Identifying the Factors Affecting Prioritization of Granting Facilities to Bank Customers and Ranking them Using VIKOR Rough Method (Case Study: Tejarat Bank)

- Banks should optimally allocate their financial resources to qualified customers. Optimal allocation of financial resources provides the conditions for the banks’ economic activity continuation. To grant facilities to customers, the factors affecting the granting facilities to banks’ customers need to be properly identified. In this study, Delphi method was used to identify the factors affecting granting facilities to banks' customers. Then, using the VIKOR Rough Theory, these customers were prioritized aimed at granting facilities to them. The results showed that the factors of location of the facilities granted and the type of the facilities use (use of received facilities in the subject of the regulated contract), history of activity, value of customer capital, type of collateral, having previous liabilities, good reputation of the applicant, and estimated return on capital, respectively, were identified as the most important factors in granting facilities. Finally, the customers were ranked by VIKOR Rough method to receive the banking facilities .


Review of Literature
Assessing and granting of facilities is a theoretical subject and its non-quantitative nature makes it difficult to accurately measure and prove it in credit decisions. Credit decisions, like all techniques, the basic criteria provided by experts are used. These criteria are not fixed scientific rules and are the product of human thought and theory and subject to change (Shahgholian et al., 2011). Applying these criteria ensures the return of the allocated resources and expected profits within a given period. Considering each of the credit criteria individually is not a reliable base for taking credit decisions, but a set of criteria that can provide a reliable basis for making decisions needs to be considered. Additionally, granting of facilities requires sufficient skill and experience. To achieve the principle of resources return, accuracy and precision based on the necessary criteria is needed when granting facilities. Non-organized rules for granting facilities pave the way for the approval of projects that are not qualified. Research suggests that criteria needed for granting vary across countries. Table 1 summarizes the criteria in the three countries of Australia, Japan and Norway (Aghaei, 2009). Table 1: The criteria for granting facilities in Japan, Australia and Norway (Aghaei, 2009) country criteria Banking facilities are the main outputs of banks through which the wandering liquidity of society is injected into defined and purposeful economic bases. It means that a bank with equipment of resources (including equity and types of deposits or other liabilities) consumes them for pre-specified purposes (Amiri & Amiri, 2015). In other words, it is assumed that a bank will make a profit by creating these revenue-generating assets at the end of each financial period and expand its business by accumulated profits and new resources, including increasing capital or creating other liabilities. However, in developmental banks, which are usually set up by government capitals, achieving national and economic goals is more important than bank profitability (Amiri & Amiri, 2015). Rough set theory was developed in the 1980s by Pawlak. This theory states and examines the issues in which there is uncertainty and ambiguity. It is commonly used to find inconsistencies and relationships (Pawlak et al., 2003). The most important characteristics of this theory are: -Optimized algorithm for finding patterns in data.
-Finding relationships that are not discovered by statistical methods.
-Ability of using qualitative and quantitative information.
-Finding a minimal set of data that are useful for classification (such as minimizing dimensions and number of information).
-Assessing the importance of data. Generating decision-making rules from information (Pawlak et al., 2003) VIKOR is a Serbian abbreviation of Vlse Kriterijumsk Optimizacija Kompromisno Resenje which is one of the most widely used models in decision making and selecting top option. This model has been developed since 1984 on the basis of a collective agreement (consensus) method with conflicting criteria and is generally used to solve discrete problems. This method has been developed for multi-criteria optimization of complex systems. This method focuses on the classification and selection of a set of options and identifies adaptive responses to a problem with conflicting criteria so that it is able to help decision makers achieve a final decision. Here, the adaptive answer is the nearest justified answer to the ideal answer (Asgharpour, 2011). Khamse et al. (2007) developed an expert system to grant loans to customers. Their expert system is based on quantitative and qualitative factors. Che et al. (2010) in Taiwan presented a DEA-FAHP approach for making decision on bank loans. They evaluated the performance of companies by FAHP method. The weight of criteria and data of companies were obtained using fuzzy hierarchy method. This article develops a dynamic correction general equilibrium model that includes a financial sector to analyze the effects of liquidity shock and credit risk on the Brazilian economy. Using data for the Brazilian economy from 1995 to 2009, the parameters of this structure were measured through Bayesian methods. Impulse response distribution has been calculated to describe the dynamic effects of external shocks. The results showed that the credit risk is almost the same and the default risk depends on the structural characteristics. Kighobadi and Khodami (2013) used data mining of financial statements for granting facilities. The way of making decisions about granting facilities for customers is important since lack of accurate evaluation of customers can lead to past maturity and delayed debt , reduced banks capacity to grant facilities, and finally bad debts. This study was conducted to model the validation of customers in the bank using neural network, decision tree and support-vector machine methods. For this purpose, financial and qualitative data were collected from a random sample of 300 customers (218 creditworthy customers and 82 non-creditworthy customers) received credit facilities from legal companies in Melli Bank branches of Tehran. In this research, after reviewing the credit records of the customers, 31 explanatory variables were evaluated and the results showed that data mining techniques are highly efficient for customer validation and neural network model prediction performance is better than other models. Castro (2013) evaluated the macroeconomic factors in credit risk in the banking system. In this paper, the relationship between economic progress and the risks of bank facilities in a specific group of countries (Greece, Ireland, Portugal, Spain and Italy) affected by adverse economic and financial conditions was analyzed. Using dynamic data approaches, it was concluded that bank credit risk is significantly affected by the macroeconomic environment. The results showed that when gross domestic products (GDP) growth and the stock and housing price index change, unemployment rate, interest rate and credit growth will be also positively affected by a concept of real exchange rate. Imbierowicz and Rauch (2014) evaluated the relationship between liquidity risk and credit risk in banks. They evaluated the relationship between two main sources of bank risk default, including liquidity risk and credit risk. They used a sample of almost all US commercial banks in the period 1998-2010 to evaluate the relationship between these two sources of risk. The results revealed that none of risk groups have significant inverse economic relationship. However, they do affect the probability of banks' predictions. Both risks increase banks' probabilities separately, the effect of their interaction depends on the general level of banking risk and can exacerbate or reduce the risk of default. Karimi et al. (2015) examined the factors affecting the credit risk of commercial bank customers. This article evaluates the factors affecting the banks' delayed loans and credit risk of real customers of Tejarat Bank branches of Neka. The data needed to analyze this relationship were extracted from 2,545 real customer records received during 2011 to 2002 and logistic regression was used to evaluate the data. The results of this research revealed that the duration of the facilities, the rate of the facilities, the type of collateral and the type of facilities have a significant effect on the receivables and the obligatory or no-obligatory nature of facilities and the rate of facilities had no significant effect on the probability of default. The probability of non-repayment increases with reducing repayment period and increasing facilities rates. Moreover, with regard to the types of collateral for granting loan, the greatest effect in reducing the probability of non-repayment is related to the bank deposit and the least effect is related to promissory note. In addition, the greatest effect on increasing the possibility of non-repayment is related to loan facilities and the least effect is related to participation facilities. Manab et al. (2015) investigated the factors affecting credit risk in Malaysia. The aim of this study was to investigate the factors determining the credit risk and to evaluate the effect of earnings management on credit risk prediction. The results revealed that the liquidity ratio in determining credit risk was moderated before and after earnings management. Moreover, the productivity ratio in the non-moderated model was significant; while, the profitability ratio in the moderated model was significant. Amiri and Amiri (2015) performed technical and economical evaluation of loan applications using fuzzy analytic network technique. In this study, effective criteria in evaluating loan applicant projects were identified and analyzed and a model was presented to evaluate the projects. In the evaluation section, using the survey form, the pairwise comparisons matrix, and the fuzzy metric network analysis method, the criteria weights were determined and by determining the value of each criterion, the result of each criterion was obtained. Turan (2016) evaluated the factors affecting credit in banking. Banks face the problems of the payment of loans that is a serious risk for them. Hence, banks effectively manage risk. Credit risk is more commonly recognized as the potential risk that a bank granting the facilities will not be able to meet its repayment in accordance with the agreed terms. The banks that manage risk effectively evaluate their risks in details.
The banks must use the efficiency of external funds since banking activities are determined by external budgets.
Banks give credit to their customers to receive their funds. Banks are also exposed to credit risk. Credit risk is close to the potential return on capital. The results of the studies showed that credit risk is the most important risk for banks. Hierarchy analysis as one of the multiple criterion decision making techniques is used in the evaluation of these criteria. At the end of the study, the weights of the factors affecting credit risk were found. Ghenimi et al. (2017) investigated the effects of liquidity risk and credit risk on bank stability. The global financial crisis has caused a series of bank failures. This study investigates the main sources of bank fragility. This study used a sample of 49 banks in the MENA region during 2006-2012 to investigate the relationship between credit risk and liquidity risk and its effect on bank stability. The results revealed that credit risk and liquidity risk were not inversely associated with remaining time. However, both risks affect the stability of the bank separately and their interaction causes bank instability.

Methodology
The current research is applied in terms of objective. It is an applied study as it uses scientific rules and principles and seeks to solve a problem on the one hand (Khaki, 2008) and identify the factors affecting the granting of facilities and the ranking of the customers for the granting of facilities on the other hand. It is also considered a field study in terms of method. In this paper, the previous data and the Delphi method are used to identify the key and effective factors in granting facilities for bank customers. In the first step, the most frequent factors are selected from previous studies and the important factors are identified based on bank experts' opinions. Then, using the Delphi method, the most important factors affecting the granting of facilities will be identified among all the factors. In the Delphi method, in order to identify the factors affecting the granting facilities to customers by banks, a checklist of these factors is extracted from previous studies and classified using experts' opinions. A list of factors is provided to the banking experts through a questionnaire and they are asked to identify the key and important factors affecting the granting of facilities to banks' customers. In this step, only the selection of key factors is considered. By collecting questionnaires and summarizing the experts' opinions in three rounds, the key factors are finally selected. Then, using the pairwise comparisons questionnaire, the experts' opinions are collected for pairwise comparison of factors and the opinions are pooled and finally the effective weight of each factor affecting granting of the facilities for customers is obtained. In this step of the research, the customers who have received bank facilities in the past will be ranked using the identified factors and their effective weights and Rough VIKOR method to demonstrate the effectiveness of this method.

3-1-AHP Rough steps for factors weighting
AHP is widely used as one of the most popular methods in various decision-making issues, especially in weighting of factors. AHP can measure preferences' consistency, control tangible and intangible criteria, and manage decisions about subjective judgments. Given the uncertainty and ambiguity of decision-making, this research introduces the Rough number to combine with the AHP to collect individual judgments and calculate the relative importance of each factor. The AHP Rough method is described below (Zhu et al., 2015).
Step 1: Matrix of K th paired comparisons is defined as matrix (1) )1( B So that is the k th expert judgment for comparing factor i with factor j. m is the number of experts and n is the number of factors.
Step 2: The pairwise comparisons of the experts are examined in terms of inconsistency rate by Expert Choice software and if the inconsistency rate is less than 0.1, the pairwise comparison is consistent, and if it is greater than 0.1, the pairwise comparison numbers should be corrected.
Step 3: In this section, to combine the personal judgment of the experts, the geometric mean method is proposed as relation (2), since it retains the inverse feature of the pairwise comparative matrices without violating Pareto principles (Forman & Peniwati, 1998).
Thus, M rough pairwise comparison is formed as follows: Step 4: Calculating the interval weight of each factor using the following equations: There are K decision makers whose opinions are equally important in the final decision (k = 1,2,…, K) There are m options for selecting (i = 1,2,…, m) There are n factors / indicators for decision making (j = 1,2,…, n) The method steps: The first step is to form an individual decision matrix using the opinions of bank experts. In matrix (1), the rows indicate the options that are the past customers received the facilities and the columns are the status of key factors in granting facilities to customers.
Where is the function of option i in relation to the criterion j for the expert k. Then, the group decision matrix is formed as matrix (7).
Step 2: Transforming component in the matrix F to the Rough number to form the F Rough group evaluation matrix using equations (9) and (10).
Thus, can be shown as a Rough number defined by its lower limit as equations 11 and 12: yij are the low approximation and high approximation components for k. and are the number of components that fall into the low approximation and the high approximation of , respectively. The RN ( ) can be determined by the following equation (13).
Where and are the lower limit and the upper limit of the RN ( ) in the decision matrix k. Therefore, a set of rough numbers in the form of a relation (14) can be formed. , respectively, and m is the number of experts. Then, we can form the F Rough group decision matrix as matrix (18).
Step 3: Ideal positive * and negative options are determined using the rules of relations (19) to (20). If j criterion is a profit type, the ideal positive and negative values will be in the form of equations (19) and (20).
If the criterion is a loss type, the ideal positive and negative values will be in the form of equations (21) and (22).
Step 4: In this step, the value of the utility index Si and the regret index Ri of the options are calculated using equations (23) to (26). It should be noted that the weight of the factors was determined in the identification step. In each formula, the first part of the formula corresponds to the profit type criteria and the second part corresponds to cost type criteria, that in the absence of any of them, the corresponding value would be zero. Step 5: The VIKOR Q index is calculated based on the equations (27) and (28). First, V that is a number between zero and one must be determined depending on the decision maker's opinion. V is a weight for the maximum group utility strategy, which is usually considered as 0.5.
Step 6: The descending ranking of options based on VIKOR Index value, utility value, and regret value (Huang et al., 2009).
Step 7: Selecting the best option, with the lowest Q, will be achieved if the following two conditions are met (Rao, 2012): Condition 1 (The acceptance characteristics): )33 ( 1.2 1 1 So that A [2] is the option ranked second based on the lowest Q value, A [1] is the best option with the lowest Q value and m the number of options (Zhou & Tian, 2008). Second condition (The acceptance stability in decision making): The option A [1] must also have the best rank in Si or Ri or both. This solution is consistent throughout the decisionmaking process, which can be in three forms: "voting with majority rule" (when v> 0.5 is needed) or "by consensus" (v = 0.5) or "by opposite vote"(v <0.5). If one of the above conditions was not met, a set of compromise solutions is suggested as follows: 1-If only the second condition is not met, option A [1] and A [2] or 2-If the first condition is not met, option A [1] , A [2] and ... and A [k] . (Rao, 2012) A [k] is an option in the position of k that equation ½ is true for it.

Data analysis
In this research, the factors were identified through interviews with experts and questionnaire (Delphi method). The factors were identified in three stages using Delphi method. Based on past studies, research literature, interviews, and online completion of questionnaires by 32 experts and implementing the first round of Delphi, a total of 30 factors were identified. These factors are listed in Table (1). Type of facilities granted Karimi et al. 2015 Additionally, at the end of the first round, the respondents identified other factors that are effective in granting banking facilities. These factors include location of the facilities granted and type of using the facilities in that region, financial transparency, work honesty, considering the professional ethics, capacity assessment, short term facilities and customer personality. In the second round, the experts' opinions were collected through a questionnaire. A total of 37 factors were used to select the factors that are most important in this step. All items were deigned on the 5-point Likert scale based on their importance (very high=5, high=4, moderate=3, low=2 and very low=1) to determine the importance of each of the factors. In this step, the considered level of agreement for selection of the factors based on the opinion of the experts was the mean score of 4 and higher. The mean score 4 indicates high and very high agreement among the group members. In this round, 7 factors were selected. Then, in the third step, Delphi method was used to review the results. In the third round, the factors with mean scores of above 4 were obtained, indicating closeness of the opinions. Hence, Delphi method was stopped in the third round and 7 factors were selected. The results of factor identification are presented in Table 3. Location for use of facilities grated and type of using the facilities in that region As the effective weight of each of the key and important factors is used in the next steps of the research, by using Saaty pairwise comparisons, these factors were compared in pairs by 10 experts.
Step 1: Matrix of K expert pairwise comparisons matrix is defined as matrix (1).
Step 2: The experts' pairwise comparisons were examined in terms of inconsistency rates by Expert Choice software and if the inconsistency rate is less than 0.1, the pairwise comparison is consistent and if it is greater than 0.1, the pairwise comparison numbers should be corrected. Step 4: Calculating the Rough weigh of the factors using equations (4) and (5):  The steps for the Rough VIKOR method to rank customers are as follows: Step 1: Forming the individual decision matrix is done through using the opinions of three banking experts and transforming their component fij in the F matrix to the Rough number to form the Rough F group evaluation matrix. After calculation, the F matrix was completed. The elements of this matrix include the Rough number ranges. These elements are listed in Table (4). Step 2: In this step, the ideal positive and negative options will be identified. The result of the calculations is as described in Table (5). Step 3: In this step, the value of the utility index and the regret index of the options will be calculated. The values of utility and regret indices are in accordance with   Step 4: In this step, we calculate the VIKOR Q index. In this step, the value of V is considered 0.5. The values of the VIKOR index can be seen in Table (10). Step 5: In this step, the descending ranking of the customers (options) will be done based on the values of VIKOR, utility and regret indices and weight of the effective factors will be determined. This ranking can be seen in Table  11.  Step 6: In this step, given the descending ranking of the previous step, the final ranking of options (customers who received the facilities) is presented. The final ranking of the customers received the facilities is shown in Table  12.
For the first and second final rank, that is customer 7 and 1, we first examine the first conditions for these two options. The results show that the first condition has not been met but the second has been met. When the first condition is not met, the equation (34) is used to obtain the optimal VIKOR index. Now, as the VIKOR index values of both customers 1 and 7 are smaller than this value, the lowest VIKOR index value, that is, the first customer is ranked the first and is preferred to the customer 7. The rest of customers were ranked accordingly as it is shown in Table (12).  4  14  5  2  6  8  7  18  8  12  9  20  10  5  11  15  12  4  13  13  14  10  15  11  16  17 17 19 18 The data are based on the facilities provided to customers who have received facilities in the past. After the final ranking of the customers scientifically, the researcher referred to Tejarat Bank and obtained information on the status of the customers whose data were used in this research. It was qualitatively found that customers 1, 7, and 9 with top ranks in the scientific rankings had excellent status in terms of repayment of the received facilities to Tejarat Bank. Accordingly, the customers in the middle ranks of the table had normal status and it was found that the customers in the final ranks had poor status in the repayment of their received facilities to the Tejarat Bank. This result suggests that the method of ranking based on Rough VIKOR can be applied to all customers referred to bank from this time onwards to receive the banking facilities and the customers who are in poor status should be rejected in order to prevent financial and credit costs and outsourcing costs of follow-ups, imposed on banks.

Conclusion and recommendations for future studies
In this study, the key and effective factors were identified. These factors included location for use of granted facilities and type of use of facilities in that region, history of activity, and level of customer capital, type of collateral, having previous liabilities, good reputation of the applicant, and estimating the rate of return. Then, the weights of the key and important factors were obtained. It was concluded that estimating the rate of return was ranked in terms of importance and the history of activity was ranked the second. It should be noted here that the first and second ranks had about 80% importance among the factors, indicating very high importance of these two factors in terms of Pareto 20-80 strategy. Finally, Rough VIKOR method was applied and the customers who had received loans, facilities and credits from Tejarat Bank in the past were ranked. According to the analysis, the results show that the Rough VIKOR-based ranking method can be applied to all customers who refer to bank since this time onwards to receive facilities and the customers who are in poor status should be rejected in order to prevent financial and credit costs and outsourcing costs of follow-ups, imposed on banks. In this section, recommendations are provided for future researchers in this field and development of this research. These recommendations include: -This study provided a new approach for Tejarat Bank and other researchers can investigate the effectiveness of this method in the intended bank after implementing this new method in bank and achieving the quantitative goals of bank and investigate this method further.
-Researchers can also calculate the rate of reduction in overhead costs incurred by providing facilities to inappropriate individuals on the bank, using the economic and financial models after applying this method in the intended bank and transform the efficiency of this method into comprehensible numbers.
-This research was conducted on real customers. Other researchers can take steps towards more effective implementation of this research for all customers in future studies by classifying customers according to the banking system classification and applying this method in each of the classifications.