dimensions of direct and indirect reputations.,en, based on this system, an improved fuzzy evaluation approach (IFEA) integrating the method of fuzzy comprehensive evaluation (FCE), the analytic hierarchy process (AHP), and the factor analysis (FA) are proposed for evaluating the reputation of IFPs. Finally, a case study based on the data of 20 peer-to-peer (P2P) lending platforms from “Home of Online Loans” (HOL) in China is used to illustrate the IFEA. Results show that the IFEA can reduce uncertainty and randomness in the determination process of indicator weight and membership degree and therefore accurately obtain the reputation level of IFPs and help investors make better decisions. Meanwhile, the key factors in determining the reputation of IFPs are identified, thereby improving the reputation level of the IFPs.


Introduction
With the increasing application of emerging information technology such as cloud computing (CC), big data (BD), and artificial intelligence (AI) in the financial field, Internet financial platforms (IFPs) have rapidly spread around the world [1]. IFPs include platforms of peer-to-peer (P2P) lending, crowd-funding, online banking, and supply chain finance [2,3]. e emergence of IFPs not only effectively broadens the business boundary of financial services but also promotes the effectiveness of optimal allocation of financial resources. However, the credit risk and liquidity risk are becoming more serious problems due to the cross-market operating characteristics of IFPs [4,5]. For example, because of malicious fraud, improper operation, and loss of contact, more than 6000 P2P lending platforms have gone bankrupt in China by the beginning of 2021, which brought huge economic loss to investors [6]. Besides, frequent "thunderstorm incidents" of IFPs such as the "Ezubao" event in 2015, the "Tuandaiwang" event in 2019 exposed the huge investment risks of IFPs. In this context, investors often encounter great investment risk in the area of the Internet finance.
As an invisible contract, reputation plays a positive role in reducing the investment risk of IFPs [7]. Since a good reputation can attract more investors to invest [8,9], IFPs often try their best to restrain their default behaviors for long-term benefits. It was proved that reputation had a positive impact on the establishment of the trust mechanism of the P2P lending market [10] and the reduction of the defaults of the P2P lending borrowers [11]. In addition, many third-party credit rating agencies have tried to measure the investment risk of IFPs from the aspects of reputation. For instance, the reputation indicator of P2P lending platforms created by "Home of Online Loans" (HOL), the credit reputation rating ranking list of the P2P lending platforms launched by "Wang Dai Tian Yan" (WDTY), and the reputation rating of the P2P lending platform proposed by "Rong 360" (R360). In practice, due to the information asymmetry between the IFPs and investors [12,13], investors can only choose bidding projects based on the information disclosed by IFPs. Besides, IFPs usually disclose information that is good for enhancing their reputation. In this case, investors' role is ineffective in the transaction process, and they only can make investment decisions based on the reputation of IFPs. us, it is necessary to establish a scientific evaluation system and effective approach for evaluating the reputation levels of IFPs and to reduce the investment risks for investors.
In recent years, the reputation problem of IFPs has attracted growing attention, but it is still in its infancy. First, most of the existing literature mainly focuses on the reputation of borrowers and investors in the IFP. ey pay more attention to the mechanism [14][15][16][17][18][19], influencing factors [20][21][22], and the measurement of reputation [23].
is study regarding with evaluating the reputation of the IFP itself has not been adequately presented in the available literature. Meanwhile, the reputation evaluation method concerning the ambiguity of evaluation results is relatively lacking. Second, the previous studies concentrate on constructing a reputation evaluation indicator system from the perspective of the direct reputation indicators [20][21][22]. e indirect reputation of IFPs has been ignored. However, because of the time lag characteristic of the direct reputation information [24], the current method based on direct reputation may delay the evaluation.
e indirect reputation information, such as the real-time evaluation by stakeholders of IFPs, can make up the time lag limitation of the direct reputation. us, the evaluation system for the integration of direct reputation and indirect reputation elements should be constructed. ird, for improving the objectivity and credibility of the reputation evaluation results of IFPs, a multiple criteria decision-making (MCDM) approach applying for evaluation of multiple attributes is developed to handle uncertainty and subjective vagueness during the decision-making process. Recently, several studies have used MCDM approaches, including decision-making trial and evaluation laboratory (DEMA-TEL), analytic hierarchical process (AHP), technique for order performance by similarity to ideal solution (TOPSIS), and so on, either independently [25][26][27] or hybridization of two or more MCDM approaches [28,29]. However, these MCDM methods ignored the comprehensive consideration of subjective and objective indicator weights. For example, in the TOPSIS, the weight is determined in advance, and its value is usually subjective. In the DEMATEL, the relative weight of the experts is usually not considered when summarizing the experts' subjective judgments into the group assessment. erefore, addressing these research gaps inspired us to propose a comprehensive evaluation approach based on fuzzy MCDM considering the objective indicator weights.
To address these research gaps, this study focuses on the reputation evaluation problem of IFPs. A reputation evaluation indicator system including 6 criteria and 24 indicators is constructed from the two dimensions of direct and indirect reputations. Next, an improved fuzzy evaluation approach (IFEA) is designed for reputation evaluation. In this approach, fuzzy comprehensive evaluation (FCE), analytic hierarchy process (AHP), and factor analysis (FA) are integrated to evaluate the reputation level of IFPs. e case study based on the data of 20 P2P lending platforms in China has been carried out to verify the effectiveness and applicability of IFEA. e contributions of this work include the following three points. (1) Direct and indirect reputations of IFPs are considered for constructing a reputation evaluation indicator system. e system not only fully considers the capability basis of IFPs (e.g., scale strength, financial performance, service quality, capital liquidity, and development potential) but also comprehensively examines the impact of the evaluation of stakeholders on the reputation of IFPs. (2) For evaluating the reputation of IFPs, IFEA is designed by the hybridization of three approaches (e.g. FCE, AHP, and FA), which expands the application of the traditional fuzzy MCDM approaches. Compared with other MCDM approaches (e.g., TOPSIS, DEMATEL, and AHP), the IFEA emphasizes the comprehensive consideration of subjective and objective indicator weights, which reduces uncertainty and randomness in the determination process of indicator weight and membership degree. (3) e reputation level and the impact of essential indicators on the reputation of IFPs are measured quantitatively. It is of great significance for investors to identify the platforms with high investment risks and to make better investment decisions. Moreover, it can also help managers to improve the reputation of IFPs by optimizing related factors. e rest of this study is organized as follows: Section 2 reviews the existing literature, which concerns the mechanism and influencing factors of IFPs, the reputation evaluation problem, and the FCE method. Section 3 constructs the reputation evaluation indicator system of IFPs. In Section 4, IFEA proposes the reputation evaluation of IFPs. Section 5 presents the case study and discusses the results. Section 6 concludes and provides directions for future research.

Literature Review
Since the investment risk of the internet finance increases, many researchers have paid attention to the reputation evaluation problem of the IFPs. is study focuses on three research streams; the mechanism and influencing factors of the reputation of IFPs, the reputation evaluation problem, and the FCE method.
First, a significant issue of this work is the reputation of IFPs. Although this issue is significantly critical, it is still in its early stage. In terms of the reputation mechanism in IFPs, Yang and Lee found that the reputation can significantly affect the trust of lenders on the P2P lending platforms [14]. Kuwabara et al. pointed out that reputation had a curve effect on the success rate of the P2P lending [15]. Lin et al. found that the network reputation of the circle of friends can restrain the default behavior of the P2P lending borrowers 2 Discrete Dynamics in Nature and Society [16]. Ding et al. proved that there was an effective reputation mechanism in the P2P lending market by analyzing the transaction data of 78,000 borrowers in the P2P lending platform "renrendai.com" [17]. Shi et al. found that the reputation of the P2P lending platforms played a direct or indirect role in investors' investment choices [18]. Davies and Giovannetti pointed out that reputation played an important role in the success of crowd-funding projects [19].
In terms of influencing factors of reputation, the influencing factors of direct reputation are often only concerned. For example, third-party credit rating agencies, such as HOL [20], WDTY [21], and R360 [22], calculate the reputation level of IFPs based on indicators such as transaction volume per month, average rate of return, platform background, leverage ratio, net capital inflow, and loan dispersion. Moreover, some other factors, such as capital inflow [30], capital adequacy ratio [31], and information transparency [32], are considered to have a significant influence on the reputation of the IFPs. Second, the reputation evaluation problem is another important stream in this study. Pang and Yang proposed a social reputation loss model for the disconnection of P2P platform borrowers and proved the disconnection proposition such as the gradual decline of the social reputation loss of borrowers with the delay of the disconnection time point [23]. Fang et al. proposed a beta-based trust and reputation evaluation system (BTRES) for the wireless sensor networks' node trust and reputation evaluation [33]. Panagopoulos et al. proposed a robust reputation system consisting of a new reputation measurement and attack prevention mechanism [34]. Feng et al. proposed a hierarchical and configurable reputation evaluation method based on collaborative filtering (CF) for evaluating the service reputation of the cloud manufacturing enterprises on CMFG service platform [35]. Zhang et al. proposed a novel and effective reputation evaluation method, which can calculate the global and dynamic reputation value of an enterprise by using a time-aware hyperlink-induced topic search algorithm [36]. Wang et al. proposed a reputation measurement method for cloud services based on feedback levels [37]. Dong et al. proposed a second-order reputation evaluation model [38].
ird, this study also contributes to the literature on the FCE method. e FCE method combines the fuzzy sets with the evaluation and converts the qualitative evaluation into a quantitative evaluation according to the membership theory of fuzzy mathematics [39,40]. In recent years, the FCE method is widely used in the field of economics and finance [41]. For instance, Chen and Wang used the intuitive fuzzy number to evaluate the performance of the lending project of the international financial organizations [42]. Guo et al. constructed an evaluation model with multiple selection evaluation sets and proposed an FCE method based on the operations of the interval numbers for evaluating the laboratory performance in the university [43]. Cao and Xiong proposed a quantitative model of the credit evaluation index based on the fuzzy analytic hierarchy process (FAHP) [26]. Li et al. proposed an evaluation model of financing credit for scientific and technological small-medium enterprises (STSMEs), which improved the AHP and FCE by introducing a cloud model [44]. Zhong developed a financial investment risk comprehensive evaluation model combining the AHP and the FCE methods [45]. Yu and Li proposed a method of the importance of design factors of product innovation considering customer demands. In this method, the priority ranking of design factors of product innovation from the perspective of customer demand is calculated through the gray correlation method and fuzzy TOPSIS [25]. Sangaiah et al. integrated the fuzzy decision-making trial and evaluation laboratory (DEMATEL) model and TOPSIS approach for evaluating global software development project outcome factors [28]. Shaverdi et al. developed a new financial performance evaluation framework for ranking Iranian petrochemical companies based on the fuzzy AHP and fuzzy technique for order preference by similarity to the ideal solution (TOPSIS) [29].
In conclusion, although the aforementioned literature discussed either reputation evaluation problem of IFPs or FCE method from different perspectives, there is still a limitation that needs to be addressed. e following conclusions can be summarized: (1) e majority of the extant literature regarding reputation evaluation problem of the IFPs focuses on the reputation mechanism or influencing factors. Besides, establishing the reputation evaluation indicator system focuses only on the influencing factors of direct reputation. In this study, the influencing factors of the indirect reputation of the IFPs are still considered as reputation evaluation indicators of the IFPs by comparing them with the HOL [20], WDTY [21], and R360 [22]. us, we construct the reputation evaluation indicator system based on the direct and indirect reputations.
(2) An empirical or quantitative approach relying on only clear, transparent, and easily quantifiable data of individuals or enterprises as the basis for reputation evaluation is popular in the existing literature. However, the results of the aforementioned studies [23,[33][34][35][36][37][38] ignore the uncertainty and ambiguity in reputation evaluation. In this study, an improved fuzzy evaluation approach is developed to evaluate the reputation of the IFPs. (3) In previous studies regarding the FCE method, the FCE method independently [42,43], the method combining FCE and AHP [26,44,45], the method combining FCE and TOPSIS [25], the method combining FCE, TOPSIS and DEMATEL [28], and the method combining FCE, AHP, and TOPSIS [29] are often developed for evaluation, but the combined method rarely includes FA. In practice, the AHP, TOPSIS, and DEMATEL rely on the subjective judgment of experts regarding the indicator weights and ignore the consideration of objective indicator weights. e objective indicator weights calculated by FA should be concerned. erefore, it is greatly beneficial to improve the evaluation method by integrating FCE, AHP, and FA.
Discrete Dynamics in Nature and Society

Construction of the Reputation Evaluation Indicator System on IFPs
With the existence of the information asymmetry, investors tend to choose IFPs with a good reputation when making investment decisions. In order to attract more investors, IFPs often disclose information to enhance their reputation. erefore, it is necessary to choose appropriate reputation indicators to quantify the reputation of IFPs.
Mohtashemi and Mui pointed out that reputation formation can be investigated from the two aspects of direct interaction experience and recommendation of other entities and, that is, direct and indirect reputations [24]. Based on a comprehensive analysis of studies on the impact of the basic information and transaction information on the reputation of IFPs, we divide the direct reputation evaluation indicators of IFPs into the following five categories. (i) Scale strength indicators, such as transaction volume per month, loan bid number, investment amount per capita, and loan balance. (ii) Financial performance indicators, such as total assets, asset-liability ratio, operating income, and registered capital. (iii) Service quality indicators, such as the average rate of return, information transparency, average loan term, full bidding period, and platform overdue loan rate. (iv) Capital liquidity indicators, such as the net capital inflow, capital adequacy ratio, loan dispersion. (v) Development potential indicators, such as the platform background, operating time, net profit growth rate, and operating revenue growth rate. However, since the direct reputation information is limited in terms of timeliness, feedback evaluation from other participants of Internet finance is often needed as the indirect reputation of the platform to make up for the lack of timeliness of the direct reputation information. e main participants of Internet finance include borrowers, investors, IFPs, and regulatory authorities. As such, the indirect reputation evaluation indicators of Internet financial platforms are as follows: (vi) Stakeholder evaluation for the platform, such as investors feedback score, regulatory authorities feedback score, borrowers feedback score, and peer platforms feedback score. Finally, the reputation evaluation indicator system including 6 criteria and 24 indicators was obtained.

IFEA for Evaluating Reputation of IFPs
In this study, IFEA integrating FCE and AHP with FA is developed for the reputation rating of IFPs. e combined method is based on the fuzzy comprehensive evaluation theory and comprehensive weighting method. e detailed steps of the evaluation process are shown in Figure 1. e multilevel decomposition to the evaluation question is carried on, and each level domain is established; the rating of reputation fuzzy evaluation is determined; the membership degree of each indicator to the corresponding comments is established and the fuzzy evaluation matrix is obtained; the group decision AHP method is used to determine the subjective weights of indicators; the method of FA is also used to determine the objective weights of indicators; the comprehensive weights of indicators are obtained according to the subjective and objective weights. e comprehensive evaluation value is obtained according to the indicator weight and the fuzzy evaluation vector.  Table 1). To solve the comparability problem of the different data, data standardization is usually required for indicators in the criterion layer i before data analysis. e indicator original data should be transformed into standardized values between 0 and 1 to eliminate the effect of indicators' dimension. Let x ki be the original value of the k th sample in the i th indicator, y ki be the standardized value of the k th sample in the i th indicator, and N be the number of samples.
e positive indicators mean that the higher original value of the indicator, the better reputation of the Internet financial platform is. en, the data standardized value y ki can be expressed by the following equation [48]: e negative indicators mean that the higher original value of the indicator, the worse reputation of the Internet financial platform is. en, the data standardized value y ki can be expressed by the following equation [48]: Standardize the qualitative indicators. According to the suggestion of senior managers and researchers familiar with reputation evaluation of Internet finance, the scoring criteria is formulated for qualitative indicators of IFPs, as given in Table 2.

Step 2: Determining the Rating of the Reputation Fuzzy
Evaluation. According to Li et al. [44], this study takes the grades of the reputation evaluation on IFPs as the comment set, with five levels of "excellent," "good," "general," "bad," and "poor." e interval of the 5-level scale corresponding to each indicator will be divided by using the normal distribution of the 5-level interval method. As shown in Figure 2, (a) and (b) are the domain division diagrams of positive and negative indicators of the reputation evaluation, respectively. e critical value of the rating 1-5 scale of the reputation evaluation indicator will be calculated based on the sample data by using the normal distribution of the 5-level interval method. e detailed classification criteria of positive, negative, and qualitative indicators regarding "excellent," "good," "general," "bad," and "poor" ratings are given in Table 3, where μ and σ represent the mean value and standard deviation of the indicator X i for all the IFPs in the sample data, respectively.  [46,47], HOL [20] Operating time X 18 e time when the platform is still operating normally so far Positive HOL [20], WDTY [21] Net profit growth rate X 19 e ratio of the net profit of the current period to the net profit of the previous period Positive Literature [46,47] Operating revenue growth rate X 20 e ratio of the increase in operating income of the current period to the total operating income of the previous period

Positive
Literature [46,47]  e membership relation of each indicator to the reputation alternative comment set is called the membership function K(x). e closer K(x) is to 1, the higher the membership of x to K. e closer K(x) is to 0, the lower the membership of x to K.
For the positive indicators, the calculation formula of the membership degree of the rating j comment is by the following equation: For the negative indicators, the calculation formula of the membership degree of the rating j comment is by the following equation:  Table-3 Building judgment matrix from expert decision group Aggregating the group judgment matrix by geometric mean method (GMM) Obtaining the weights of the subjective weight of the index X i Calculating the correlation coefficient r ij , and building the correlation coefficient matrix E Determining the number of common factors, and building the score coefficient matrix S of factors Calculating the objective evaluation coefficient, and obtain objective weight of the index X i  Discrete Dynamics in Nature and Society e membership degree of the rating j+1 comment is 1−K(x), where x represents the actual value of the indicators, and x j and x j+1 are the critical values of the two reputation levels adjacent to the actual value of the indicator. After calculating the membership degree of the comments on level j and level j+1, the membership degree of the other three comments was 0. e fuzzy evaluation matrix K formed by the membership degree is expressed by the following equation: where m ij represents the membership degree of indicator X i in the reputation level L j , and M X i represents the membership vector of the indicator X i .

4.4.
Step 4: Calculating the Subjective Weight of the Indicator by Applying AHP. e group decision AHP method is developed on the basis of traditional AHP [49]. e basic idea is to ask a group of experts to give a judgment matrix for the same indicator attribute based on the premise that the hierarchy structure has been established. erefore, in order to avoid the subjective weight of indicators being influenced by the subjective assumption of a single expert, the group decision AHP is adopted to determine the subjective weight of each reputation evaluation indicator in this study.
Let c 1 ij , c 2 ij , . . . , c h ij be the different judgments of h experts in the group on the importance of indicator i and j of Internet financial platform. e 9-point scale method is adopted to form judgment matrix C k � (c k ij ) n×n , where 1 ≤ k ≤ h. e valuation rule of expert k on the comparison scale c k ij between indicators X i and X j is given in Table 4. In this study, the geometric mean method (GMM) is used to aggregate the group judgment matrix C � (c ij ) n×n . Each element c ij is calculated by the following equation: According to the following equation, the maximum eigenvalue λ max and the eigenvector W s of the judgment matrix C are calculated: where W s � (α 1 , α 2 , . . . , α i , . . . , α n ), and α 1 , α 2 , . . . , α i , . . . , α n are the components of the eigenvector W s .
To check the consistency of the judgment matrix C, CI is first calculated by the following equation.
CI is an indicator used to measure the amount (degree) of deviation from consistency in a judgment matrix. en, the random consistency ratio CR is calculated by the following equation:

Poor
Bad General Good Excellent Discrete Dynamics in Nature and Society 7 where RI is called the random indicator and is used to reconcile the different requirements of related CI. In this study, if CR < 0.1, the judgment matrix satisfies the requirement of consistency, and the component α i of the eigenvector W s is the subjective weight of the indicator X i .
Otherwise, the judgment matrix should be modified.

4.5.
Step 5: Calculating the Objective Weight of the Indicator by Applying FA. e FA is to reduce the variables with complicated relations into a few comprehensive factors by studying the dependence relation inside the correlation matrix and adopting the idea of dimensionality reduction [50]. In this study, the collected data were processed by FA to obtain the objective weight of each indicator. r ij is the correlation coefficient between indicator X i and X j ; x ki is the value of indicator X i of Internet financial platform k; x i is the mean of the indicator X i ; x kj is the value of indicator X j of Internet financial platform k; x j is the mean of the indicator X j ; and r ij is calculated by the following equation: e correlation coefficient matrix E is calculated by the following equation: e eigenvalues of the matrix E are λ 1 , λ 2 , . . . , λ n , and the eigenvectors of the matrix E are μ 1 , μ 2 , . . . , μ n . So, the load matrix A of the factor is expressed by the following equation: A � a 11 a 12 · · · a 1n a 21 a 22 · · · a 2n ⋮ ⋮ ⋮ ⋮ a n1 a n2 · · · a nn e variance contribution rate of the factor j is g j ; then, g j � n i�1 a 2 ij , j � 1, 2, . . . , n.
When p j�1 g j / n j�1 g j ≥ 85%, that is, the cumulative variance contribution rate was more than 85%; then, the number of eigenvalues is selected as the number p of common factors. Next, the score function of each factor is obtained by the regression method. Finally, the score coefficient matrix S of factors is expressed by the following equation: e objective evaluation coefficient of each indicator is calculated by the following equation: where e i represents the objective evaluation coefficient of indicator X i ; and S ij represents the score coefficient of the indicator X i with respect to factor j. Next, the objective evaluation coefficients of each indicator are normalized, as shown in the following equation.
where β i is the objective weight value of the indicator X i .

Step 6: Calculating the Reputation Evaluation Value of
IFPs. e subjective weight α i is obtained by the group decision AHP method in Section 4.4, and the objective weight β i is obtained by FA in Section 4.5. e normalized formula of multiplication is used to determine the comprehensive weight of each indicator. e comprehensive weight w i of indicator X i is expressed by the following equation: where n is the number of indicators. e fuzzy comprehensive evaluation vector P is obtained by the indicator weight w i and the fuzzy evaluation matrix K, where P � (p 1 , p 2 , p 3 , p 4 , p 5 ). Based on the aforementioned "five levels" of reputation, the score set D for reputation evaluation is obtained. In this study, we set D � (100, 80, 60, 40, 20) T , and the reputation evaluation Table 4: Valuation of c k ij with a scale of 1-9. Scale Importance level 1 Reputation indicator X i is as important as X j 3 Reputation indicator X i is slightly more important than X j 5 Reputation indicator X i is obviously more important than X j 7 Reputation indicator X i is strongly more important than X j 9 Reputation indicator X i is far more important than X j 2, 4, 6, 8 Between two importance levels Reciprocal If indicator X i compares with X j , the scale a ij � 1/a ji 8 Discrete Dynamics in Nature and Society value R of the Internet financial platform is expressed by the following equation: R � P × D � p 1 , p 2 , . . . , p 7 ×(100, 80, 60, 40, 20) T � 100p 1 + 80p 2 + · · · + 20p 5 .

(17)
We determine the reputation level of IFPs according to the calculation of the reputation evaluation value. e detailed rating rules are given in Table 5.

Data Sample.
In this study, the transaction data of the P2P lending platforms are selected as samples to verify the performance of IFEA. e octopus data collector was used to capture (obtain) the monthly transaction data of 20 P2P lending platforms during the period from January to June 2019 (data capture time: July 24, 2019) from HOL [20]. Data include net capital inflow, transaction volume per month, loan amount per capita, borrower per month, operating time, loan balance, registered capital, investment amount per capita, platform background, platform rate of return, average loan term, and other information. By querying the financial reports of 20 P2P lending platforms in 2018, we can obtain data such as total assets, asset-liability ratio, operating income, registered capital, net profit growth rate, and operating income growth rate. From the interactive community of HOL, the qualitative evaluations of the P2P lending platform from participants of the Internet finance are obtained. e positive and negative indicator data are standardized according to equations (1) and (2); for qualitative indicator data, it is standardized according to the scoring rules of qualitative indicators in Table 2. e standardized result of the reputation evaluation indicators data of the P2P lending platforms is given in Table 6. Due to space limitation, only the processing results of some indicators of some platforms are given. Tables 6 and 3, each reputation evaluation indicator of IFPs is divided into five ratings: "excellent," "good," "general," "bad," and "poor," and it calculates the critical value of each rating of the indicator. e following examples will demonstrate the calculation process of the critical value of the rating 1-5 scale of positive, negative, and qualitative indicators.

Calculating the Critical Value of the Rating and Membership Degree of Indicators. According to
e critical values of the rating 1-5 scale of positive indicators are divided as follows: take transaction volume per month X 1 for example. e mean value of indicator X 1 of 20 P2P lending platforms is 1201222.3, and the standard deviation is 952327.0. According to the calculation formula of the critical value of the positive indicator rating in Table 3 e critical values of the rating 1-5 scale of the negative indicators are divided as follows: for asset-liability ratio X 6 , the mean value of indicator X 6 of 20 P2P lending platforms is 0.499, and the standard deviation is 0.297. According to the calculation formula of the critical value of negative indicator rating in Table 3 By analogy, the critical value of other indicators is calculated according to the above rules. e critical values of the rating 1-5 scale for all 24 indicators are given in Table 7.
According to the critical value of the rating 1-5 scale of each indicator in Table 7 and the membership function equations (3) and (4), take the internet financial platform PF1 as an example to calculate the membership degree.
For the membership degree of the positive indicator, the value of the indicator X 1 of PF1 is 2007634.4 thousand yuan, so the indicator rating is between "excellent" and "good." us, according to equation (3), the membership degree of an "excellent" rating of this indicator is K x 1 � ((2007634.4 − 1963083.9)/(2915410.9 − 1963083.9)) � 0.047, and its membership degree of the "good" rating of this indicator is 1 − K x 1 � 0.953. e membership vector of the indicator X 1 of PF1 is M X 1 � (0.047, 0.953, 0, 0, 0). e membership vector of other positive indicators of PF1 can be obtained similarly.
For the membership degree of a negative indicator, in the case of X 6 of PF1, the value of the indicator is 44.57%, which is less than the critical value of the "general" level 73.65% and more than the critical value of "good" level 44.01%. According to equation (4), the membership degree of "good" rating of this indicator is K x 6 � ((73.65% − 44.57%)/(73.65%− 44.01%)) � 0.981, and the membership degree of "general" rating of this indicator is 1 − K x 6 � 0.019. e membership vector of the indicator X 6 of PF1 is M X 6 � (0, 0.981, 0.019, 0, 0). e membership vector of other negative indicators of PF1 can be obtained in the same way.
In summary, according to aforementioned rules, the membership degrees of all the 24 indicators of the PF1 are given in Table 8.

Calculating the Subjective Weight of Indicators.
In order to achieve the reputation evaluation indicator system in Table 1, 10 experts including 3 associate professors and 7 doctoral candidates in the field of Internet finance are selected to score the importance of each reputation evaluation indicator according to the 1-9 scale method in Table 4. e comparative judgment matrix of the 10 experts was obtained. According to equation (6), the indicator comparison judgment matrix of the 10 experts was assembled. e judgment matrix and weights of the criterion layer indices are given in Table 9.
e judgment matrix and weights of the indicator layer indices are given in Tables 10-15.
Whereas, Tables 10-15 are the judgment matrices and weights of indicator layer indices in criterion B 1 , B 2 , B 3 , B 4 , B 5 , and B 6 , respectively. e subjective weight of indicator X 1 is α 1 � 0.2502 × 0.3626 � 0.0907, the subjective weight of X 2 is α 2 � 0.2502 × 0.2382 � 0.0596, and the subjective weight of X 5 is α 5 � 0.2578 × 0.2650 � 0.0683. All the subjective weights of the 24 indicators are given in Table 16.

Calculating the Objective Weight of Indicators.
According to the data of the 24 indicators of the 20 P2P lending platforms, Bartlett sphericity and the KMO test in SPSS20.0 statistical analysis software are used to verify whether the original variables are suitable for the factor analysis. en, 8 common factors are extracted according to the gravel analysis diagram, as given in Table 17.
e score coefficient matrix of the 8 factors is obtained by regression calculation by the SPSS software. e results are given in Table 18.
According to equation (14), the score coefficient matrix of the factors is calculated to obtain the objective evaluation coefficient of the indicator. In case of X 1 , the detailed steps of the objective weight calculation process of this indicator are demonstrated as follows.
Similarly, the objective evaluation coefficient of the other indicators can be obtained.
Meanwhile, the objective weight of the indicator is obtained by normalizing the objective evaluation coefficient according to equation (16). e objective weight of indicator X 1 is β 1 � 0.0453. e objective weights of other indicators are given in Table 16.

Fuzzy Comprehensive Evaluation.
According to equation (16), the comprehensive weights of indicators are obtained. As given in Table 16, the higher the comprehensive weight values of the reputation evaluation indicators such as the "asset-liability ratio," the "transaction volume per month," the "operating income," and the "total assets rank," the greater their impact on the reputation of IFPs.
According to Table 16 e first-order fuzzy synthesis vector from the indicators layer to the criterion layer is calculated. Taking PF1, for example, the first-order fuzzy synthesis vector of the scale strength is as follows: Discrete Dynamics in Nature and Society       Similarly, the first-order fuzzy synthesis vector of the financial performance is P 2 � (0, 0.3391, 0.3896, 0.2713, 0), the first-order fuzzy synthesis vector of the service quality is P 3 � (0.2452, 0.1514, 0.3672, 0.0465, 0.1897), the first-order fuzzy synthesis vector of the capital liquidity is P 4 � (0, 0.3708, 0.6292, 0, 0), the first-order fuzzy synthesis vector of the development potential is P 5 � (0.2328, 0.4332, 0.2940, 0.0400, 0), and the first-order fuzzy synthesis   vector of the stakeholder evaluation for the platform is P 6 � (0, 0.8555, 0.1445, 0, 0).
Next, the second-order fuzzy synthesis vector from the criterion layer to the target layer is calculated as follows: erefore, the reputation level of the platform PF1 belongs to the "excellent" rating with a membership degree of 0.0784, the membership in the "good" rating is 0.4216, the membership in the "general" rating is 0.3710, the membership in the "bad" rating is 0.1042, and the membership in the "poor" rating is 0.0247. According to equation (17), the final reputation comprehensive evaluation value of PF1 is obtained.  According to the rating rules of the reputation level in Table 5, it can be determined that the reputation level of the Internet financial platform PF1 is "good." e reputation levels of the other 19 IFPs are given in Table 19.
e results in Table 19 provide that the reputation level of the 20 IFPs is between "good" and "low." Six platforms are in the reputation rating of "good," 11 platforms are in the reputation rating of "general," and 3 platforms are in the reputation rating of "bad," and it has good rating differentiation. e three IFPs with the "bad" reputation level (PF9, PF18, and PF20) are consistent with the reputation status quo of the platforms, respectively. For example, according to the financial report of the platform PF9 in 2018, it is found that the scale strength of the platform is relatively weak. e total assets and operating income are relatively low compared with other platforms. e assetliability ratio is relatively high, and the profit growth rate is negative. In terms of capital liquidity, the net capital inflow is negative, and the capital adequacy ratio is lower than other platforms. In addition, the existing online information media disclosed that PF9 had been investigated in March 2020 due to the illegal fund-raising, which further verified the effectiveness and adaptability of the evaluation results of the IFEA.
To further explore the impact of various reputation evaluation indicators on the reputation of the PF9, the impact of each reputation indicators on the reputation evaluation value of PF9 is calculated. As shown in Figure 3, the order of factors of reputation of PF9 is the indicators X 6 , X 1 , X 7 , and X 5 . erefore, if managers want to improve the reputation of the PF9, the "asset-liability ratio" of PF9 should be reduced, and the "transaction volume per month," "operating income," and "total assets" of the PF9 should be enhanced.
In this work, Table 16 provides that the weights of "assetliability ratio," "operating income," and "total assets" are the highest in direct reputation evaluation indicators, which indicates that the financial performance is crucial for direct reputation of the IFPs. Besides, the weight of "investors feedback score" is the highest in indirect reputation evaluation indicators, which indicates that the evaluation of investors is attached more important for indirect reputation of the IFPs.
Moreover, the reputation level of the entire Internet finance industry can be obtained by appropriately expanding the sample based on IFEA. Besides, the results can provide decision-making references on the investment of Internet finance for the investors. Meanwhile, the results of the IFEA can also help the managers find ways to improve the reputation of the platform. In detail, the financial performance and evaluation of investors have a great influence on the direct and indirect reputations of the IFPs. us, the managers can improve the reputation level of the platform by optimizing these factors. 5.6. Discussion regarding the Results of IFEA, TOPSIS, and DEMATEL. In this study, IFEA-integrated FCE, AHP, and FA is designed for evaluating the reputation of the IFPs. In this subsection, IFEA is compared with TOPSIS [29] and DEMATEL [28] to validate its performance in terms of the comparative analysis of the 24 reputation indicators. e overall importance weights and ranking of the reputation indicators among the IFPs obtained by applying TOPSIS, DEMATEL, and IFEA are given in Table 20. e results of the IFEA show that the weights and ranking of the reputation indicators X 6 >X 1 >X 7 >X 5 >X 3 >X 2 are the highestranking among the 24 indicators. Similarly, the results of TOPSIS show that X 1 >X 5 >X 3 >X 12 >X 2 >X 17 are highly significant indicators. e results of DEMATEL show X 6 >X 12 >X 3 >X 2 >X 5 >X 4 as the highest priority reputation indicators. Subsequently, the relative weights obtained by IFEA are compared with TOPSIS and DEMATEL. We can   find that the indicators X 1 >X 5 >X 3 >X 2 have a significant impact, and they are consistent with TOPSIS, the indicators X 6 >X 3 >X 2 have significant impact, and they are consistent with DEMATEL too. In other words, the highly significant indicators obtained from the IFEA are almost consistent with the TOPSIS and DEMATEL, which indicates that IFEA has a great performance for displaying the effectiveness of the reputation indicators. Moreover, Kendall's coefficient of concordance computed for TOPSIS, DEMATEL, and IFEA rankings is 0.673, which indicates a very high correlation among rankings. erefore, we can conclude that the IFEA is a robust and efficient approach for evaluating the reputation of IFPs. e evaluation results of IFPs improved by the IFEA comprehensively consider the objectiveness and fuzziness of the results, which can reduce uncertainty and randomness in the determination process of the indicator weight and membership degree. By emphasizing these reputation indicators, the managers can obtain the key factors in determining the reputation of IFPs.

Conclusions and Future Research
e focus of this study is to design a reputation evaluation approach for IFPs. Since the credit challenge of IFPs commonly exposed in China recently, it is urgent and beneficial to construct a reputation evaluation system for the Chinese IFPs to reduce the investment risk and to help investors make better decisions.
e research results are shown as follows: (1) e reputation evaluation indicator system of the IFPs, which includes 6 criteria (e.g., scale strength, financial performance, service quality, capital liquidity, development potential, and stakeholder evaluation for the platform) and 24 indicators, is constructed from the two dimensions of direct and indirect reputations. e results of the case study show that this system can more comprehensively reflect the reputation levels of the IFPs, and the financial performance and evaluation of investors have a great influence on the direct and indirect reputation of the IFPs, respectively.
(2) e methods of FCE, AHP, and FA are integrated to develop an improved fuzzy evaluation approach (IFEA) for evaluating the reputation of IFPs. Results of the case study are presented to show that IFEA can significantly distinguish the reputation level of the IFPs and effectively identify the IFPs with high investment risks. e reputation evaluation results of IFPs improved by the IFEA comprehensively consider the objectiveness and fuzziness of the results compared with other MCDM approaches (e.g., TOPSIS and DEMATEL), which can improve the robustness and closeness with the reality of the evaluation results. With the reputation evaluation results of IFPs, which is more objective and reliable, the investors can make the correct investing decisions and reduce the investment risk of Internet finance. Moreover, it can also help managers to find out the key factors of reputation in determining the reputation of IFPs, such as asset-liability ratio, operating income, total assets, and investors feedback score, thereby improving the reputation level of IFPs by optimizing these factors.
is study makes several contributions to the field of the MCDM approach and its applications. First, the IFEA is designed for evaluating the reputation level of IFPs, which is easy to operate and can help investors make the better investing decisions. Second, the IFEA considers the uncertainty of a complex large group decision-making and combines the subjective weighting method and objective weighting method during the indicator weight in decisionmaking problems. It not only overcomes the shortcomings of the traditional subjective factors' empowerment method but also takes full account of objective factors. ird, the IFEA expands the application of the traditional fuzzy MCDM approaches. It can not only evaluate the reputation of IFPs but also apply to reputation evaluation of other industry platforms (e.g., e-commerce platform and logistics information platform).
is study can be further extended. e reputation evaluation indicators are summarized based on literature and the related reputation evaluation indicator system of the third-party credit rating agencies in this work. Since the factors influencing the reputation of IFPs varies with the change of external environments, it is recommended that big data can be used to discover the potential factors. Besides, the method of artificial intelligence, such as the support vector machine (SVM) and neural network (NN), can also be

Data Availability
e data used to support this research article are available from the first author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.