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Report Evaluation Model for Analysts in Mutual Fund Companies.doc Document Transcript

  • 1. Report Evaluation Model for Analysts in Mutual Fund Companies Hsin-Yuan Chang*, Insurance and Financial Management Department, Takming University of Science and Technology, 56, Sec.1, Huanshan Rd., Nei Hu, Taipei 11451, Taiwan, R.O.C. E-mail: Yu Ching Ho Logistics Management Department, Dahan Institute of Technology, No.1, Shjen Street, Dahan ,Sincheng Hualien 971 Taiwan , R.O.C. Abstract This study develops an evaluation and selection model of brokerage firm’s research reports by modified Delphi method and AHP. This model provides a distinct approach to examine brokerage firm’s research reports. We establish four main- criteria and nineteen sub-criteria to evaluate brokerage firm’s research reports. The primary criterion is the objective of brokerage firm’s research reports. No bias statement, no serious omission and detail description of information source are key sub-criteria to reach objective. Consistent evaluation of target firm’s industry is also 1
  • 2. important evaluation sub-criterion. Keywords Modified Delphi method, AHP, Brokerage firm’s research reports, Objective 1. Introduction The major function of analysts in mutual fund companies is to provide investment target selection suggestions to portfolio managers. With the boarder range of investment area, to visit every company directly in the universe becomes a mission impossible. In order to increase their understanding of the investment targets, analysts must rely on research reports from all kinds of sources. Although these reports play an important role in making investment decisions, the purposes of issuing reports may differ from each other. For example, industrial statistical data published by government is aim for increasing the transparency of markets, but investment banks issue research papers may be in a willing to promote their IPO stocks. Academic research shows that research reports from brokerage firms are often optimistic or biased due to the brokerage firm analysts’ career concerns and conflicts of interest inside the brokerage firm (e.g. Elton et al. ,1986; Womack, 1996; Barber et al., 2001, 2003; Hong & Kubik, 2003; Azzi, Bird, Ghiringhelli & Rossi, 2006; Cowen, Groysberg & Healy, 2006; Jacob, Rock & Weber, 2008). Therefore, carefully evaluation and selection between reports become a key successful factor of creating superior investment performance. Most related literatures focus on analyzing the information content of the brokerage firm’s research reports or why and how those reports are biased. We lack an approach 2
  • 3. to identify a most valuable brokerage firm’s research reports. To establish an evaluation and selection model of brokerage firm’s research reports is the main purpose of our study. Analysts must evaluate the value of each report and decide a valuable report by various selection criteria such as assumption of the research report, timely published, conscientious, objective, etc., simultaneously. In this study, a model incorporated with the Modified Delphi method and the Analytical Hierarchy Processing (AHP) method to select the most valuable brokerage firm’s research reports is proposed. The Modified Delphi method is adopted to extract the criteria from asking the opinions of a panel of experts, and the AHP method is used to decide the priority of those criteria gathered from the Modified Delphi method and compute the relative weight of each alternative research reports. To enhance investment performance of mutual funds, predictive suggestions of investment targets from analysts are essential. Research reports with good quality help analysts provide precise suggestions. Facing variety reports, this evaluation and selection model supports analysts identify useful reports easily. This study attempts to make a contribution to a better appreciation of brokerage firm’s research reports through the viewpoint of analysts. The remainder of this paper is organized as follows: Section 2 describes the research methodology we use in this study. Section 3 develops the model. Section 4 discusses and concludes. 2. Research methodology The purpose of this study is to establish a model to help investors to evaluate and 3
  • 4. select the valuable brokerage firm’s research reports by the Modified Delphi method and the AHP method. Before developing the model, we will introduce the Modified Delphi method and AHP in general. Modified Delphi method The Delphi method is an approach to elicit experts’ opinion by an iterative process without face to face grouping discussion. It is a systematic process that attempts to obtain group consensus in much more open and in-depth research ( MacCarthy & Atthirawong, 2003). Series stages of questionnaires are designed to elicit and refine common opinions within a pre-selected panel of experts via mail. Murry and Hammons (1995) proposed the Modified Delphi method which enables researchers to shorten the determination process. The difference between these two methods is that the Modified Delphi method needs to develop a structured questionnaire by literature review or expert interview instead of open-ended questionnaire in the first stage. By using structured questionnaire, the research horizon will be shortened and objective- related criteria could be determined faster. Because the research burden of ANALYSTS is heavy, that would be a tough work to have them discuss together by face to face meeting. Therefore using the Modified Delphi method is an appropriate approach to collect opinions of ANALYSTS about the criteria decisions they used to evaluate and select brokerage firm’s research reports without disturbance. Analytical hierarchy process The Analytic Hierarchy Process developed by Satty is a kind of multi-criteria 4
  • 5. decision making (MCDM) techniques and enables decision makers to represent the simultaneous interaction of many factors in complex and unstructured situations. It helps them to identify and set priorities on the basis of their objectives and their knowledge and experience of each problem and provide a structured approach to decision making (Saaty, 1999). The AHP is performed well to solve complex decision-making problems in different areas, such as planning (Kwak & Lee, 2002; Radash & Kwak, 1998), resources evaluation and allocation (Alphonce, 1997; Jaber & Mohsen, 2001; Hsu, Wu & Li, 2008), measuring performance (Frei & Harker, 1999; Ahsan & Bartlema, 2004), choosing the best policy after finding a set of alternatives (Poh and Ang, 1999; Chang et al., 2007), setting priorities (Schniederjans and Wilson, 1991). The first step is to decompose a complex situation into relevant main criteria and sub-criteria, then using these criteria to establish a hierarchy structure. A basic hierarchy model of AHP including four levels (Figure 1). The top level is the goal we want to achieve. The second and third levels are criteria and sub- criteria respectively. Since human being could not compare too many elements simultaneously, the elements in each main criteria and sub-criteria should not exceed seven. Under this limitation, it may carry on the reasonable comparison and easier ensure the consistency (Satty, 1980). The bottom level is the replacement alternatives. Goal A Criteria B1 B2 B3 Sub-criteria C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 Alternatives D1 D2 D3 5
  • 6. Figure 1. A basic hierarchy model of AHP To derive the priorities of main criteria and sub-criteria within the hierarchy structure, AHP incorporates the comparison judgments of all decision makers into a final decision, without having to elicit their utility functions on subjective and objective criteria, by pair-wise comparisons of the alternatives and check their consistency (Saaty, 1990). The various hierarchies’ elements weight computation are shown as follow: (1). Establish the pair-wise comparison matrix A If there are n elements, it must carry out n(n-1)/2 elements pair-wise comparisons. Let C1, C2, L , Cn denote the set of elements, while aij represents a quantified judgment on a pair of elements Ci, Cj. The relative importance of two elements is rated using a scale with the values 1, 3, 5, 7, and 9, where 1 refers to “equally important”, 3 denotes “slightly more important”, 5 equals “strongly more important”, 7 represents “demonstrably more important” and 9 denotes “absolutely more important”. This yields an n-by-n matrix A as follows: C1 C2 K Cn C1  1 a12 L a1n  C 1/ a 1 L a2 n  A =  aij  = 2  12   M  M  , (1) M O M    Cn 1/ a1n 1/ a2 n L 1  Where aij = 1 and aij = 1/ aij , i, j = 1, 2, ..., n. In matrix A, the problem turn into assign the n elements C1, C2, …, Cn a set of numerical weights W1, W2, …, Wn that reflects the recorded judgments. If A is a consistency matrix, the relations between weights Wi and judgments aij are simply given by Wi / W j = aij (for i, j = 1, 2, ..., n. ) 6
  • 7. and matrix A as follows: C1 C2 K Cn C1  w1 / w1 w1 / w2 L w1 / wn  C w / w w2 / w2 L w2 / wn  A= 2 2 1  , (2) M  M M O M    Cn  wn / w1 wn / w2 L wn / wn  (2) Eigenvalue and Eigenvector calculation Matrix A multiply the elements weight vector ( x ) equal to nx , that is ( A - nI ) x =0, the x is the Eigenvalue ( n ) of Eigenvector. Due to aij is the decision makers’ subjective judgment comparison and appraisal, the true value ( Wi / W j ) may be a little different, so that Ax = n.x is unable to set up. Satty (1990) suggested that the largest eigenvalue λ max be: n Wj λmax = ∑ aij , (3) j =1 Wi If A is a consistency matrix, eigenvector X can be calculated by ( A − λmax I ) X = 0 , (4) (3) Consistency test The essential idea of AHP is that a matrix A of rank n is only consistent if it has one positive eigenvalue n = λmax while all other eigenvalues are zero. Further, Saaty developed the consistency index (CI) to measure the deviation from a consistent matrix: 7
  • 8. CI = (λmax − n) /(n − 1) , (5) The consistency ratio (CR) is introduced to aid the decision on revising the matrix or not. It is defined as the ratio of the CI to the so-called random index (RI) which is a CI of randomly generated matrices: CR = CI / RI . (6) For n = 3 the required consistency ratio (CR Goal ) should be less than 0.05, for n = 4 it should be less than 0.08 and for n ≥ 5 it should be less than 0.10 to get a sufficient consistent matrix. Otherwise the matrix should be revised (Saaty, 1994). Once the priorities weights of each main criteria is established, then the relative performance measures of the alternatives can be calculated in terms of each main criteria and the best alternative is decided by relative performance scores. 3. Model development A series steps to perform the AHP analysis are described as follows: Step 1: Defining the evaluation criteria and sub-criteria used to select the valuable brokerage firm’s research reports and establishing an AHP-based hierarchical structure The goal of our study is to select a valuable brokerage firm’s research reports. This is the top level of the AHP-based model. Then we must break down our goal into several elements as main criteria and sub-criteria, and arranges them hierarchically through the Modified Delphi method. Although there are many literature discussed 8
  • 9. brokerage firm analysts’ research reports, but there is few researches focused on the topic we discuss in this study. By literature review, expert interview and some Taiwan government regulations, the modified Delphi structure questionnaires are developed. These regulations stipulate some norms that researchers of investment company or securities company must obey before they publish research reports. After referring to these literatures and in-depth expert interview, we select 28 indicators and organize them into questionnaire to perform the Modified Delphi method. We sent the Modified Delphi questionnaire to thirteen ANALYSTS, then analyze the opinion feedback and extract decision elements, including four main criteria and nineteen sub- criteria. All the criteria and denotation are summarized in Table 1. A hierarchy structure shown as figure 2 is arranged by deep interview with three experts to ensure the rationality of the hierarchy structure. Table 1. The criteria extract by the Modified Delphi method Criteria Definition Main criteria 1. assumption of research reports (C1) Sub-criteria for C1  value investing (SC1)  (SC1)Ways to search for undervalued stocks  financial model (SC2)  (SC2)Stock evaluation using common models  consistent evaluation  (SC3)consistent evaluation principals for all stocks of target firm’s in the same industry industry (SC3)  (SC4)coherent evaluation process for the whole  coherent evaluation industry of target firm’s industry (SC4) Main criteria 2. timely research (C2)  popular issues (SC5) 9
  • 10.  market trend (SC6)  (SC5)Address relevant opinions about popular  predictions before issues in today’s market market shock (SC7)  (SC6)Address relevant opinions about future market trend  (SC7)Address relevant opinions before market shock Main criteria 3 conscientious (C3)  Honest stock  (SC8)The recommendation are based on unbiased recommendation and reasonable judgements (SC8)  (SC9)Work experience of brokerage firm’s  work experience of research team in the investment related industries brokerage firm’s  (SC10)Work experience of brokerage firm’s research team (SC9) research team in the industries which they covered  industry experience  (SC11)Choose suitable models and make sure the of brokerage firm’s methodology of the model using is correct research team (SC10)  (SC12)Evaluate the inputs of models carefully  using financial model  (SC13)Confirm the correctness of all the data correctly (SC11)  evaluating financial accounting data correctly (SC12)  careful examination of every numeral and statement published (SC13) Objective (C4)  Applying  (SC14) Refer to opinions of professionals or authoritative information from authorities information (SC14)  (SC15)Confirm and compare data/ information  establishing multi- from different resources information resources  (SC16)Clear description of each data/ information (SC15) sources  detail description of  (SC17)Data is not fake or been changed information source  (SC18)Statements are unbiased and not related to (SC16) self interests 10
  • 11.  true record (SC17)  (SC19) no serious omission  no bias statement (SC18)  no serious omission (SC19) 11
  • 12. Value investing Financial model Assumption of research reports Consistent evaluation of target firm’s industry Coherent evaluation of target firm’s industry Address relevant opinions about popular issues in today ’s market Address relevant opinions about Timely research future market trend Address relevant opinions before market shock Honest stock recommendation Work experience of brokerage Valuable firm’s research team brokerage firm ’s Industry experience of brokerage research firm’s research team reports Conscientious Using financial model correctly Evaluating financial accounting data correctly Careful examination of every numeral and statement published Applying authoritative information Establishing multi -information resources Detail description of information source Objective True record No bias statement No serious omission 12
  • 13. Figure 2. The hierarchy structure of AHP-based model Step 2: Establishing pair-wise comparison matrix of each factor Based on the hierarchy structure, an AHP questionnaire is developed to make a pair-wise comparisons in order to determine the relative priorities of each criteria. The pair-wise comparisons are based on the scale of relative importance that assumes values between 1 and 9. This scale can be applied with ease to criteria that can be defined numerically as well as to those cannot be defined numerically. Relative importance scale is presented. ANALYSTS is supposed to specify their judgments of the relative importance of each contribution of every criterion towards achieving the overall goal. In this study, a purposive expert sampling is applied to sample ten respondents from various ANALYSTS. The weights of level 2 criteria and level 3 sub-criteria are then determined for a sample group of ten individuals matching the above characteristics with each respondent making a pair-wise comparison of the decision elements and assigning them relative scores. The relative scores provided by ten experts are aggregated using the arithmetic mean method. Each decision maker in the fund company makes a pair-wise comparison of the report evaluation under nineteen subjective sub-criteria and, then, assigns those relative scores. We using the Eq. (1) and (2) to calculated the aggregate pair-wise comparison matrix. The results of the pair-wise comparison matrices about main-criteria and sub- criteria are shown as table 2 and 3. Step 3: Calculating the eigenvalue and eigenvector The comparison in Tables 2 to 3 are used to calculate the eigenvectors using Eq. 13
  • 14. (3) and (4). Table 4 summarizes the results of eigenvectors and weights for the main- criteria and sub-criteria. Step 4: Consistency test According to Eq. (5) and (6), the consistency test of each criteria level is calculated and the results are shown as table 2 and 3. The CR. of each comparison matrices are all < 0.1, indicating “consistency”. Step 5: Computing relative weight of each levels’ elements Aggregate the related scores provided by all experts using simple additive weighting and the results for each levels relative weight of the elements are shown as Table 4. After sorting the four main-criteria by relative weights, the most important main-criteria is objective(0.421), next are conscientious(0.237), assumption of research(0.227) and timely research(0.116) separately. The sub-criteria are sorted and analyzed based on relative weights under each main-criteria as shown in Table 4. The results are summarized as follows: (1) There are six sub-criteria under the most important main-criteria – objective. The highest relative weight sub-criterion is no bias statement (0.225). We observe that the relative weights of no serious omission (0.190), detail description of information source (0.183) and true record (0.172) are also important criteria for ANALYSTS to screen brokerage firm’s research reports. Applying authoritative information (0.091) seems to be less important criterion under objective. (2) With regard to the sub-criteria under conscientious, the most important criterion 14
  • 15. is industry experience (0.296). The remainder criteria sorted by relative weights are evaluating financial accounting data correctly (0.208), careful examination of every numeral and statement published (0.169), Honest stock recommendation (0.128), using financial model correctly (0.124) and work experience (0.075). (3) According to the priority of relative weight, the sub-criteria under assumptions of research reports ranked are consistent evaluation of target firm’s industry (0.351), coherent evaluation target firm’s industry (0.282), value investing (0.217) and financial model (0.149). (4) For ANALYSTS, timely research reports mean address relevant opinions about future market trend (0.470) and address relevant opinions before market shock (0.416), addressing relevant opinions about popular issues in today’s market (0.170) is not an important consideration for ANALYSTS. Step 6. Computing global priority of each sub-criterion Global priority of each sub-criterion is gathered by multiplying its relative-weight by corresponding main-criterion’s relative-weight. The results are arranged in Table 5. The top five relative-weight sub-criterion are no bias statement (0.095), no serious omission (0.080), consistent evaluation of target firm’s industry (0.080), detail description of information source (0.077) and true record (0.072) respectively. The bottom five relative-weight sub-criterion are address relevant opinions about popular issues in today’s market (0.013), work experience of brokerage firm’s research team (0.018), using financial model correctly (0.029), honest stock recommendation (0.030) and financial model (0.034) respectively. 4. Discussion 15
  • 16. As shown in Table 5, we discover that four of the top-five global priorities of sub- criteria are of objective. This result is responding to the duty of ANALYSTS, generating objective and valuable investment suggestions for mutual fund managers. Brokerage firm’s analysts usually publish over-optimistic statements to lead investors based on their own career concern or under top-management pressures. Investors like ANALYSTS may suffer serious loss for adopting an over-optimistic opinion. Therefore, they have to examine if research reports existing bias statement, serious omission or false record and describing information source particularly before accepting the investment recommendations and target price to make investment decisions. One of top-five sub-criteria is of assumption of research reports. This sub- criterion is consistent evaluation of target firm’s industry. Consistent evaluation method makes valid and meaningful comparison with similar stocks for ANALYSTS. The sixth global priority of sub-criterion is the industries’ domain knowledge or experience of the researches’ target in the firm’s research team. But the importance of work experience of brokerage firm’s research team is very low, the priority is 18. In the viewpoint of ANALYSTS, the contribution to conscientious of industry experience is greater than work experience. Consistent with Mikhail, Walther and Willis (2003), they prove that analysts become more accurate with firm-specific forecasting experience. Brokerage firm’s research team concentrates their attentions in single industry will produce more valuable research reports. Addressing relevant opinions about popular issues in today’s market is not important considerations for ANALYSTS since stock market price has reflects those popular issues; ANALYSTS is unable to acquire returns through such information. The most important task of ANALYSTS is to find out under-valued stocks and invest them now. Under-valued stocks mean their market price is lower than their real value 16
  • 17. now and will go up in the future. Therefore ANALYSTS need an objective research reports which can indicate what will happen in the future and how is the market trend. Except future market trend, addressing opinions about possible market shock could assist ANALYSTS to avoid loss. As for whether applying authoritative information or not is not an important consideration for ANALYSTS. 5. Conclusion Brokerage firm’s research reports provide investment information for institution and individual investors to make investment decisions. Prior researches focus on analyzing brokerage firm’s analyst or the relation between research reports and stock market price, and so on. This study is aimed to provide a different approach to evaluate brokerage firm’s research reports. A model with 4 main-criteria and 19 sub- criteria is developed to assist investors to sieve out the most valuable brokerage firm’s research reports by modified Delphi method and AHP. Investors, new employee of securities investment trust company and brokerage firm’s research department can benefit by our model. Investors can judge which report is more valuable and worthy to refer through the criteria in our model. In the case of new employee of securities investment trust company, our model can help them to familiarize with research practices quickly. As for brokerage firms research department, users of their research reports are existing and potential clients. If those clients do not trust brokerage firm’s research reports, then they will leave and brokerage firms will lose revenue. Our model is an important impetus for brokerage firms when producing research reports. We find the primary evaluation criterion of brokerage firm’s research reports is objective. Brokerage firm’s analysts should make sure that there are no biases and 17
  • 18. serious omissions in research reports published and declare information source to ensure the objectivity. In the meanwhile, they must evaluate target firm’s industry consistently. ANALYSTS do not care about the work experience of brokerage firm’s research team when they evaluate the usefulness of research reports. They do care about how brokerage firm’s analysts are familiar with the industries and the accuracy of analysis process since these would affect the conscientious of brokerage firm’s research reports. Reference Ahsan, M. K. and Bartlema, J. (2004), Monitoring healthcare performance by analytic hierarchy process: a developing-country perspective, International Transactions In Operational Research, 11(4), 465-478. Azzi, Sarah and Bird, Ron (2005), Prophets during gloom and doom downunder, Global Finance Journal, 15(3), 337–67. Azzi, Sarah; Bird, Ron; Ghiringhelli, Paolo; Rossi, Emanuele (2006), Biases and information in analysts' recommendations: The European experience, Journal of Asset Management, 6(5), 345-380. Barber, Brad; Lehavy, Reuven; McNichols, Maureen and Trueman, Brett (2001), Can investors profit from the prophets? Security analyst recommendations and stock returns, Journal of Finance, 56(2), 531-563. Barber, B.M.; Lehavy, R.; McNichols, M. and Trueman, Brett (2003), Reassessing the returns to analysts’ stock recommendations, Financial Analysts Journal, 59(2), 88–96. 18
  • 19. Bjerring, J.H.; Lakonishok, J. and Vermaelan, T. (1983), Stock prices and financial analysts’ recommendations, Journal of Finance, 38(1), 187–204. Bradshaw, Mark t. (2002), The use of target prices to justify sell-side analysts’ stock recommendations, Accounting Horizons, 16(1), 27-41. Brav, Alon and Lehavy, Reuven (2003), An empirical analysis of analysts’ target prices: Short-term informativeness and long-term dynamics, Journal of Finance, 58(5), 1933-1967. Chang, Che-Wei; Wu, Cheng-Ru; Lin, Chin-Tsai and Chen, Huang-Chu (2007), An application of AHP and sensitivity analysis for selecting the best slicing machine, Computer & Industrial Engineering, 52, 296-307. Chang, Che-Wei; Wu, Cheng-Ru; Lin and Chen, Huang-Chu (2008), Using expert technology to select unstable slicing machine to control wafer slicing quality via fuzzy AHP, Expert Systems with Applications, 34, 2210-2220. Cowen, A.; Groysberg, B. and Healy, P.M. (2006), Which types of analyst firms are more optimistic?, Journal of Accounting and Economics, 41(1/2), 146–199. Elton, J. Edwin, Martin J. Gruber, and Seth Grossman (1986), Discrete expectational data and portfolio performance, Journal of Finance, 41(3), 699-714. Hong, Harrison and Kubik, Jeffrey D. (2003), Analyzing the analysts: Career concerns and Biased Earnings forecasts, Journal of Finance, 58(1), 313-351. Hsu, Pi-Fang; Wu, Cheng-Ru and Li, Zhao-Rong (2008), Optimizing resource-based allocation for senior citizen housing to ensure a competitive advantage using the analytic hierarchy process, Building and Environment, 43, 90-97. Jacob, John; Rock, Steve and Weber, David P. (2008), Do non-investment bank analysts make better earnings forecasts?, Journal of Accounting, Auditing & 19
  • 20. Finance, 23(1), 23-61. Jegadeesh, Narasimhan; Kim, Joonghyuk; Krische, Susan D. and Lee, Charles M. C. (2004), Analyzing the analysts: When do recommendations add value?, Journal of Finance, 59(3), 1083-1124. MacCarthy, B. and Atthirawong, W. (2003), Factors affecting location decisions in international operations: a Delphi study, International Journal of Operations and production Management, 23(7), 794-818. Michaely, Roni and Womack, Kent L. (1999), Conflict of interest and the credibility of underwriter analyst recommendations, The Review of Financial Studies, 12(4), 653-686. Mikhail, Michael B., Walther, Beverly R. and Willis, Richard H. (2003), The effect of experience on security analyst underreaction, The Journal of Accounting and Economics, 35, 101–116 Ryan, Paul and Taffler, Richard (2006), Do brokerage houses add value? The market impact of UK sell-side analyst recommendation changes, The British Accounting Review, 38, 371–386. Saaty, T. (1999), Decision making for leaders: The analytic hierarchy process for decisions in a complex world, RWS Publications, Pittsburgh. Stickel, S.E. (1995), The anatomy of the performance of buy and sell recommendations, Financial Analysts Journal, 51(5), 25–39. Womack, Kent L. (1996), Do brokerage analysts’ recommendations have investment value?, Journal of Finance, 51(1), 137-167. 20
  • 21. 21
  • 22. Table 2 The pair-wise comparison matrix of the main-criteria Goal C1 C2 C3 C4 C1 1.000 1.210 1.134 0.794 C2 0.826 1.000 0.266 0.306 C3 0.882 3.759 1.000 0.299 C4 1.259 3.268 3.344 1.000 λ max = 4.271; CI = 0.09; RI = 0.90; CR = 0.1≦0.1 Table 3 The pair-wise comparison matrices of sub-criteria C1 SC1 SC2 SC3 SC4 SC1 1.000 1.375 0.564 0.893 SC2 0.727 1.000 0.461 0.461 SC3 1.773 2.169 1.000 1.238 SC4 1.120 2.169 0.808 1.000 λ max = 4.027; CI = 0.009; RI = 0.90; CR = 0.01≦0.1 C2 SC5 SC6 SC7 SC5 1.000 0.188 0.357 SC6 5.319 1.000 0.871 SC7 2.801 1.148 1.000 λ max = 3.0696; CI = 0.0348; RI = 0.58; CR = 0.06≦0.1 C3 SC8 SC9 SC10 SC11 SC12 SC13 SC8 1.000 2.431 0.214 2.271 0.459 0.468 SC9 0.411 1.000 0.189 0.701 0.668 0.437 SC10 4.673 5.291 1.000 1.876 0.837 1.334 SC11 0.440 1.427 0.533 1.000 0.702 1.275 SC12 2.179 1.497 1.195 1.425 1.000 1.292 SC13 2.137 2.288 0.750 0.784 0.774 1.000 λ max = 6.496; CI = 0.0992; RI = 1.24; CR = 0.08≦0.1 C4 SC14 SC15 SC16 SC17 SC18 SC19 SC14 1.000 0.223 0.439 0.776 0.777 0.433 SC15 4.484 1.000 0.492 0.454 0.454 0.475 SC16 2.278 2.033 1.000 0.981 0.940 0.717 SC17 1.289 2.203 1.019 1.000 0.605 1.063 SC18 1.287 2.203 1.064 1.653 1.000 1.772 SC19 2.309 2.105 1.395 0.941 0.564 1.000 λ max = 6.496; CI = 0.0992; RI = 1.24; CR = 0.08≦0.1 22
  • 23. Table 4 The eigenvectors and weights for the main-criteria and sub-criteria Main-criteria Relative-weights Sub-criteria Relative-weights C1 0.227 SC1 0.217 SC2 0.149 SC3 0.351 SC4 0.282 C2 0.116 SC5 0.114 SC6 0.470 SC7 0.416 C3 0.237 SC8 0.128 SC9 0.075 SC10 0.296 SC11 0.124 SC12 0.208 SC13 0.169 C4 0.421 SC14 0.091 SC15 0.139 SC16 0.183 SC17 0.172 SC18 0.225 SC19 0.190 23
  • 24. Table 5 Global priority of sub-criteria Main-criteria Sub-criteria Relative-weights Global priority C1 SC1 0.049 10 SC2 0.034 15 SC3 0.080 2 SC4 0.064 7 C2 SC5 0.013 19 SC6 0.055 9 SC7 0.048 12 C3 SC8 0.030 16 SC9 0.018 18 SC10 0.070 6 SC11 0.029 17 SC12 0.049 10 SC13 0.040 13 C4 SC14 0.038 14 SC15 0.059 8 SC16 0.077 4 SC17 0.072 5 SC18 0.095 1 SC19 0.080 2 24