Multi-Criteria Decision-Making Model Evaluating the Performance of Vietnamese Commercial Banks

The commercial banks (CBs) performance evaluating has been a necessary problem in currently integration trend and usually implemented by a committee of experts under criteria selected. Therefore, it is considered as a Multi Criteria Decision Making model (MCDM). Nowadays, there have been many researches proposing various standards and models to evaluate and rank CBs. But in Vietnam, the number of studies related to the Vietnamese banking evaluation model have still been limited. As a result, this study develops a multi-criteria decision model integrating Fuzzy Analytical Hierarchy Process (FAHP) and Fuzzy the Technique for Order of Preference by Similarity to Ideal Solution (FTOPSIS). The proposed model has evaluated and ranked five Vietnamese commercial banks including CTG, VCB, BIDV, TCB and MB. The paper revealed their ranks. Besides, the results of the research show that the Analytical Hierarchy Process (AHP) model is suitable for applying it to the process evaluating bank performance.


Introduction
In most countries, commercial bank is one of the most important financial institutions. It can attract financial flows, offer offering credit and various financial services. These activities have a vital impact on national economic development. Therefore, CBs should be evaluated and analyzed by the modern and accurate techniques to rank CBs in the banking system and improve their performances.
Vietnam has still on the way international integration, which brings both opportunities and challenges for the economy, especially the banking system. Economic integration brings a healthily and equally competitive environment to CBs. Moreover, it brings exchange opportunities and international cooperation in fiscal and monetary policy planning, foreign exchange management, risk inspection and monitoring. Therefore, the position and prestige of Vietnamese CBs in the global transaction banking will be enhanced. Besides these opportunities, the banking system has to face competition from international banks in terms of price, service, distribution… Meanwhile, Vietnamese CBs are highly unlikely to assert their position in international markets because of their weak competitive abilities (Pham, 2010) There aren't any banks which can fully satisfy all customers' requirements obviously. If a bank has an advantage in this respect, it will have disadvantages in other respects. Therefore, in the open market with the participation of more domestic and international banks, Vietnamese CBs must promote their strengths and improve their weaknesses in order to maintain and increase market share as well as profits. It creates a need to reassess Vietnamese CBs performance by the most accurate and modern techniques in order to satisfy many different objects.
Optimal selection process is related to evaluating many different options which based on a set of standards. This process is considered as Multi-criteria Decision Making (MCDM). Professor Zadeh (1965) researched on fuzzy set theory to solve blurring and unclear problem. Fuzzy decision-making makes approximate decision instead of absolute one. Fuzzy MCDM is one of the most important fields in the analysis of making decisions. As mentioned above, the decision-making depends on a lot of standards. The proportion of each decision correspond with criteria, the importance weighs of different criteria are evaluated by linguistic value and presented by fuzzy numbers. This study develops a multi-criteria decision making model integrating AHP and TOPSIS under a set of criteria to evaluate and rank CBs in Vietnam. This paper is organized as follow. In section 2, we overview previous researches to propose a model and criteria. In section 3, we define data and methodology to evaluate banks. In section 4, we illustrate empirical results. In section 5, we discuss about the results. Anh in the last section, we conclude the paper by reviewing our research.

Literature Review
Performance is how economic resources should be used to achieve the objective of the business (N. Venkatraman and Ramanujam V., 1986). It is a complicated definition, should be analyzed under different ways. It is considered as an important factor when researching the business policy of the enterprise (Dess and Robinson, 1984). Ngo and Le (2008) pointed out that performance is a general economic indicator. It shows the possibility of using human, financial and material resources in order to maximize profit for business. Performance is evaluated based on the results that the business can achieve in a certain period of time and this result is the difference between the degree of completion and target (Cetindere, Duran & Yetisen, 2015).
From those points of view, it can be seen that the definition of performance is various. It can be defined in many different ways depending on the purpose of the research. The definition of performance used in this study is an economic category showing the relationship between benefit and cost, it reflects the ability of an enterprise appropriately using and allocating inputs in order to produce outputs.
The majority of economists and analysts use ROA and ROE to approach performance (citation). They are the important indicators for evaluating bank performance. However, using only 2 indicators had certain shortcomings (Avkiran (1997) Lindblom & Koch (2002) Chapman et al. (2007. Many researchers have developed some financial indicators to assess fully and accurately the performance of CBs. The studies used the model of Schierenbeck's ROE Scheme (also called basic ROE model) (Badreldin (2009); Tamosaitiene (2011)). These models are based on the Dupont analysis, divided ROE into three distinct elements: net profit margin, risk margin and equity multiplier. The model used in the study by Collier and McGowan (2010) broke down ROE into net profit margin, asset turnover and equity multiplier.
In 2010, European Central Bank introduced a financial index combining three categories: traditional category, economic category and market category. Nguyen (2012) used Financial Soundness Indicators (FSIs) to evaluate charted capital, asset quality, performance and liquidity of CBs in Vietnam.
Realizing that the simple description of financial situation through financial ratios was not sufficient to assess performance in today's volatile environment (T. Chen and C. Chen, 2008), many researchers have used non-financial indicators to assess the bank's performance. Abdelgawad and Fayek (2010) mentioned 8 factors affecting bank performance: profitability, productivity, human resources management, risk management, sales effectiveness, service quality, capital management and competitive position. Barros and Wanke (2016) found 3 important factors in bank performance: labor cost, capital cost and market shares. In another study, Barros and Wanke (2015) pointed out that Malaysia financial market applying the rules of cultural barriers to foreign banks led to lower bank performance.
The studies of Wirnkar and Tanko (2008), Phan (2013) analyzed financial performance of the banking system through 5 key aspects of bank's activities: capital adequacy, asset quality, management quality, earnings ability and liquidity. J.Stankeviciene and Mencaite E (2012) pointed out that financial aspect was the most important one affecting bank performance. Besides, customer aspect also contributed to performance of the banking system significantly.
There are various research methodologies used to evaluate and rank CBs, such as Balanced Scorecard (BSC), Multi-criteria decision making (MCDM), Artificial intelligence (AI), Data Envelopment Analysis (DEA), Integrating Linear Programming. Meanwhile, Multi-criteria decision making mainly includes: Analytic hierarchy process (AHP), Analytic network process (ANP), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS).The banking performance evaluation is complicated with linguistic judgments under each criterion, this study develops a multi-criteria decision making model integrating AHP and TOPSIS under a set of criteria to evaluate and rank CBs in Vietnam. Meanwhile, TOPSIS and AHP have been the optimal methods to handle and rank fuzzy numbers so far.

Methodology and Data Description
In this section, we define data and methodology to evaluate bank. We start with the concepts of fuzzy set which will help us after then. There are many different concepts of fuzzy set. This study defines it as follows (Dubois and Prade, 1978;Kaufmann and Gupta, 1991). Basing on database from both the financial reports of 05 banks and knowledge about them, we make committee of 3 decision makers (experts) to assess them. Then expert members will hold responsible for evaluating CBs with respect to criteria selected.

Fuzzy Sets
As fuzzy set will intervene in our evaluation model, we first present it here.
Fuzzy set A in a universe U is expressed as:  1991). The larger the function value of () A fx is, the stronger the degree of membership for x in A will be.

Triangular Fuzzy Numbers
The triangular fuzzy numbers are used in this study because they are simply calculated and widely applied in studies relating to economics and governance. Characteristics and natures of the triangular fuzzy numbers are expressed as follows: A normalized triangular fuzzy number A can be defined as A (a, b, c, 1). The membership function f A (x) of A in expressed as (Kaufmann and Gupta, 1991). between A and B can be expressed as follows: x ( , , ), A k a k a k a k  For xU  1 1 2 3 3 2 1 ( , , ) (1/ ,1/ ,1/ ) a a a a a a  

Multi-Criteria Decision-Making Model to Evaluate and Rank CBs
As mentioned above, this paper uses the fuzzy sets indicating the weights of the criteria and the ratings of the alternatives in evaluation model applied to case study in section 4 after.
Based on the criteria selected to evaluate CBs, this study developed a fuzzy multiple criteria decision -making model integrating fuzzy AHP and fuzzy TOPSIS to assess and rank CBs. First, the fuzzy AHP method is used to determine the weights of the criteria based on the comparatively linguistic evaluatings of the decision makers. After having the ratings of the alternatives to each criterion, this paper aggregates them for the final fuzzy results of the alternatives. Then the fuzzy TOPSIS are used to handle them and give the final results for the evaluation to CBs. It is expressed as follows:

Importance Weighs of Each Criterion
This study defines the importance weighs of each criterion by fuzzy AHP approach of Chang's (1996) (pairwise comparisons). for k = 1,2,…,n; k # i. Then the weight vector is given by: In which, Linguistic values and corresponding fuzzy numbers for each alternative are expressed in  This study evaluated 5 banks under 26 criteria, including both financial and non-financial criteria. To solve this problem, this study developed an integrated multi-criteria decision making AHP -TOPSIS to determine the weight of criteria and the evaluation rate for 5 banks under each criteria.
AHP method showed the fuzzy weight of criteria. The table (4.3) showed that the financial criteria is the most important one affecting the bank performance (0.43), followed by customer perspective (0.38) and qualitative criteria (0.18). Because banking industry is a special service sector, whose performance has close relationship with the customer's satisfaction. Therefore, in order to maintain high performance, the banking system must enhance financial indicators, maintain the loyalty and trust of customers and build new markets to attract new customers.
Besides, the fuzzy TOPSIS method determined the final value to rank 5 banks and show the standard satisfaction among 5 banks. The table (4.6) told us that the bank had the best performance (Vietcombank) is more dominant in financial indicators over other CBs. Moreover, qualitative criteria are good. Besides, Techcombank and MB are two banks having the worst performance among 5 proposed banks. We can explain that because these banks had worse financial performance than other banks, while financial criteria are the most important factors affecting bank performance.

Conclusion
This research showed the multi-criteria decision -making model to evaluate and rank CBs, comprising the steps of: (i) determining the evaluation criteria; (ii) determining the weighted average with criteria; (iii) determining the CBs' proportion of value by the panel of experts based on criteria; (iv) determining integration value of the CBs' weighted percentages; (v) evaluating and ranking CBs. Proposed model is applied to help the institutions evaluate and rank CBs in the system. The use of fuzzy set theory through the use of linguistic variables helped to soften the decision-making process, especially in the case of evaluation criteria including both qualitative and quantitative criteria with unclear input information. The following research can be applied the proposed model to solve the problem for all banks in the system and compare the result obtained from the proposed model with different decision-making models.