A fuzzy group multi-criteria enterprise architecture framework selection model Expert Systems with Applications 39 (2012) 1165–1173 Contents lists available at ScienceDirect Expert Systems with Applications j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / e s w a A fuzzy group multi-criteria enterprise architecture framework selection model Faramak Zandi a, Madjid Tavana b,⇑ a Information Technology Management and Industrial Engineering, Faculty of Technology and Engineering, Alzahra University, Vanak, Tehran 19938-91176, Iran b Management Information Systems, Lindback Distinguished Chair of Information Systems, La Salle University, Philadelphia, PA 19141, USA a r t i c l e i n f o Keywords: Multi-criteria decision making Enterprise architecture Fuzzy logic Risk failure mode and effects analysis 0957-4174/$ - see front matter � 2011 Elsevier Ltd. A doi:10.1016/j.eswa.2011.07.120 ⇑ Corresponding author. Tel.: +1 (215) 951 1129; fa E-mail addresses: zandi@iust.ac.ir (F. Zandi), tavan URL: http://lasalle.edu/~tavana (M. Tavana). a b s t r a c t A large body of intuitive and analytical models has evolved over the last several decades to assist deci- sion makers (DMs) in enterprise architecture (EA) framework selection. While these models have made great strides in EA framework evaluation, the intuitive models lack a structured framework and the analytical models do not capture intuitive preferences of multiple DMs. Furthermore, crisp data are fundamentally indispensable in traditional EA framework selection methods. However, the data in real-world problems are often imprecise or ambiguous. The prior research in EA framework selection does not embrace both qualitative and quantitative criteria exhibiting imprecise and ambiguous value judgments. In this paper, we propose a novel fuzzy group multi-criteria model for EA framework eval- uation and selection. The contribution of the proposed model is fourfold: (1) it takes into consideration the qualitative and quantitative criteria and their respective value judgments; (2) it considers verbal expressions and linguistic variables for qualitative judgments which lead to ambiguity in the decision process; (3) it handles imprecise or vague judgments; and (4) it uses a meaningful and robust multi- criteria model to aggregate both qualitative and quantitative data. We use a real-world case study to demonstrate the applicability of the proposed framework and exhibit the efficacy of the procedures and algorithms. � 2011 Elsevier Ltd. All rights reserved. 1. Introduction The increasing global competition and the rapid advances in information systems have led organizations to search for more effective and efficient ways to manage their business. The enter- prise architecture (EA) frameworks can ensure interoperability of information systems and improve the effectiveness and effi- ciency of business organizations. However, the increasing turbulence in the business environment and the larger number of alternatives with conflicting criteria has made the selection of EA frameworks a difficult and complex task. The EA frame- work selection problems are multi-criteria problems that em- brace both qualitative and quantitative criteria. Nevertheless, the traditional selection methods overemphasize quantitative and economic analysis and often neglect to consider qualitative and non-economic data in the formal selection process. When facing such multi-criteria problems, the literature and research show that the following difficulties may be encountered in the decision process: ll rights reserved. x: +1 (267) 295 2854. a@lasalle.edu (M. Tavana). 1. Decision makers (DMs) often use verbal expressions and linguistic variables for qualitative judgments which lead to ambi- guity in the decision process (Poyhonen, Hamalainen, & Salo, 1997). 2. DMs often provide imprecise or vague information due to lack of expertise or unavailability of data (Kim & Ahn, 1999). 3. Meaningful and robust aggregation of qualitative and quantita- tive data causes difficulties in the decision process (Valls & Torra, 2000). 4. A decision process is not complete without fully taking into consideration all the criteria and their respective value judg- ments (Belton & Stewart, 2002; Yang & Xu, 2002). Before an organization takes up a particular EA framework, there is need to consider and evaluate the possible alternative frameworks, and then select an appropriate one through a collab- orative effort involving all key stakeholders (Gammelgêard, Simonsson, & Lindstrèom, 2007). Over the past several years, the selection of EA frameworks has garnered considerable attention from both practitioners and academics. Fayad and Hamu (2000) have presented a detailed list of guidelines and attributes for selec- tion of EA frameworks. Tang, Han, and Chen (2004) have studied and compared the EA frameworks analytically and provided a model of understanding through analyzing the goals, inputs and outcomes of six architecture frameworks. Nonetheless, these stud- ies did not consider any uncertainties such as uncertainty in the http://dx.doi.org/10.1016/j.eswa.2011.07.120 mailto:zandi@iust.ac.ir mailto:tavana@lasalle.edu http://lasalle.edu/~tavana http://dx.doi.org/10.1016/j.eswa.2011.07.120 http://www.sciencedirect.com/science/journal/09574174 http://www.elsevier.com/locate/eswa eI The fuzzy weighted collective impact matrix with respect to the impact of m risk criteriaeL The fuzzy weighted collective likelihood matrix with respect to the likelihood of m risk criteriaeD The fuzzy weighted collective detection matrix with respect to the detection of m risk criteriaeI K The individual fuzzy impact matrix with respect to the impact of m risk criteria evaluated by the EA framework selection team member (EAFT)keLK The individual fuzzy likelihood matrix with respect to the likelihood of mrisk criteria evaluated by the EA framework selection team member (EAFT)keDK The individual fuzzy detection matrix with respect to the detection of m risk criteria evaluated by the EA framework selection team member (EAFT)k w(vp)K The voting power of the EA framework selection team member (EAFT)k for scoring (K = 1, 2, . . . , l) wj The importance weight of the jth criterion ~eijðIÞ The fuzzy weighted collective impact value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k ~eijðLÞ The fuzzy weighted collective likelihood value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k ~eijðDÞ The fuzzy weighted collective detection value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k ~ekijðIÞ The individual fuzzy impact value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k ~ekijðLÞ The individual fuzzy likelihood value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k ~ekijðDÞ The individual fuzzy detection value of the EA framework with respect to the risk criterion j evaluated by the EA framework selection team member (EAFT)k cj The jth criterion Ai The ith EA framework m The number of risk criteria l The number of EA framework selection team members n The number of EA frameworks ReP N The fuzzy risk priority numbers (RPN) matrix R The ordinal rank matrix R½Eðr~pnijÞ� The ordinal rank of Eðr~pnijÞ Eðr~pnijÞ The possibilistic mean value of r~pnij r~pnij The fuzzy risk priority number (RPN) for the ith EA framework with respect to the risk criterion j V The vector of the EA frameworks risks vi The risk of the jth EA framework 1166 F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 subjective judgments or uncertainties due to lack of data and incomplete information. Multi-criteria decision making methods have also been suc- cessfully applied in various decision making situations that have many similar features with EA framework selection problems. The multi-criteria methods used to evaluate EA frameworks based on quantitative measurements include Technique for Or- der Preference by Similarity to Ideal Solution (TOPSIS) (Hwang & Yoon, 1981; Kahraman, Ates�, Çevik, Gülbay, & Erdoğan, 2007; Shih, 2008); Simple Additive Weighting (SAW) (Chou, Chang, & Shen, 2008; Zavadskas, Turskis, Dejus, & Viteikiene, 2007); Linear Programming Techniques for Multidimensional Analysis of Preference (LINMAP) (Xia, Li, Zhou, & Wang, 2006); COmplex PRoportional Assessment (COPRAS) (Kaklauskas et al., 2006; Zavadskas, Turskis, Tamošaitienė, & Marina, 2008). The multi-criteria methods used to evaluate EA frameworks based on qualitative measurements not converted to quantitative vari- ables include methods of verbal decision-making analysis (Berke- ley, Humphreys, Larichev, & Moshkovich, 1991; Andre’eva, Larichev, Flanders, & Brown, 1995; Larichev, 1992; Larichev, Brown, & Andre’eva, 1995; Larichev & Moshkovich, 1997; Flanders, Brown, Andre’eva, & Larichev, 1998). Comparative pref- erence methods based on pairwise comparison of alternatives include ELECTRE (Costa, Almeida, & Miranda, 2003; Roy, 1996) and PROMETHEE I and II (Brans, Vincke, & Mareschal, 1986; Diakoulaki & Koumoutsos, 1991; Wang & Yang, 2007). The multi-criteria methods used to evaluate EA frameworks based on qualitative measurements converted to quantitative variables include two widely known groups of methods, i.e. Analytic Hierarchy Process (AHP) (Ghodsypour & O’brien, 1998; Saaty, 1994) and fuzzy set theory methods (Roztocki & Weistroffer, 2006; Zimmermann, 2000). Traditional assessment techniques overemphasize quantitative and economic analysis and often neglect to consider qualitative and non-economic factors in the formal selection process. Fur- thermore, crisp data are fundamentally indispensable in tradi- tional EA framework selection methods. However, the data in real-world problems are often imprecise or ambiguous. The prior research in EA framework selection does not embrace both qual- itative and quantitative criteria exhibiting imprecise and ambig- uous value judgments. In this paper, we propose a novel fuzzy group multi-criteria model for EA framework evaluation and selection that takes into consideration (1) the qualitative and quantitative criteria and their respective value judgments; (2) the verbal expressions and linguistic variables for qualitative judgments which lead to ambiguity in the decision process; and (3) imprecise or vague judgments. The five EA frameworks considered in this study include: Federal Enterprise Architecture Framework (FEAF), Zachman Framework for Enterprise Architec- ture (ZACHMAN), The Open Group Architecture Framework (TOGAF), Treasury Enterprise Architecture Framework (TEAF), and Department of Defense Architecture Framework (DoDAF). See Urbaczewski and Mrdalj (2006) for an excellent review of the five EA frameworks considered in our study. The next section presents the mathematical notations and definitions used in our model. In Section 3, we illustrate the details of the proposed model followed by a real-life case study to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms. In Sec- tion 5, we conclude with our conclusions and future research directions. 2. The mathematical notations and definitions Let us introduce the following mathematical notations and definitions: 3. The proposed model The model depicted in Fig. 1 is proposed to assess the alterna- tive EA frameworks and consists of several steps modularized into five phases: Fig. 1. The proposed framework. F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 1167 In summary, we. � have group members estimate the impact, probability of occur- rence and probability of detection of certain risks involved in the selection of EA frameworks, � aggregate across group members by forming a weighted average, � calculate expected impact by multiplying impact and probabilities, � use an additive weighting scheme to aggregate across impact categories, � defuzzify results by forming expected values, � transform evaluations into Borda scores, and � select the alternative with the lowest risk score. Phase 1: Establishing the EA framework selection team. In the first phase, we establish an EA framework selection team. Let us assume that l EA framework selection team members are chosen to rank the EA frameworks: EAFT ¼ ½ðEAFTÞ1;ðEAFTÞ2; . . . ;ðEAFTÞk; . . . ;ðEAFTÞl� Phase 2: Identifying the EA frameworks. In this phase, the selec- tion team identifies a set of EA frameworks. Let us further assume that the selection team has identified n EA frameworks: A ¼ ½A1; A2; . . . ; An� Phase 3: Identifying the qualitative and quantitative risk criteria. In this step, the EA framework selection team identifies a set of qual- itative and quantitative risk criteria associated with the EA frame- works. Let c1,c2, . . . , cm and w1,w2, . . . , wm be the risk criteria and their importance weights, respectively. ð3Þ Phase 4: Prioritizing the EA framework risks. In this phase, the EA framework selection team prioritizes the EA frameworks according to the following five steps: Step 4.1: Constructing the individual fuzzy EA framework risk matrices. In this step, the fuzzy individual EA framework risks are assessed based on the following three attributes associated with a risk event: the impact, likelihood and detection of the qualitative and quantitative risks identified in Phase 3. The goal is to identify, quantify and remove or reduce risks in an EA framework. 4.1.1. Calculating the impact value of the EA frameworks. A project risk is defined as ‘‘an uncertain event or condition that, if it occurs, has a positive or negative effect on a project’s objectives’’ (PMI, 2009). The EA framework risk is represented by the impact attri- bute in our model. The EA framework selection team uses a fuzzy set [1–10] to assign an impact number (I) to each EA framework. The impact value guidelines in Table 1 suggested by Carbone and Tippett (2004) are used to assign the impact values. These fuzzy numbers are used to prioritize the EA frameworks with respect to the impact of the risk criteria. The individual fuzzy impact matrix with respect to the impact of m risk criteria evaluated by the EA framework selection team member (EAFT)k will be as follows: ð1Þ Let ~ekijðIÞbe the following trapezoidal fuzzy number: ~ekijðIÞ¼ e k ijðIÞ � �o ; ekijðIÞ � �a ; ekijðIÞ � �b ; ekijðIÞ � �c� � ð2Þ Consequently, substituting Eq. (2) into matrix (1), it can be rewrit- ten as: 4.1.2. Calculating the likelihood values of the EA frameworks. Next, we consider the risk occurrence frequencies in our model by assigning a likelihood ranking (L) to each EA framework Table 2 The likelihood value guidelines. Very unlikely Probably will not occur Equal chance of occurring or not Will probably occur Very likely to occur Fuzzy number 1 or 2 Fuzzy number 3 or 4 Fuzzy number 5 or 6 Fuzzy number 7 or 8 Fuzzy number 9 or 10 Table 1 The impact value guidelines. Very low Low Average High Very high Fuzzy number 1 or 2 Fuzzy number 3 or 4 Fuzzy number 5 or 6 Fuzzy number 7 or 8 Fuzzy number 9 or 10 1168 F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 using fuzzy numbers 1–10. The likelihood value guidelines in Table 2 suggested by Carbone and Tippett (2004) are used to assign the impact values. These fuzzy numbers are used to prioritize the EA frameworks with respect to the impact of the risk criteria. The individual fuzzy likelihood matrix with respect to the likelihood of m risk criteria evaluated by the EA framework selection team member (EAFT)k will be as follows: ð4Þ Let ~ekijðLÞ be the following trapezoidal fuzzy number: ~ekijðLÞ¼ e k ijðLÞ � �o ; ekijðLÞ � �a ; ekijðLÞ � �b ; ekijðLÞ � �c� � ð5Þ Consequently, substituting Eq. (5) into matrix (4), it can be rewrit- ten as: ð6Þ 4.1.3. Calculating the detection values of the EA frameworks. Detection values represent the organization’s ability to detect the risk event with enough time to plan for a contingency and act upon the risk (Carbone & Tippett, 2004). The detection value is a mea- sure of being able to predict the specific risk event in the future. The goal is to detect the risk as early as possible. Those risks with high detection values may need one additional control mechanism for early warning. Each EA framework is assigned a detection value (D), again using fuzzy numbers 1–10. This ranks the ability of planned tests in each EA framework to detect risk events in time. The detection value guidelines in Table 3 suggested by Carbone and Tippett (2004) are used to assign the detection values. Certainly, the detection assignment is subjective, but no more so than the assignment of the likelihood and impact values for the common risk matrix method. The individual fuzzy detection matrix with respect to the detection of m risk criteria evaluated by the EA framework selection team member (EAFT)k will be as follows: ð7Þ Let ~ekijðDÞ be the following trapezoidal fuzzy number: ~ekijðDÞ¼ e k ijðDÞ � �o ; ekijðDÞ � �a ; ekijðDÞ � �b ; ekijðDÞ � �c� � ð8Þ Consequently, substituting Eq. (8) into matrix (7), it can be rewrit- ten as: ð9Þ Table 3 The detection value guidelines. Highly effective and it is almost certain that the risk will be detected with adequate time Moderately high effectiveness Medium effectiveness Unproven or unreliable; or effectiveness of detection method is unknown to detect in time There is no detection method available or known that will provide an alert with enough time to plan for a contingency Fuzzy number 1 or 2 Fuzzy number 3 or 4 Fuzzy number 5 or 6 Fuzzy number 7 or 8 Fuzzy number 9 or 10 F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 1169 Step 4.2: Constructing the fuzzy weighted collective EA framework risk matrices. In this step, the fuzzy weighted collective EA frame- work risks are assessed based on the likelihood, impact and detec- tion of the identified risks as follows: 4.2.1. Calculating the impact values of the EA frameworks. The fuz- zy weighted collective impact matrix with respect to the impact of m risk criteria will be as follows: ð10Þ or: ð11Þ ð16Þ where: ~eijðIÞ¼ Pl k¼1ðwðvpÞkÞ ~e k ijðIÞ h i Pl k¼1 w vpð Þk ð12Þ 4.2.2. Calculating the likelihood values of the EA frameworks. The fuzzy weighted collective likelihood matrix with respect to the likelihood of m risk criteria will be as follows: or: ð14Þ where: ~eijðLÞ¼ Pl k¼1ðwðvpÞkÞ ~e k ijðLÞ h i Pl k¼1wðvpÞk ð15Þ 4.2.3. Calculating the detection values of the EA frameworks. The fuzzy weighted collective detection matrix with respect to the detection of m risk criteria will be as follows: or: ð17Þ ð13Þ 1170 F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 where: ~eijðDÞ¼ Pl k¼1ðwðvpÞkÞ ~e k ijðDÞ h i Pl k¼1 wðvpÞk ð18Þ Step 4.3: Constructing the fuzzy RPN matrix. Next, we calculate the fuzzy RPN by multiplying the three fuzzy impact, likelihood and detection values. This has to be done for each EA framework with respect to the risk criteria. The EA frameworks that have the highest RPN should be given the lowest selection priority and those with the lowest RPN should be given the highest selection priority. Therefore, the fuzzy RPN matrix will be as follows: ð19Þ or: ð20Þ where: r~pnij ¼ ~eijðIÞ:~eijðLÞ:~eijðDÞ ð21Þ Step 4.4: Constructing the ordinal rank matrix. Next, we rank the n EA frameworks based on Borda’s score. That is, for each strategic criterion of preference ordering of the EA frameworks, scores of n � 1,n � 2, . . . , 1, 0 are assigned to the first, second . . . and the last ranked framework: ð22Þ Since r~pnij is a trapezoidal fuzzy number, r~pnij ¼ððrpnijÞ o ; ðrpnijÞ a ;ðrpnijÞ b ;ðrpnijÞ cÞ, its expected value can be derived as follows: Eðr~pnijÞ¼ ðrpnijÞ o þðrpnijÞ a 2 þ ðrpnijÞ c �ðrpnijÞ b 6 ð23Þ Step 4.5: Calculating the EA frameworks risks. The vector of the EA frameworks risks will be calculated as follows: V ¼ ½v 1 v 2 � � � v n � T ð24Þ where: ~v i ¼ Pm j¼1ðwjÞR½Eðr~pnijÞ�Pn i¼1 Pm j¼1wj R½Eðr~pnijÞ� ð25Þ Phase 5: Selecting the optimal EA framework. In this phase, the optimal EA frameworks ranking is determined based on the risks values obtained in phase (4). For this purpose, these values are con- sidered as the coefficients of the objective functions in the follow- ing proposed mathematical model with a series of applicable constraints such as critical impact and RPN values. Min Z2 ¼ v 1:x1 þ v 2:x2 þ�� �þ v n:xn ðModel PÞ Subject to : f1ðx1; x2; . . . ; xnÞ6 0 f2ðx1; x2; . . . ; xnÞ6 0 .. . frðx1; x2; . . . ; xnÞ6 0 x1 þ x2 þ�� �þ xn ¼ 1 xi ¼ 0; 1ði ¼ 1; 2; . . . ; nÞ where: fi(x1,x2, . . . , xn) is a given function of the n EA frameworks. In the next section, we present a real-life case study to demonstrate the applicability of the proposed model and exhibit the efficacy of the procedures and algorithms. 4. The case study The Institute for Energy and Hydro Technology (IEHT) is the largest energy institute in Iran. IEHT is located on a 65 acre campus and has a 50,000 person training capacity per month. The institute employs over 80 full-time and 100 part-time faculties. We used the group EA approach proposed in this study to select an EA for IEHT. A committee of nine DMs from marketing, finance, and information technology was formed to participate to evaluate the following five frameworks: ZACHMAN, TEAF, TOGAF, DoDAF and FEAF. Phase 1: In this phase, we worked with the management team and established an EA framework selection team which included: (ITPT)1: The information technology manager (ITPT)2: The research and development manager (ITPT)3: The capital budgeting manager (ITPT)4: The quality assurance manager Phase 2: In this phase, the EA framework selection team agreed to consider the following five EA frameworks suggested by Urb- aczewski and Mrdalj (2006): A1: ZACHMAN A2: TEAF A3: TOGAF A4: DoDAF A5: FEAF Phase 3: In this phase, the selection team decided to consider the strategic criteria presented in Table 4 for the evaluation and selection of the EA frameworks. Phase 4: In this phase, we used Eqs. (1)–(18) and calculated the impact, likelihood and detection values of the EA frameworks pre- sented in Tables 5–7: In step 4.3, we used Eqs. (19)–(21) and calculated the possibilis- tic mean values of the fuzzy risk priority numbers (RPN) provided in Table 8. In step 4.4, we used Eqs. (22) and (23) and constructed the ordinal rank matrix given in Table 9: F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 1171 In step 4.5, we used Eqs. (24) and (25) and calculated the vector of the EA framework risks given in Table 10. These risks values were determined according to the following importance weight vector: ðw1; w2; . . . ; w8Þ¼ ð0:15; 0:5; 0:5; 0:1; 0:13; 0:1; 0:17; 0:25Þ Phase 5: In this phase, the selection team identified the follow- ing constraints for each EA framework with respect to the risk im- pacts. All constraints were set less than or equal to the critical impact value (8). Next, the optimal EA framework was identified using the following mathematical model: Max:Z ¼ 0:29xFEAF þ 0:21xZACHMAN þ 0:16xTOGAF þ 0:06xTEAF þ 0:28xDODAF ðModel PÞ Subject to : Eð~eZACHMAN1ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN2ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN3ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN4ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN5ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN6ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN7ðIÞÞ:xZACHMAN 6 8; Eð~eZACHMAN8ðIÞÞ:xZACHMAN 6 8; Eð~eTEAF1ðIÞÞ:xTEAF 6 8; Eð~eTEAF2ðIÞÞ:xTEAF 6 8; Eð~eTEAF3ðIÞÞ:xTEAF 6 8; Eð~eTEAF4ðIÞÞ:xTEAF 6 8; Eð~eTEAF5ðIÞÞ:xTEAF 6 8; Eð~eTEAF6ðIÞÞ:xTEAF 6 8; Eð~eTEAF7ðIÞÞ:xTEAF 6 8; Eð~eTEAF8ðIÞÞ:xTEAF 6 8; Eð~eTOGAF1ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF2ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF3ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF4ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF5ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF6ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF7ðIÞÞ:xTOGAF 6 8; Eð~eTOGAF8ðIÞÞ:xTOGAF 6 8; Eð~eDODAF1ðIÞÞ:xDODAF 6 8; Eð~eDODAF2ðIÞÞ:xDODAF 6 8; Eð~eDODAF3ðIÞÞ:xDODAF 6 8; Eð~eDODAF4ðIÞÞ:xDODAF 6 8; Eð~eDODAF5ðIÞÞ:xDODAF 6 8; Eð~eDODAF6ðIÞÞ:xDODAF 6 8; Eð~eDODAF7ðIÞÞ:xDODAF 6 8; Eð~eDODAF8ðIÞÞ:xDODAF 6 8; Eð~eFEAF1ðIÞÞ:xFEAF 6 8; Eð~eFEAF2ðIÞÞ:xFEAF 6 8; Eð~eFEAF3ðIÞÞ:xFEAF 6 8; Eð~eFEAF4ðIÞÞ:xFEAF 6 8; Eð~eFEAF5ðIÞÞ:xFEAF 6 8; Eð~eFEAF6ðIÞÞ:xFEAF 6 8; Eð~eFEAF7ðIÞÞ:xFEAF 6 8; Eð~eFEAF8ðIÞÞ:xFEAF 6 8; xFEAF þ xZACHMAN þ xTOGAF þ xTEAF þ xDODAF ¼ 1 xFEAF; xZACHMAN; xTOGAF; xTEAF; xDODAF ¼ 0; 1 The results from model (P) identified TEAF framework as the opti- mal EA framework. We communicated our findings to the IEHT management who proceeded with the implementation of our recommendation. Table 4 Strategic risk criteria associated with the enterprise architecture frameworks. Risk criteria Description Organizational risk The stability of the management; organizational support for User risk The lack of user involvement during the EA framework deve Requirement risk Frequently changing requirements; incorrect, unclear, inade Structural risk The strategic orientation of the application; quite number o Team risk Insufficient knowledge or inadequate experience among tea Complexity risk Whether new the enterprise architecture is used; the compl of links to existing systems is required Competition risk Strong competitor reactions that may prevent the enterprise Market risk The acceptance of customers, vendors and business partners the application become obsolete due to the introduction of Table 5 The impact values of the EA frameworks. Criteria FEAF ZACHMAN Organizational risk (7.6, 8.4, 0.1, 0.1) (8.6, 9.4, 0.1, 0.1) User risk (9.6, 10.4, 0.1, 0.1) (8.6, 9.4, 0.1, 0.1) Requirement risk (8.6, 9.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) Structural risk (8.6, 9.4, 0.1, 0.1) (8.6, 9.4, 0.1, 0.1) Team risk (6.6, 7.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) Complexity risk (8.6, 9.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) Competition risk (4.6, 5.4, 0.1, 0.1) (5.6, 6.4, 0.1, 0.1) Market risk (3.6, 4.4, 0.1, 0.1) (4.6, 5.4, 0.1, 0.1) 5. Conclusions and future research directions In this paper, we proposed a novel fuzzy group multi-criteria model for EA framework evaluation and selection. The contribution of the proposed model is fourfold: (1) it takes into consideration the qualitative and quantitative criteria and their respective value judgments; (2) it considers verbal expressions and linguistic vari- ables for qualitative judgments which lead to ambiguity in the decision making process; (3) it handles imprecise or vague judg- ments; and (4) it uses a meaningful and robust multi-criteria mod- el to aggregate both qualitative and quantitative data. We applied the model to select the best EA framework in a com- plex system with multiple and competing criteria and values. Organizations often fail in practice to follow a systematic and well-structured decision-making process for assessing potential EA frameworks. We have shown that our model considers the mul- ti-dimensional nature of such problems and generates vital development of the Enterprise Architecture lopment; unfavorable attitudes of users towards a new enterprise architecture quate, or ambiguous requirements f department are to be involved; the business process needs to be changed a lot m members exity of the processes being automated; whether a large number from obtaining the expected outcome of the application; unanticipated change in the industry or market; new enterprise architecture TOGAF TEAF DoDAF (9.6, 10.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) (9.6, 10.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (8.6, 9.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (8.6, 9.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (7.6, 8.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) (4.6, 5.4, 0.1, 0.1) (6.6, 7.4, 0.1, 0.1) (2.6, 3.4, 0.1, 0.1) (2.6, 3.4, 0.1, 0.1) (4.6, 5.4, 0.1, 0.1) Table 8 The possibilistic mean values of the fuzzy risk priority numbers (RPN). Criteria FEAF ZACHMAN TOGAF TEAF DoDAF Organizational risk 144 90 150 42 280 User risk 450 324 320 224 144 Requirement risk 108 80 32 40 126 Structural risk 486 576 320 224 567 Team Risk 196 245 320 192 320 Complexity risk 189 98 144 80 140 Competition risk 270 240 280 200 378 Market risk 192 175 105 105 315 Table 9 The ordinal rank matrix. Criteria FEAF ZACHMAN TOGAF TEAF DoDAF Organizational risk 2 1 3 0 4 User risk 4 3 2 1 0 Requirement risk 3 2 0 1 4 Structural risk 2 4 1 0 3 Team risk 1 2 3.5 0 3.5 Complexity risk 4 1 3 0 2 Competition risk 2 1 3 0 4 Market risk 3 2 0.5 0.5 4 Table 10 The vector of the EA framework risks. The risks vector FEAF ZACHMAN TOGAF TEAF DoDAF V 0.29 0.21 0.16 0.06 0.28 Table 6 The likelihood values of the EA frameworks. Criteria FEAF ZACHMAN TOGAF TEAF DoDAF Organizational risk (5.75, 6.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (2.75, 3.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) User risk (8.75, 9.25, 0.25, 0.25) (8.75, 9.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) Requirement risk (5.75, 6.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (3.75, 4.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (5.75, 6.25, 0.25, 0.25) Structural risk (8.75, 9.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) (8.75, 9.25, 0.25, 0.25) Team risk (3.75, 4.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) (3.75, 4.25, 0.25, 0.25) (4.75, 5.25, 0.25, 0.25) Complexity risk (2.75, 3.25, 0.25, 0.25) (1.75, 2.25, 0.25, 0.25) (2.75, 3.25, 0.25, 0.25) (1.75, 2.25, 0.25, 0.25) (3.75, 4.25, 0.25, 0.25) Competition risk (8.75, 9.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (7.75, 8.25, 0.25, 0.25) (8.75, 9.25, 0.25, 0.25) Market risk (7.75, 8.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) (6.75, 7.25, 0.25, 0.25) (8.75, 9.25, 0.25, 0.25) Table 7 The detection values of the EA frameworks. Criteria FEAF ZACHMAN TOGAF TEAF DoDAF Organizational risk (2.9, 3.1, 0.1, 0.1) (1.9, 2.1, 0.1, 0.1) (1.9, 2.1, 0.1, 0.1) (1.9, 2.1, 0.1, 0.1) (3.9, 4.1, 0.1, 0.1) User risk (4.9, 5.1, 0.1, 0.1) (3.9, 4.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (3.9, 4.1, 0.1, 0.1) (1.9, 2.1, 0.1, 0.1) Requirement risk (1.9, 2.1, 0.1, 0.1) (1.9, 2.1, 0.1, 0.1) (0.9, 1.1, 0.1, 0.1) (0.9, 1.1, 0.1, 0.1) (2.9, 3.1, 0.1, 0.1) Structural risk (5.9, 6.1, 0.1, 0.1) (7.9, 8.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (3.9, 4.1, 0.1, 0.1) (6.9, 7.1, 0.1, 0.1) Team risk (6.9, 7.1, 0.1, 0.1) (6.9, 7.1, 0.1, 0.1) (7.9, 8.1, 0.1, 0.1) (5.9, 6.1, 0.1, 0.1) (7.9, 8.1, 0.1, 0.1) Complexity risk (6.9, 7.1, 0.1, 0.1) (6.9, 7.1, 0.1, 0.1) (5.9, 6.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) Competition risk (5.9, 6.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (5.9, 6.1, 0.1, 0.1) Market risk (5.9, 6.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (4.9, 5.1, 0.1, 0.1) (6.9, 7.1, 0.1, 0.1) 1172 F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 information for selecting the most appropriate framework. While previous studies have valued multi-criteria frameworks, they have failed to consider both subjective and objective judgments in a sys- tematic and consistent model. The proposed framework supports both qualitative and quantitative decision criteria, as well as differ- ent types of risk for both quantitative and qualitative criteria. In addition, the DMs may be able to provide only imprecise or va- gue information because of time constraints or lack of data. Further- more, the DM may feel more comfortable evaluating qualitative criteria by using linguistic variables resulting in two potential prob- lems: (1) how to reconcile quantitative and qualitative criteria and (2) how to deal with imprecise and vague information rationally and consistently. We showed that the proposed framework is able to address these problems and can assist the DMs reach a robust decision. Finally, the case study showed that a combined analysis can generate valuable insight that can help the DMs to select the most suitable framework from a range of competing alternatives. Our model is intended to assist the DMs in the EA framework selection process. In fact, human judgment is the core input in this process. Our approach helps the DMs to think systematically about complex multi-criteria problems and improves the quality of the decisions. We decompose the EA framework selection process into manageable steps and integrate the results to arrive at a solution consistent with managerial goals and objectives. This decomposi- tion encourages the DMs to carefully consider the elements of uncertainty. The proposed structured framework does not imply a deterministic approach in EA framework selection problems. While our approach enables the DMs to assimilate the information and organize their beliefs in a formal systematic approach, it should be used in conjunction with management experience. Man- agerial judgment is an integral component of EA framework selec- tion decisions; therefore, the effectiveness of the model relies heavily on the DM’s cognitive capabilities. There are a variety of extensions to this research. First, EA is a new discipline and it will not mature without substantial new re- search (Langenberg & Wegmann, 2004). We hope the framework proposed in this study will stimulate new research in the fields of EA and multi-criteria decision making. Second, by identifying the unique features of the proposed framework, researchers can further study the applicability of the proposed method to other multi-criteria problems embracing both qualitative and quantita- tive criteria with imprecise or ambiguous value judgments. It is our hope that the discussions, issues and ideas set forth in this paper will motivate further enhancement to this framework. References Andre’eva, Y., Larichev, O., Flanders, N., & Brown, R. (1995). Complexity and uncertainty in Arctic resource decision: The example of the Yamal pipeline. Polar Geography and Geology, 19, 22–35. Berkeley, D., Humphreys, P., Larichev, O., & Moshkovich, H. (1991). Aiding strategic decision making: Derivation and development of ASTRIDA. In Y. Vecsenyi & H. Sol (Eds.), Environment for supporting decision processes. Amsterdam: North- Holland. F. Zandi, M. Tavana / Expert Systems with Applications 39 (2012) 1165–1173 1173 Belton, V., & Stewart, T. J. (2002). Multiple criteria decision analysis: An integrated approach. Norwell, MA: Kluwer. Brans, J. P., Vincke, Ph., & Mareschal, B. (1986). How to select and how to rank projects: The PROMETHEE method. European Journal of Operational Research, 24, 228–238. Carbone, T. A., & Tippett, D. D. (2004). Project risk management using the project risk FMEA. Engineering Management Journal, 16(4), 28–35. Chou, S., Chang, Y., & Shen, C. (2008). A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/ subjective attributes. European Journal of Operational Research, 189(1), 132–145. Costa, A. P. C. S., Almeida, A. T., & Miranda, C. M. G. (2003). Multicriteria support to sort information systems portfolio. Journal of the Academy of Business and Economics, 2(1), 237–247. Diakoulaki, D., & Koumoutsos, N. (1991). Cardinal ranking of alternatives actions: Extension of PROMETHEE method. European Journal of Operational Research, 53, 337–347. Fayad, M., & Hamu, D. (2000). Enterprise frameworks: Guidelines for selection. ACM Computing Survey, 32(1), 1–23. Gammelgêard, M., Simonsson, M., & Lindstrèom, E. (2007). An IT management assessment framework: Evaluating enterprise architecture scenarios. Information Systems and E-Business Management, 5(4), 415–435. Ghodsypour, S. H., & O’brien, C. (1998). A decision support system for supplier selection using an integrated analytical hierarchy process and linear programming. International Journal of Production Economics, 56, 199–212. Flanders, N. E., Brown, R. V., Andre’eva, Y., & Larichev, O. (1998). Justifying public decisions in Arctic oil and gas development: American and Russian approaches. Arctic, 51(3), 262–279. Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making: Methods and applications. Berlin, Heidelberg: Springer. Kahraman, C., Ates�, N. Y., Çevik, S., Gülbay, M., & Erdoğan, S. A. (2007). Hierarchical fuzzy TOPSIS model for selection among logistics information technologies. Journal of Enterprise Information Management, 20(2), 143–168. Kaklauskas, A., Zavadskas, E. K., Raslanas, S., Ginevicius, R., Komka, A., & Malinauskas, P. (2006). Selection of low-e windows in retrofit of public buildings by applying multiple criteria method COPRAS: A Lithuanian case. Energy and Buildings, 38(5), 454–462. Kim, S. H., & Ahn, B. S. (1999). Interactive group decision making procedure under incomplete information. European Journal of Operational Research, 116(3), 498–507. Langenberg, K., Wegmann, A. (2004). Enterprise architecture: What aspects is current research targeting. Technical Reports in Computer and Communication Sciences, no. 2004-77, École Polytechnique Fédérale de Lausanne, Faculté I& C, School of Computer and Communication Sciences, Lausanne, Switzerland. Larichev, O. (1992). Cognitive validity in design of decision-aiding techniques. Journal of Multi-Criteria Decision Analysis, 1(3), 127–138. Larichev, O., Brown, R., & Andre’eva, E. (1995). Categorical decision analysis for environmental management: A Siberian gas distributing case. In J.-P. Caverni, M. Bar-Hillel, F. H. Barron, & H. Jungermann (Eds.), Contribution to decision making (pp. 55–286). Amsterdam: North-Holland. Larichev, O., & Moshkovich, H. (1997). Verbal decision analysis for unstructured problems. Boston: Kluwer Academic Publishers. Poyhonen, M. A., Hamalainen, R. P., & Salo, A. A. (1997). An experiment on the numerical modelling of verbal ratio statements. Journal of Multi-Criteria Decision Analysis, 6(1), 1–10. Project Management Institute. (2009). A Guide to the Project Management Body of Knowledge (PMBOK� Guide) – 3rd Ed. Project Management Institute. Roztocki, N., & Weistroffer, H. R. (2006). Evaluating information technology investments: A fuzzy activity-based costing approach. Journal of Information Science and Technology, 2(4), 30–43. Roy, B. (1996). Multicriteria methodology for decision aiding. Dordrecht: Kluwer Academic. Saaty, T. L. (1994). How to make a decision: The analytic hierarchy process. Interfaces, 24(6), 19–43. Shih, H. S. (2008). Incremental analysis for MCDM with an application to group TOPSIS. European Journal of Operational Research, 186(2), 720–734. Tang, A., Han, J., Chen, P. (2004). A comparative analysis of architecture frameworks, Technical Report, Swinburne University of Technology. Urbaczewski, L., & Mrdalj, S. (2006). A Comparison of Enterprise Architecture Frameworks. Issues in Information Systems, 7(2), 18–23. Valls, A., & Torra, V. (2000). Using classification as an aggregation tool in MCDM. Fuzzy Sets and Systems, 15(1), 159–168. Wang, J. J., & Yang, D. L. (2007). Using a hybrid multi-criteria decision aid method for information systems outsourcing. Computers and Operations Research, 34(12), 3691–3700. Xia, H. C., Li, D. F., Zhou, J. Y., & Wang, J. M. (2006). Fuzzy LINMAP method for multiattribute decision making under fuzzy environments. Journal of Computer and System Sciences, 72(4), 741–759. Yang, J. B., & Xu, D. L. (2002). On the evidential reasoning algorithm for multiattribute decision analysis under uncertainty. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 32(3), 289–304. Zavadskas, E. K., Turskis, Z., Dejus, T., & Viteikiene, M. (2007). Sensitivity analysis of a simple additive weight method. International Journal of Management and Decision Making, 8(5-6), 555–574. Zavadskas, E. K., Turskis, Z., Tamošaitienė, J., & Marina, V. (2008). Multicriteria selection of project managers by applying grey criteria. Technological and Economic Development of Economy, 14(4), 462–477. Zimmermann, H. J. (2000). An application-oriented view of modelling uncertainty. European Journal of Operational Research, 122(2), 190–198. A fuzzy group multi-criteria enterprise architecture framework selection model 1 Introduction 2 The mathematical notations and definitions 3 The proposed model 4 The case study 5 Conclusions and future research directions References