Expert Systems with Applications 39 (2012) 2783–2793 Contents lists available at SciVerse ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa A hybrid fuzzy MCDM approach for evaluating website quality of professional accounting firms Wen-Chin Chou a,⇑, Yi-Ping Cheng b a b Department of Finance, Yu Da University, Chaochiao, Miaoli 36143, Taiwan Department of Information Management, Kainan University, Luchu, Taoyuan 33857, Taiwan a r t i c l e i n f o Keywords: CPA firms Website quality Fuzzy analytic network process (FANP) Fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (FVIKOR) a b s t r a c t Due to the popularity of internet, the CPAs can develop websites that properly deliver professional information and represent their firms. Effective use of CPA firm websites can increase communication with existing clients and attract potential clients. This study aims to build a hybrid approach that combines the fuzzy analytic network process (FANP) and fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (FVIKOR) for evaluating website quality of the top-four CPA firms in Taiwan and provide worthwhile recommendations for enhancing website design and content. The results show that CPA firms included in this study do not utilize the Internet to its full potential and need to improve their websites. Deloitte has the best overall performance, follow by PricewaterhouseCoopers, Ernst & Young, and KPMG. Additionally, the top-five evaluation criteria in order of importance are richness, understandability, assurance, relevance, and reliability. Therefore, the findings of this study can help CPAs identify the strengths and weaknesses of their own websites and in comparison with those of their competitors, and then make resource allocation decisions about how to improve the status quo and achieve ideal websites. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The professional service firms, such as certified public accountant (CPA) firms, are knowledge-intensive businesses. CPA firms prepare, maintain and/or review their clients’ financial statements and records. They also assist clients with the calculation of taxes and the submission of tax returns. Recent advances in communication and technology have enhanced the accounting profession’s capability to communicate with broader viewers (Janvrin, Gary, & Clem, 2009). Many CPA firms use dedicated websites to present their image and as a promotional tool to share information with current and potential clients, prospective employees, and other third parties (Elfrink, 2002; Luthy & Carver, 2004). In addition, they also provide updated accounting trends and regulations, conduct online seminars on international specialty areas, run Q&A sessions, or offer free consulting services (Borgia & Shrager, 2000). Effective use of a website can enhance public recognition, build brand image, improve service to existing clients, supply information to potential employees, and reduce the time and effort required to acquire profitable new clients (Clikeman, Smith, & Walden, 1998; Elfrink, 2002; Roxas, Peek, Peek, & Hagemann, 2000). However, ⇑ Corresponding author. Address: No. 168, Hsueh-fu Rd., Tanwen Village, Chaochiao Township, Miaoli County 36143, Taiwan. Tel.: +886 37 651 188x6215; fax: +886 37 651 223. E-mail addresses: wcchou@ydu.edu.tw, choueunice@hotmail.com (W.-C. Chou). 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.08.138 too many CPA home pages are cluttered, contain more narratives than necessary, or send the incorrect message (Teleki, 2007). Therefore, it is important for CPAs to measure their websites’ quality level and to make resource allocation decisions about how to improve the status quo and achieve ideal websites. In line with the multi-dimensional characteristics of website quality, the problem is a kind of multi-criteria decision-making (MCDM) problems, which requires MCDM methods for achieving an effective problem-solving system. MCDM provides a framework for an inter-websites comparison involving the evaluation of multi-criteria (Bilsel, Büyüközkan, & Ruan, 2006; Büyüközkan, Ruan, & ~lu, 2007). Several traditional MCDM methods are based on Feyziog the additive concept along with the independence assumption where each individual criterion is not always completely independent (Leung, Hui, & Zheng, 2003; Wu & Lee, 2007). Hence, an analytic network process (ANP) was developed by Saaty (1996) to overcome the problem of dependence and feedback among criteria. Recently, a compromise ranking method, namely the VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method, has been introduced as an applicable technique for implementation within MCDM (Opricovic & Tzeng, 2004; Tzeng, Lin, & Opricovic, 2005). It introduces an aggregating function based on the particular measure of closeness to the ideal solution (Opricovic & Tzeng, 2004). In reality, exact numerical values may not always be adequate to present the decision-making process, since human perception, judgment, intuition, and preference remain vague and 2784 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 difficult to measure. Fuzzy logic, or fuzzy set theory (Zadeh, 1965) is a way of addressing vague concepts and provides a means for representing uncertainty in order to handle the vagueness involved in the real situation (Chen & Wang, 2009). Therefore, the purpose of this study is to provide a more effective approach for evaluating website quality of the CPA firms. Specifically, the study proposes a hybrid MCDM approach combining fuzzy ANP and fuzzy VIKOR to deal with imprecise, uncertain, and complex decision-making problems and then to determine the preferable compromise rank from a set of alternatives. For the determination of the relative importance of evaluation criteria, fuzzy ANP is used since it is based on pair-wise comparisons and allows the utilization of linguistic variables. Then, the weights obtained through fuzzy ANP are combined with fuzzy VIKOR to compute weighted gap between the status quo and the ideal point for websites. In fuzzy ANP and fuzzy VIKOR, linguistic preferences can be converted to fuzzy numbers. Furthermore, in order to verify the practicality and usefulness of this hybrid evaluation approach, an empirical study of the topfour CPA firm websites in Taiwan is offered to illustrate the application of the proposed approach. The findings of this study can help CPAs form a clear picture of their websites’ quality level and then prioritize the strategies for improvement. Hence, this hybrid fuzzy MCDM approach represents an effective tool for evaluating CPA firm websites. 2. The concept of website quality 2.1. Accounting firm website evaluation There are a few articles with regard to accounting firm websites in the literature. Clikeman et al. (1998) demonstrated how to design an accounting firm website and examined 131 small and mediumsized accounting firm websites. The authors indicated that an interesting and effective website should include various key features, such as mission statement, description of service and employment opportunities, biographies of partners, free information, electronic forms for inquiries, and ease of navigation. In addition, the findings showed these websites performed poorly in online guest book, search engine for website, music or other audio, client testimonials, and links to client. Roxas et al. (2000) conducted a content analysis of the web pages of 346 accounting firms in terms of client choice factors, search engine and directories registration, value added features, and graphics. The researchers suggested that accounting firms must register their websites with search engines that are commonly available and must encourage more interactivity with existing and potential clients by providing free information such as newsletters and linkages to relevant websites. The studies of Clikeman et al. (1998) and Roxas et al. (2000) identified the existence of certain website characteristics. These characteristics, however, may not indicate the ease of use of the site. Clikeman and Walden (1998) surveyed 56 small- and medium-sized accounting firms on their Internet marketing experiences. The finding indicated that the main motivations for developing websites were keeping up with technology and attracting new clients. Chen, Tseng, and Chang (2005) explored the internet applications of 73 accounting firms in Taiwan. The researchers found that approximately half of the accounting firms had started to use the internet in business related activities and the main reasons for implementing the internet were sharing internal resources, enforcing communication with clients and cost saving. Luthy and Carver (2004) explored the cyber presence and on-line activities of the ‘‘Big Four’’ accounting firms in the USA and offered a critique of each site’s strengths and weaknesses as a benchmark for other accounting firms’ cyber efforts. They only reviewed the websites to see if there were any substantial problem in navigability, usability, and con- tent. Janvrin et al. (2009) examined the perceptions of 12 professional accounting association websites from the perspective of college students using an empirically validated instrument. The finding indicated that both beginning college students and accounting majors perceived that these websites were effective in providing accounting career information. The researchers examined user satisfaction using a seven-point Likert scale from strongly disagree to strongly agree, but did not have provide a clear picture of overall website’s quality level in numerical scores. The above discussion identifies a gap in the literature as to how CPAs will appropriately measure their websites’ quality by a comprehensive and systematic MCDM approach. It is important to bridge this gap and address CPAs’ concerns. 2.2. Website quality Quality is a characteristic of a product or service that reflects how well it meets the needs of its consumers (Nagel & Cilliers, 1990). Madu and Madu (2002) have noted that dimensions of e-quality may be different from the traditional practice of quality. Aladwani and Palvia (2002) considered Web quality to be a complex thing and multi-dimensional measurement in nature. DeLone and McLean’s updated information systems (IS) success model (2003) consists of three quality factors: information quality, system quality, and service quality. The three quality factors of a website will play an important role in affecting the users’ perceptions (Cao, Zhang, & Seydel, 2005). The details of each quality factor are described below. System quality is not only a measure of the information processing system itself but also an engineering-oriented performance characteristic (Ahn, Ryu, & Han, 2007; Negash, Ryan, & Igbaria, 2003). High level of system quality may provide users with more convenience, privacy, and faster responses (Ahn et al., 2007). System quality can be measured using accessibility, navigability, usability, and privacy. Accessibility evaluates whether information can be accessed efficiently, and whether the site can be located using standard resource discovery tools (Smith, 2001). Accessibility is also the ability of the website to be accessed by disabled users (Mohanty, Seth, & Mukadam, 2007). Navigability measures how easy it is for users to access the information they want on the websites, including standard menu structure, home-page links, standard page design, search engines and directories, and the indication of user position in the menu structure (Han & Mills, 2006; Schmidt, Cantallops, & dos Santos, 2008; Smith, 2001). Usability is a quality or attribute that represents how easy user interfaces are to use and how quick they are in helping users perform tasks (Nielsen, 2003). Website usability is concerned with how easy and intuitive it is for personals to learn to use and interact with a website in order to quickly and easily accomplish their tasks (Preece, 2001). Privacy refers to the extent to which users’ privacy rights are protected, privacy and security policies are clearly disclosed, and exchanges of information with users are encrypted (Smith, 2001). Information quality is the quality of the information produced and delivered by a system (Lee & Kozar, 2006). If the system does not provide the needed information, users will be dissatisfied and then leave it (Bai, Law, & Wen, 2008). However, having useful and updated information keeps a client visiting the website (Roxas et al., 2000). To entice users to revisit, the website needs to provide with appropriate, complete and clear information (DeLone & McLean, 2003). Typical characteristics of information quality include relevance, understandability, richness, and currency. Relevance refers to the extent to which the information on the website is related to the information needs of the user. Different parts of the website should be designed to meet the needs of different group of visitors (Cao et al., 2005), such as accountants, general visitors, researchers, and students. Understandability refers to ease of understanding and clearness of the information (Lee & Kozar, 2785 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 2006), such as documents written in plain language. Richness refers to detailed level and scope of information content. That is, information contained on the website are rich in content (Bilsel et al., 2006). Currency refers to up-to-date information. Last update/review date is a critical way of notifying users of the currency of content (Bilsel et al., 2006; Smith, 2001). Service quality refers to the overall support delivered by the website. That is, how well a delivered service level matches customer expectations (Ahn et al., 2007; Lee & Kozar, 2006). Service quality can be measured using responsiveness, reliability, assurance, and empathy. Reliability involves the website’s consistency of performance and dependability, focusing on whether the website is right, useful, and dependable (Negash et al., 2003). It is associated with the technical function of the site such as speed and ability to quickly download information (Madu & Madu, 2002; Zeithaml, 2002). Responsiveness deals with the provision of information on frequently asked questions (FAQs) and prompts assistance for solving problems (Ahn et al., 2007; Ho & Lee, 2007). FAQs are very helpful because they show that CPAs have insight into a client’s thought processes (Teleki, 2007). To communicate with customers, e-service providers can implement various service functions into the website such as complaint management systems (Lee & Kozar, 2006). Assurance refers to the ability of the personnel behind the firm’s website to inspire trust and confidence, as well as display knowledge and courtesy (Madu & Madu, 2002; Webb & Webb, 2004). Empathy refers to the extent to which a website provides caring, individualized information and attention to users and has users’ best interest at heart (Cao et al., 2005), such as easy way to sign up for monthly newsletter and e-mail reminders before tax season (Carr, 2003; Roxas et al., 2000). In accordance with the evaluation criteria mentioned above, this study will evaluate the CPA firm websites from the perspectives of system quality, information quality, and service quality. 3. A two-stage methodology for CPA firm websites This study proposed a two-stage methodology combining fuzzy ANP and fuzzy VIKOR for evaluating CPA firm websites. First, the fuzzy ANP is used to analyze the relative weights of the criteria. Then, the fuzzy VIKOR is used to evaluate website quality of CPA firms and rank the order among them. The concepts of the fuzzy set theory and details of the analytical methods are explained in the following subsections. 3.1. Fuzzy sets and fuzzy number e in a universe of discourse X is characterized by A fuzzy set Q membership function le ðxÞ, which associates with each element Q x in X, a real number in the interval [0, 1]. The function e (Chen, 2001). termed the grade of membership of x in Q 8 xl > < ml ; l  x  m ux leQ ðxÞ ¼ um ; m6x6u > : 0; otherwise leQ ðxÞ is ð1Þ e ¼ ðl; m; uÞ, The triangular fuzzy number above can be shown as Q where l and u represent fuzzy probabilities between the lower and upper boundaries of evaluation information (see Fig. 1). Ase 1 ¼ ðl1 ; m1 ; u1 Þ and Q e 2 ¼ ðl2 ; m2 ; u2 Þ, sume two fuzzy numbers Q the algebraic operation for the triangular fuzzy number can be displayed as follows: e 2 ¼ ðl1 ; m1 ; u1 Þ  ðl2 ; m2 ; u2 Þ e1  Q Q ¼ ðl1 þ l2 ; m1 þ m2 ; u1 þ u2 Þ ð2Þ e 2 ¼ ðl1 ; m1 ; u1 Þ  ðl2 ; m2 ; u2 Þ ¼ ðl1 l2 ; m1 m2 ; u1 u2 Þ; e1  Q Q li > 0; mi > 0; ui > 0 ð3Þ e 2 ¼ ðl1 ; m1 ; u1 ÞHðl2 ; m2 ; u2 Þ ¼ ðl1  u2 ; m1  m2 ; u1  l2 Þ e 1 HQ Q e 2 ¼ ðl1 ; m1 ; u1 Þ=ðl2 ; m2 ; u2 Þ ¼ ðl1 =u2 ; m1 =m2 ; u1 =l2 Þ; e 1=Q Q > 0; mi > 0; ui > 0 ð4Þ li ð5Þ 3.2. Fuzzy ANP (FANP) method The ANP, developed by Saaty (1996), provides a means to input judgments. The ANP also provides measurements to derive ratio scale priorities for the distribution of influence between factors and groups of factors in the decision (Saaty, 2003). The evaluators’ judgments and preferences are hard to quantify in exact numerical values due to the inherent vagueness of human language. The traditional ANP method does not express human thinking completely; therefore, this study uses fuzzy ratios instead of crisp values to handle the difficulty of assigning ratios and derives criteria fuzzy weights by the geometric mean method. As shown in Table 1, each membership function of linguistic scale is defined by three parameters of the symmetric triangular fuzzy number. This study applies fuzzy extent analysis (Chang, 1996) to compute the weight vectors of the evaluation criteria. 3.2.1. Fuzzy extent analysis method Let E = {e1, e2, e3, . . . , ea} be an object set, and T = {t1, t2, t3, . . . , tb} be a goal set. Each object is taken and extent analysis for each goal is performed, respectively. Therefore, b extent analysis values for each object can be obtained, with the following signs: e2 ;...; Q eb ; e1 ;...; Q Q gi gi gi i ¼ 1; 2; . . . ; a; ð6Þ e jg Q i where all the (j = 1, 2, . . . , b) are triangular fuzzy numbers (TFNs). The steps of Chang’ fuzzy extent analysis can be given as in the following: Table 1 Membership function of linguistic scale. Fig. 1. The membership function of the triangular fuzzy number. Linguistic scale Positive triangular fuzzy numbers Positive reciprocal triangular fuzzy numbers Absolutely importance Intermediate Very strongly Intermediate Strong Intermediate Weakly Intermediate Equally importance (8, 9, 10) (7, 8, 9) (6, 7, 8) (5, 6, 7) (4, 5, 6) (3, 4, 5) (2, 3, 4) (1, 2, 3) (1, 1, 1) (1/10, 1/9, 1/8) (1/9, 1/8, 1/7) (1/8, 1/7, 1/6) (1/7, 1/6, 1/5) (1/6, 1/5, 1/4) (1/5,1/4,1/3) (1/4,1/3,1/2) (1/3, 1/2, 1) (1, 1, 1) 2786 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 Step 1: The value of fuzzy synthetic extent with respect to the ith object is defined as e Si ¼ b X j¼1 " b a X X ej  Q gi i¼1 j¼1 ej Q gi #1 0 j¼1 ej ¼ Q gi b X lj ; j¼1 b X mj ; j¼1 b X j¼1 uj ð7Þ ! ð8Þ P P e j 1 and to obtain ½ aj¼1 bj¼1 Q g i  , perform the fuzzy addition operj e g (j = 1, 2, . . . , b) values such that ation of Q i b a X X i¼1 j¼1 a X ej ¼ Q gi i¼1 li ; a X mi ; i¼1 a X ui i¼1 ! ð9Þ and then compute the inverse of the vector in Eq. (10), such that: " b a X X i¼1 j¼1 ej Q gi #1 ¼  1 Pa i¼1 ui 0 0 WV 0 ¼ ðd ðP1 Þ; d ðP2 Þ; . . . ; d ðPa ÞÞT P ej To obtain bj¼1 Q g i , perform the fuzzy addition operation of b extent analysis values for a particular matrix such that: b X 0 Assume that d ðP i Þ ¼ min VðSi P Sk Þ for k = 1, 2, . . . , a; k – i. Then the weight vector is given by 1 ; Pa i¼1 mi 1 ; Pa i¼1 li  ð10Þ e 1 ¼ ðl1 ; m1 ; u1 Þ and Q e 2 ¼ ðl2 ; m2 ; u2 Þ are two trianguStep 2: As Q e2 P Q e 1 defined lar fuzzy numbers, the degree of possibility of Q as: e2 P Q e 1 Þ ¼ sup½minðl ðxÞ; l ðyÞÞ Vð Q e e Q1 Q2 yPx ð11Þ and can be equivalently expressed as follows: e2 P Q e 1 Þ ¼ hgtð Q e1 \ Q e 2 Þ ¼ l ðzÞ Vð Q e Q2 8 1; if m2 P m1 > < if l1 P u2 ¼ 0; > l1 u2 : ; otherwise ð14Þ where Pi (i = 1, 2, . . . , a) are a elements. Step 4: Via normalization, the normalized weight vectors are WV ¼ ðdðP1 Þ; dðP2 Þ; . . . ; dðP a ÞÞT ð15Þ where WV is a non-fuzzy number. 3.2.2. Calculation steps of FANP Step 1: Conducting pair-wise comparisons on the elements using the scale given in Table 1. The scale ranges from equal importance to extreme importance. These measurements are derived by asking, ‘‘How much importance does a criterion have compared to another criterion with respect to our interests or preferences?’’ (Huang, Tzeng, & Ong, 2005). Step 2: Computing relative importance weights for each element and testing the consistency ratio (CR). If the CR is greater than 0.1, the result is not consistent, and the pair-wise compare ¼ ½~rij  be a ison matrix must be revised by the evaluator. Let R fuzzy judgment matrix with triangular fuzzy number e is ~r ij ¼ ðlij ; mij ; uij Þ and form R = [mij]. If R is consistent, then R consistent (Lin, 2010). Step 3: Placing the results of these computations within the unweighted supermatrix. The supermatrix concept resembles a Markov chain process. To obtain global priorities in a system with interdependent influences, the local priority vectors are added to the appropriate columns of a matrix, which is known as a supermatrix. The supermatrix representation of a hierarchy with three levels is as follows: ð16Þ ð12Þ ðm2 u2 Þðm1 l1 Þ where z is the ordinate of the highest intersection point Z bee 1 and Q e 2 , we need tween le and le (see Fig. 2). To compare Q Q1 Q2 e 2 Þ and Vð Q e2 P Q e 1Þ . e1 P Q both values of Vð Q Step 3: The degree possibility for a convex fuzzy number to be e j (i = 1, 2, . . . , k) numbers can be greater than k convex fuzzy Q defined by e PQ e 1; Q e 2; . . . Q e k Þ ¼ V½ð Q e PQ e 1 Þ and ð Q e PQ e 2 Þ and    and ð Q e PQ e k Þ Vð Q e PQ e i Þ; i ¼ 1; 2; 3; . . . ; k: ¼ min Vð Q ð13Þ µQ ( x) Q2 1 Q1 where WDG is a vector that represents the impact of the ‘‘goal’’ on the ‘‘dimensions’’; WCD is a matrix that represents the impact of the ‘‘dimensions’’ on each element of the ‘‘criteria.’’ WDD and WCC would indicate the inner dependence among ‘‘dimensions’’ and ‘‘criteria,’’ respectively. Step 4: Performing pair-wise comparisons on the clusters as they influence each cluster to which they are connected with respect to the given control criterion. Step 5: Weighting the blocks of the unweighted supermatrix by the corresponding cluster priorities, such that the result is column-stochastic (weighted supermatrix). Step 6: To achieve convergence of the importance weights, the weighted (stochastic) supermatrix is raised to power. This matrix is called the limit supermatrix. Subsequently, the relative weights of all criteria obtained in the limit supermatrix are integrated with performance values of the alternatives using fuzzy VIKOR method. V ( Q 2 ≥ Q1 ) 0 3.3. Fuzzy VIKOR method Z l2 m 2 l1 z u 2 m1 e2 P Q e 1 Þ. Fig. 2. The degree of possibility Vð Q u1 x The VIKOR method was developed by Opricovic (1998) to solve MCDM problems with conflicting and non-commensurable criteria (Opricovic & Tzeng, 2004). This method considers two distance measurements, Bj and Gj, based on an aggregating function (Lp – metric) in the compromising programming method in order W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 to provide information about utility and regret; the best alternative has the maximum group utility for decision-makers and ensures the least regret (Opricovic & Tzeng, 2004, 2007). This study modifies the traditional VIKOR method regarding the measure of closeness to an ideal alternative. The modified fuzzy VIKOR method offers more rational formulas for computing the gaps between the status quo and the ideal point for websites (i.e., unimproved gaps). This method includes the following steps: 2787 Alternatives alt1 and alt2, if only the condition CN2 is not satisfied, or Alternatives alt1, alt2, . . . , altk, if the condition CN1 is not satisfied; and altk is determined by the relation H(altk)  H(alt1) DH (the positions of these alternatives are ‘‘in closeness’’). 4. Implementation of the hybrid MCDM approach 4.1. Problem description Step 1: Determining the best ~f i and the worst ~f  i values of all criterion functions, i = 1, 2, . . . , n. If the criterion i represents a ben~ efit, then ~f i ¼ max ~f ij and ~f  i ¼ min f ij ; if the criterion i j j ~ represents a cost, then ~f i ¼ min ~f ij and ~f  i ¼ max f ij . Alternaj j ~  ~ tively, the best f i is the aspired level and the worst f i is the tolerable level. e j . These values repree j and G Step 2: Computing the values of B sent group utility and individual regret for the alternative altj, respectively, with the relations ej ¼ B n X i¼1 h i e i ð~f i  ~f ij Þ=ð~f i  ~f i Þ ; for j ¼ 1; . . . :; m; w h i e j ¼ max ð~f   ~f ij Þ=ð~f   ~f  Þ j i ¼ 1; 2; . . . ; ng; for j G i i i ð17Þ i ¼ 1; . . . ; m; ð18Þ ~ i ) are introduced in order to where the weights of the criteria (w express the relative importance of criteria as computed by the fuzzy ANP method. e j ). Its formula is: Step 3: Computing the aggregate value ( H h i ej  G e  Þ=ð G e  G e  Þ; ej  B e  Þ=ð B e  B e  Þ þ ð1  v Þ½ð G e j ¼ v ðB H for j ¼ 1; . . . :; m ð19Þ e  ¼ min G e  ¼ max G ~ j , and G e j; e  ¼ min B e  ¼ max B ej, B ej, G where B j j j v is introducedj as a weight for the strategy of maximizing group utility, whereas 1  v is the weight of the individual regret. In ej order to obtain an absolute relation for the index relations H of these alternatives, the best B⁄ would be zero; the worst Bwould be equal to one; the best G⁄ would be zero, and the worst G- would be equal to one (Ou Yang, Shieh, Leu, & Tzeng, 2009). Eq. (19) is re-writing as ej ej ¼ vB e j þ ð1  v Þ G H ð20Þ e j , and H ej, G e j into Step 4: Defuzzifying triangular fuzzy number B crisp values. A center of area (COA) defuzzification method is used to determine the best non-fuzzy performance (BNP) value of the fuzzy numbers mainly because it is practical (Opricovic & Tzeng, 2003). The BNP value of the triangular fuzzy number (lj, mj, uj) can be found by the following equation. BNPj ¼ lj þ ½ðuj  lj Þ þ ðmj  lj Þ=3; 8j ð21Þ 1 Step 5: Proposing  the alternative alt , which is first ranked by the measure min Hj jj ¼ 1; 2; . . . ; mg as a single optimal solution. The alternative must satisfy two conditions as follows: CN1. The alternative alt1 has an acceptable advantage; in other words, H(alt2)  H(alt1) P DH where DH = (max Hj  min Hj )/ j j (m  1) and m is the number of alternatives. 1 CN2. The alternative alt is stable within the decision-making process; in other words, it is also the best ranked in B() or/ and G(). If one of the above conditions is not satisfied, then a set of compromise solutions is proposed, which consists of: Providing services online enables CPAs to serve clients remotely; however, the CPA firms do not understand how successful their websites are or how many gaps should be filled between the status quo and an ideal website. In other words, how much effort must the CPAs put into improving website quality in order to achieve their aspired levels? This raises the critical issue of how the CPAs can effectively measure their websites’ quality. A proper evaluation is required to answer this question, and a comprehensive and systematic methodology is the key to effective measurement. This study selected the top-four CPA firm websites in Taiwan as demonstration cases. The top-four CPA firms in Taiwan are Deloitte, KPMG, PricewaterhouseCoopers (PwC), and Ernst & Young (E&Y). Taiwanese top-four CPA firms entered into agreements with the ‘‘Big four’’ CPA firms in the network to share a common name, brand and quality standards. The ‘‘Big four’’ are the four largest international accountancy and professional services firms, which handle the vast majority of audits for publicly traded companies as well as many private companies. Each member firm is a legally separate and independent entity (Wikipedia, 2010). The following shows how to evaluate website quality of the top-four CPA firms in Taiwan by using the proposed hybrid MCDM approach. 4.2. Applications of the proposed approach The first phase defines the decision goal. The goal is to evaluate and rank the websites of the top-four CPA firms in Taiwan. In phase 2, the analytical structure, based on related literature and expert interviews, is used to assess the websites. This structure is initially developed based on a literature review. Then, by conducting interviews with two professors specialized in e-business and three CPAs, the analytical structure is modified. The highest scoring four criteria from each dimension are extracted to construct the evaluation framework for the CPA firm websites. As seen in Fig. 3, this MCDM problem is considered from three dimensions, including system quality, information quality, and service quality. The ‘‘system quality’’ is divided into four criteria: ‘‘accessibility (C1),’’ ‘‘navigability (C2),’’ ‘‘usability (C3),’’ and ‘‘privacy (C4).’’ The ‘‘information quality’’ consists of four criteria: ‘‘relevance (C5),’’ ‘‘understandability (C6),’’ ‘‘richness (C7),’’ and ‘‘currency (C8).’’ Finally, the ‘‘service quality’’ is composed of ‘‘responsiveness (C9),’’ ‘‘reliability (C10),’’ ‘‘assurance (C11),’’ and ‘‘empathy (C12).’’ In addition, the ‘‘alternatives’’ constitutes the four CPA firm websites. In phase 3, 10 professional users consisting of academic researchers and industrial practitioners, who often collect accounting and tax information from accounting-related websites, are asked to make pair-wise comparisons for all evaluation criteria. After computing the result of each evaluator’s assessment, the consistency ratio values are less than the acceptable threshold value (i.e., CR < 0.1). The overall results are obtained by taking the geometric mean of individual evaluations. In the following, it is given how weight vectors of the dimension with respect to the goal are obtained in detail. In Chang’s extent analysis method, first, the values of fuzzy synthetic extents with respect to the three dimensions are obtained by using Eq. (7) as follows: 2788 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 Goal Dimensions Alternatives Criteria Accessibility (C1) System quality (D1) Navigability (C2) Usability (C3) Deloitte Website Privacy (C4) Relevance (C5) CPA firms website quality evaluation Information quality (D2) KPMG Website Understandability (C6) Richness (C7) Currency (C8) PwC Website Responsiveness (C9) Service quality (D3) Reliability (C10) E&Y Website Assurance (C11) Empathy (C12) Fig. 3. The analytic structure of CPA firm websites evaluation. e S D1 ¼ ð2:126; 2:539; 3:271Þ  ð1=11:792; 1=9:218; 1=7:321Þ ¼ ð0:180; 0:275; 0:447Þ e S D2 ¼ ð2:839; 3:704; 4:681Þ  ð1=11:792; 1=9:218; 1=7:321Þ ¼ ð0:241; 0:402; 0:639Þ e S D3 ¼ ð2:356; 2:975; 3:840Þ  ð1=11:792; 1=9:218; 1=7:321Þ ¼ ð0:200; 0:323; 0:524Þ Then, the degrees of possibility are calculated by using Eq. (12) as follows: VðSD1 P SD2 Þ ¼ 0:620; VðSD1 P SD3 Þ ¼ 0:840 VðSD2 P SD1 Þ ¼ 1:000; VðSD2 P SD3 Þ ¼ 1:000 VðSD3 P SD1 Þ ¼ 1:000; VðSD3 P SD2 Þ ¼ 0:782 For each pair-wise comparison, the minimum of the degrees of possibility is found as follows: 0 d ðPD1 Þ ¼ min VðSD1 P SD2 ; SD3 Þ ¼ minð0:620; 0:840Þ ¼ 0:620 0 d ðPD2 Þ ¼ min VðSD2 P SD1 ; SD3 Þ ¼ minð1:000; 1:000Þ ¼ 1:000 0 d ðPD3 Þ ¼ min VðSD3 P SD1 ; SD2 Þ ¼ minð1:000; 0:782Þ ¼ 0:782 These values yield the following weights vector: WV 0 ¼ ð0:620; 1:000; 0:782Þ At the last step of the algorithm, the normalized weight vector of the dimension with respect to the goal is obtained as follows: WV 1 ¼ ðdðPD1 Þ; dðP D2 Þ; dðPD3 ÞÞT ¼ ð0:258; 0:416; 0:326Þ In a similar way, the normalized weight vector of the criteria with respect to system quality is calculated as follows: WV 2 ¼ ðdðPC1 Þ; dðPC2 Þ; dðPC3 Þ; dðPC4 ÞÞT ¼ ð0:194; 0:277; 0:358; 0:171Þ The normalized weight vector of the criteria with respect to information quality is calculated as follows: WV 3 ¼ ðdðPC5 Þ; dðPC6 Þ; dðPC7 Þ; dðPC8 ÞÞT ¼ ð0:272; 0:293; 0:335; 0:100Þ The normalized weight vector of the criteria with respect to service quality is calculated as follows: WV 4 ¼ ðdðPC9 Þ; dðPC10 Þ; dðPC11 Þ; dðPC12 ÞÞT ¼ ð0:207; 0:347; 0:301; 0:145Þ Tables 2 and 3 show all of the priority weights driven from the calculations explained above. Then, the evaluators compare the interdependent relationships with respect to accessibility, navigability, usability, and privacy, respectively. Table 4 gives four fuzzy comparison data of inner dependence matrices for the four criteria and the normalized weight vectors are shown in the last column. The eigenvectors displayed are appropriate to enter into the unweighted supermatrix, as shown in Table 5. Then, the evaluators conduct the pair-wise comparisons on the clusters. The unweighted supermatrix is transformed to be column-stochastic after completing the pair-wise comparisons of the clusters. Finally, the weighted supermatrix is raised to limiting powers for obtaining a steady-state outcome. The results of the limit supermatrix yielded (C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12) = (0.070, 0.067, 0.064, 0.047, 0.089, 0.113, 0.126, 0.070, 0.077, 0.087, 0.108, 0.082). Ranked by the weights, the top-five criteria in order of importance are: ‘‘richness (C7),’’ ‘‘understandability (C6),’’ ‘‘assurance (C11),’’ ‘‘relevance (C5),’’ and ‘‘reliability (C10).’’ Table 6 shows the relative weights for the 12 criteria based on the results of the ANP, as well as the relative weights as determined by the AHP. If 2789 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 Table 2 The fuzzy evaluation matrix with respect to the goal. System quality (Dl) System quality (D1) Information quality (D2) Service quality (D3) 1 1.003 0.785 Information quality (D2) 1 1.473 1.162 1 1.931 1.644 0.518 1 0.571 Service quality (D3) 0.679 1 0.812 0.997 1 1.196 0.608 0.836 1 Weights 0.860 1.231 1 1.274 1.750 1 0.258 0.416 0.326 Table 3 The fuzzy evaluation matrix with respect to the three dimensions. Accessibility (C1) With respect to system quality Accessibility (C1) 1 1 Navigability (C2) 0.908 1.335 Usability (C3) 1.236 1.783 Privacy (C4) 0.582 0.907 With respect to information quality Relevance (C5) Relevance (C5) 1 1 Understandability (C6) 0.738 1.103 Richness (C7) 0.878 1.267 Currency (C8) 0.395 0.568 With respect to service quality Responsiveness (C9) Responsiveness (C9) 1 1 Reliability (C10) 0.960 1.578 Assurance (C11) 0.897 1.282 Empathy (C12) 0.596 0.885 Navigability (C2) Usability (C3) 1 1.692 2.463 1.374 0.591 1 0.818 0.462 0.749 1 1.374 0.699 1.101 1 2.094 1.104 1 1.633 1.898 0.842 Understandability (C6) 0.612 0.907 1.356 1 1 1 0.780 1.182 1.790 0.361 0.545 0.842 Richness 0.527 0.559 1 0.369 1 2.221 2.104 1.251 Reliability 0.450 1 0.631 0.361 Assurance 0.475 0.867 1 0.411 (C10) 0.634 1 0.836 0.509 0.406 0.478 1 0.416 1.041 1 1.153 0.693 Privacy (C4) 0.561 0.728 1 0.568 0.809 1.223 1 0.800 0.728 0.905 1.250 1 (C7) 0.789 0.846 1 0.467 1.139 1.282 1 0.646 1.115 1.585 1 0.960 (C11) 0.780 1.196 1 0.574 Weights 1.103 1.431 1.762 1 1.719 2.166 2.405 1 0.194 0.277 0.358 0.171 Currency 1.188 1.187 1.547 1 (C8} 1.762 1.835 2.144 1 2.531 2.769 2.709 1 0.272 0.293 0.335 0.100 Empathy 0.799 1.442 1.041 1 (C12) 1.129 1.966 1.741 1 1.679 2.769 2.434 1 0.207 0.347 0.301 0.145 Table 4 The inner dependence matrix with respect to the four criteria. Criteria Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) Weights The inner dependence Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) matrix with 1 0.522 0.438 0.411 respect C1 1 1 0.679 0.854 0.634 1.058 0.595 0.890 1.171 1 0.582 0.626 1.473 1 0.933 0.876 1.914 1 1.463 1.192 0.946 0.683 1 0.584 1.578 1.072 1 0.896 2.285 1.719 1 1.390 1.123 0.839 0.719 1 1.681 1.141 1.116 1 2.431 1.597 1.712 1 0.350 0.234 0.227 0.189 The inner dependence Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) matrix with 1 0.719 0.467 0.386 respect to C2 1 1 1.072 1.633 0.707 1.175 0.552 0.808 0.612 1 0.467 0.416 0.933 1 0.660 0.545 1.390 1 1.052 0.735 0.851 0.950 1 0.588 1.414 1.516 1 0.812 2.141 2.141 1 1.218 1.237 1.361 0.821 1 1.813 1.835 1.231 1 2.588 2.405 1.701 1 0.314 0.326 0.215 0.145 The inner dependence Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) matrix with 1 0.860 1.117 0.534 respect to C3 1 1 1.473 2.221 1.578 2.472 0.771 1.121 0.450 1 0.786 0.324 0.679 1 1.103 0.475 1.162 1 1.512 0.693 0.000 0.661 1 0.303 0.000 0.907 1 0.418 0.000 1.272 1 0.673 0.892 1.442 1.486 1 1.297 2.107 2.392 1 1.874 3.090 3.300 1 0.207 0.329 0.357 0.107 The inner dependence Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) matrix with 1 0.644 0.624 0.851 respect to C4 1 1 0.812 1.116 0.972 1.506 1.414 2.034 0.896 1 0.826 1.180 1.231 1 1.246 1.921 1.552 1 2.032 2.778 0.664 0.492 1 1.201 1.029 0.803 1 1.762 1.604 1.210 1 2.292 0.492 0.360 0.436 1 0.707 0.521 0.568 1 1.175 0.847 0.833 1 0.238 0.166 0.232 0.364 the interrelated structure of criteria is neglected, the results of the AHP would yield (C1, C2, C3, C4, C5, C6, C7, C8, C9, C10, C11, C12) = (0.050, 0.072, 0.092, 0.044, 0.113, 0.122, 0.139, 0.042, 0.068, 0.113, 0.098, 0.047). It is interesting to contrast these two methods, as their results are obviously different in terms of derived weights and the ranking order among the 12 criteria. The contrasting outcomes indicate that interdependencies between criteria can affect real assessment processes. Therefore, adopting a suitable method is important, as it influences the accuracy of the evaluation results. After finishing a series of pair-wise comparisons, the evaluators are asked to provide linguistic values for the 12 criteria. In this study, linguistic values are used to design the evaluation questionnaire. These performance values, which are very good, good, median, poor, and very poor, are transformed by scaling them into the TFNs, as shown in Table 7. The membership functions are represented in Fig. 4. The average fuzzy performance values of each criterion for each alternative are computed using the arithmetic method. For example, the computational process of ‘‘Deloitte’’ under the ‘‘accessibility’’ criterion is illustrated as follows. ~f ¼ 11 10 X k¼1 lf11 !, ¼ ð55; 80; 95Þ 10; 10 X k¼1 mf11 !, 10; 10 X k¼1 uf11 !, 10 ! 2790 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 Table 5 Unweighted supermatrix. Website evaluation (WE) System quality (D1) Information quality (D2) Service quality (D3) Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) Relevance (C5) Understandability (C6) Richness (C7) Currency (C8) Responsiveness (C9) Reliability (C10) Assurance (C11) Empathy (C12) Goal Dimensions Criteria WE D1 D2 D3 C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 0 0.258 0.416 0.326 0 0 0 0 0 0 0 0 0 0 0 0 0 0.477 0.315 0.208 0.194 0.277 0.358 0.171 0 0 0 0 0 0 0 0 0 0.116 0.517 0.367 0 0 0 0 0.272 0.293 0.335 0.100 0 0 0 0 0 0.208 0.268 0.524 0 0 0 0 0 0 0 0 0.207 0.347 0.301 0.145 0 0 0 0 0.350 0.234 0.227 0.189 0 0 0 0 0 0 0 0 0 0 0 0 0.314 0.326 0.215 0.145 0 0 0 0 0 0 0 0 0 0 0 0 0.207 0.329 0.357 0.107 0 0 0 0 0 0 0 0 0 0 0 0 0.238 0.166 0.232 0.364 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.338 0.276 0.197 0.189 0 0 0 0 0 0 0 0 0 0 0 0 0.191 0.341 0.326 0.142 0 0 0 0 0 0 0 0 0 0 0 0 0.235 0.323 0.369 0.073 0 0 0 0 0 0 0 0 0 0 0 0 0.114 0.130 0.358 0.398 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.335 0.181 0.222 0.262 0 0 0 0 0 0 0 0 0 0 0 0 0.249 0.326 0.279 0.146 0 0 0 0 0 0 0 0 0 0 0 0 0.152 0.311 0.359 0.178 0 0 0 0 0 0 0 0 0 0 0 0 0.159 0.131 0.345 0.365 Table 6 Comparison of the fuzzy ANP and fuzzy AHP methods. Criteria Fuzzy ANP Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) Relevance (C5) Understandability (C6) Richness (C7) Currency (C8) Responsiveness (C9) Reliability (C10) Assurance (C11) Empathy (C12) Fuzzy AHP Weights Rank Weights Rank 0.070 0.067 0.064 0.047 0.089 0.113 0.126 0.070 0.077 0.087 0.108 0.082 8 10 11 12 4 2 1 8 7 5 3 6 0.050 0.072 0.092 0.044 0.113 0.122 0.139 0.042 0.068 0.113 0.098 0.047 9 7 6 11 3 2 1 12 8 3 5 10 Table 7 Linguistic scale for the rating of each website. Linguistic scale Fuzzy numbers Very poor Poor Fair Good Very good (0, 0, 25) (0, 25, 50) (25, 50, 75) (50, 75, 100) (75, 100, 100) The remainder elements of average fuzzy performance values can be obtained by the same procedure, and they are shown in Table 8. Then, the evaluators determine that a score of 100 represented the best solution, and a score of zero represented the worst solution. The weighted gaps between the status quo and the ideal point are obtained by using Eq. (17), as shown in Table 9. Next, the e j and H ej, G e j are calculated by selecting v = 0.5, as shown in values B e j and H ej, G e j are defuzzified, as shown Table 10. Finally, the values B in Table 11. To take the BNP value of Deloitte (B1) as an example, the calculation process can be done as follows: e 1 ¼ ð0:054; 0:206; 0:456Þ B B1 ¼ BNP 1 ¼ l1 þ ½ðu1  l1 Þ þ ðm1  l1 Þ=3 ¼ 0:054 þ ½ð0:456  0:054Þ þ ð0:206  0:054Þ=3 ¼ 0:239 Given these results, ‘‘Deloitte’’ has an acceptable advantage and it is also the best ranked in B() and G(). Thus, ‘‘Deloitte’’ is proposed as a single optimal solution. Moreover, Table 11 shows the values Hj are (Deloitte, KPMG, PwC, E&Y) = (0.278, 0,471, 0.347, 0.470). Therefore, the four CPA firm websites are ranked as follows: Deloitte PwC E & Y KPMG, where A B indicates that A is preferred to B. These results indicate ‘‘Deloitte’’ has the best overall performance and is the closest to the ideal solution. On the contrary, ‘‘KPMG’’ is the farthest from the ideal solution, as its Hj value (0.471) is larger than all others. 4.3. Discussion The fuzzy VIKOR method is able to derive and rank the unimproved gaps of the CPA firm websites, and the results can help CPAs understand their website’s quality level and make resource allocation decisions about how to improve the status quo. ‘‘KPMG’’ is the worst website in the VIKOR ranking. As seen in Table 9, it is evident that the main reason for ‘‘KPMG’’ being ranked lowest is due to the fact that its gaps from ‘‘information quality’’ dimension are biggest. Therefore, for ‘‘KPMG’’ to improve its performance, it must first put more emphasis on website’s understandability, richness, relevance, currency, and assurance. The ‘‘understandability (C6)’’ criterion, including ease of understanding and clearness of the information, has the highest weighted gap (0.051). The context of dropdown menu has some English words in Chinese version of ‘‘KPMG’’ website. This study suggests that the Chinese version should use Chinese language in order for Chinese users. The ‘‘richness (C5)’’ criterion has the second highest weighted gap (0.050). This study suggests that ‘‘KPMG’’ website should build a dedicated section to provide a greater variety of accounting-related information, such as corporate governance, risk management, and taxation. Such abundant information can help visitors know more accounting new knowledge. The ‘‘relevance (C4)’’ criterion has the third highest weighted gap (0.040). The website did not have a special function where different groups of browsers could receive disparate guidance. This study suggests that it should divide visitors into various categorizations, such as accountants, general visitors, researchers, and students. This will provide more relevant information for different groups of visitors and help them find desired information quickly. The ‘‘currency (C8)’’ criterion has the fourth highest weighted gap (0.039). This website offered a section on upcoming events and the latest news, but did not show the date of news release as well as the last website update. These need to be improved. The ‘‘assurance (C11)’’ criterion has the fifth highest weighted gap (0.038). The study suggests the website should provide a section of the case studies. The case studies include various solutions that the CPA firm has designed and implemented for its 2791 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 µθ ( x) 1 Very Poor 0 Poor Fair Good Very Good 25 50 75 100 x Fig. 4. Membership functions of linguistic variables for measuring the website quality. Table 8 Average fuzzy performance values of each criterion for the four websites. Criteria/websites Deloitte KPMG PwC E&Y Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) Relevance (C5) Understandability (C6) Richness (C7) Currency (C8) Responsiveness (C9) Reliability (C10) Assurance (C11) Empathy (C12) (55, 80, 95) (60, 85, 95) (45, 70, 90) (45, 70, 90) (55, 80, 100) (45, 70, 90) (55, 80, 90) (65, 90, 100) (60, 85, 95) (50, 75, 95) (65, 90, 100) (50, 75, 95) (35, 60, 85) (30, 55, 80) (40, 65, 85) (40, 65, 90) (30, 55, 80) (30, 55, 80) (35, 60, 85) (20, 45, 70) (50, 75, 95) (40, 65, 90) (40, 65, 90) (45, 70, 90) (55, 80, 100) (50, 75, 95) (60, 85, 95) (55, 80, 100) (55, 80, 95) (65, 90, 100) (60, 85, 95) (50, 75, 95) (30, 55, 80) (50, 75, 90) (55, 80, 90) (55, 80, 100) (20, 40, 65) (50, 75, 95) (40, 65, 85) (50, 75, 100) (25, 50, 75) (40, 65, 85) (45, 70, 85) (35, 60, 85) (35, 60, 85) (35, 60, 85) (45, 70, 90) (75, 100, 100) clients, such as reducing overall tax rates, increasing net profit, and identifying all the hidden costs. These previous success experiences are very important to establish the credibility of the accounting profession. ‘‘E&Y’’ is the second worst website in the VIKOR ranking. Ranking by the weighted gap, the top-five criteria are ‘‘relevance’’ (0.045), ‘‘richness’’ (0.042), ‘‘understandability’’ (0.041), ‘‘accessibility (0.041)’’, and ‘‘reliability (0.035).’’ With regard to the improvement of the ‘‘relevance’’ criterion, the international financial reporting standards (IFRS) has recently become virtually a single set of global accounting standards in the international capital markets. The adoption of IFRS is expected to enhance the competitiveness of Taiwan’s capital markets. Thus, the Taiwanese Government announced the listed companies and financial institutions would be required to prepare financial statements in accordance with IFRS in 2013. It is suggested that ‘‘E&Y’’ website should refer to the ‘‘IFRS’’ multimedia section of other websites and build a specific e-learning section to introduce IFRS related issues. It is worth noting that higher search engines rankings translate into greater traffic to the site and, subsequently, increase its degree of accessibility (Miranda-González & Bañegil-Palacios, 2004). This study chooses ‘‘Yahoo! Taiwan’’ and inputs ‘‘CPA firm’’ as keyword to evaluate the accessibility of the four CPA firm websites, because this search engine is the most frequently used by Taiwan’s Internet users. Only ‘‘Deloitte’’ CPA firm’s name is shown in the first page of ‘‘Yahoo Taiwan.’’ This study suggests that other CPA firms should improve accessibility of their website through registration in the first page of the popular search engine. According to the VIKOR, the value of the weight v has a central role in the ranking of alternatives. The evaluators can select suitable weight (v) according to their priorities: Hj (v = 0.5) would be used as they are concerned about maximum group utility and Table 9 The VIKOR weighted gap analysis of the four websites. Criteria/websites System quality Accessibility (C1) Navigability (C2) Usability (C3) Privacy (C4) Information quality Relevance (C5) Understandability (C6) Richness (C7) Currency (C8) Service quality Responsiveness (C9) Reliability (C10) Assurance (C11) Empathy (C12) Global weighted gap ⁄ Deloitte KPMG PwC Weighted gap BNP⁄ Rank Weighted gap (0.004, (0.003, (0.006, (0.005, 0.014, 0.031) 0.010, 0.027) 0.019, 0.035) 0.014, 0.026) 0.016 0.013 0.020 0.015 7 11 5 9 (0.010, (0.013, (0.010, (0.005, (0.000, 0.018, 0.040) (0.011, 0.034, 0.062) (0.013, 0.025, 0.057) (0.000, 0.007, 0.024) 0.019 0.036 0.032 0.011 (0.004, 0.012, 0.031) (0.004, 0.022, 0.044) (0.000, 0.011, 0.038) (0.004, 0.020, 0.041) (0.054, 0.206, 0.456) 0.015 0.023 0.016 0.022 0.239 Represent best non-fuzzy performance. E&Y BNP⁄ Rank Weighted gap BNP⁄ Rank Weighted gap 0.046) 0.047) 0.038) 0.028) 0.028 0.030 0.023 0.016 8 6 10 12 (0.000, 0.014, 0.031) (0.003, 0.017, 0.033) (0.003, 0.010, 0.026) (0.000, 0.009, 0.021) 0.015 0.018 0.013 0.010 10 8 11 12 (0.024, (0.003, (0.010, (0.000, 0.042, 0.017, 0.022, 0.012, 6 1 2 12 (0.018, 0.040, 0.062) (0.022, 0.051, 0.079) (0.019, 0.050, 0.082) (0.021, 0.039, 0.056) 0.040 0.051 0.050 0.039 3 1 2 4 (0.005, 0.018, 0.040) (0.000, 0.011, 0.040) (0.006, 0.019, 0.050) (0.004, 0.017, 0.035) 0.021 0.017 0.025 0.019 5 9 3 6 (0.022, (0.017, (0.019, (0.010, 0.044, 0.040, 0.038, 0.028, 9 3 7 4 (0.004, 0.019, 0.039) (0.009, 0.030, 0.052) (0.011, 0.038, 0.065) (0.008, 0.025, 0.045) (0.150, 0.389, 0.639) 0.021 0.030 0.038 0.026 0.393 11 6 5 9 (0.015, 0.035, 0.054) (0.009, 0.022, 0.044) (0.011, 0.022, 0.049) (0.004, 0.016, 0.037) (0.060, 0.210, 0.460) 0.035 0.025 0.027 0.019 0.243 1 3 2 6 0.028, 0.030, 0.022, 0.017, BNP⁄ Rank 0.056) 0.033) 0.038) 0.023) 0.041 0.018 0.023 0.012 3 10 9 11 0.067) 0.068) 0.069) 0.046) 0.045 0.041 0.042 0.028 1 3 2 8 (0.012, 0.031, 0.050) (0.013, 0.035, 0.057) (0.011, 0.032, 0.059) (0.000, 0.000, 0.021) (0.141, 0.341, 0.587) 0.031 0.035 0.034 0.007 0.356 7 5 6 12 2792 W.-C. Chou, Y.-P. Cheng / Expert Systems with Applications 39 (2012) 2783–2793 Table 10 Fuzzy values of VIKOR index. Websites Deloitte KPMG PwC E&Y ej B (0.054, 0.206, 0.456) (0.150, 0.389, 0.639) (0.060, 0.210, 0.460) (0.141, 0.341, 0.587) ej G (0.100, 0.300, 0.550) (0.300, 0.550, 0.800) (0.200, 0.450, 0.700) (0.350, 0.600, 0.800) ej H (0.077, 0.253, 0.503) (0.225, 0.469, 0.719) (0.130, 0.330, 0.580) (0.246, 0.470, 0.694) Table 11 Ranking of the four websites for VIKOR. Websites Deloitte KPMG PwC E&Y Bj ðv ¼ 1Þ Gj ðv ¼ 0Þ Hj ðv ¼ 0:5Þ Value Rank Value Rank Value Rank 0.239 0.393 0.243 0.356 1 4 2 3 0.317 0.550 0.450 0.583 1 3 2 4 0.278 0.471 0.347 0.470 1 4 2 3 the ambiguities involved in the evaluation data and effectively represents and processes them to assure a more convincing assessment process. The implications of this study are critical for website designers and CPAs as the analysis shows that there are still unimproved gaps between professional users’ perceptions and expectations of CPA firm websites. The paper will give practitioners sufficient insight into how the quality of their websites may be appropriately measured in order to allow the CPA firms to prioritize improvement actions accordingly. Future research could apply this hybrid approach flexibly to other situations. Future research could also identify additional factors that are not considered in the present study. Acknowledgements The authors would like to thank the National Science Council of Taiwan for financially supporting this research under Grant NSC99-2410-H-412-005. References individual regret; Bj (v = 1) would be used as they are concerned about maximum group utility; Gj (v = 0) would be used as they are concerned about individual regret. Table 11 shows the results that are based on different gap analysis, namely, maximal group utility (Bj), maximal regret (Gj), and combined both (Hj). However, depending on the evaluators’ maximum group utility or regret, so rankings differ. It can be seen that ‘‘E&Y’’ is better than ‘‘KPMG’’ if the evaluators highlight maximum group utility. On the other hand, ‘‘KPMG’’ is better than ‘‘E&Y’’ if the maximum level of regret is considered. 5. Conclusions The web is a fast and convenient way to disseminate useful information about business products and service (Clikeman et al., 1998), the CPAs are able to deliver professional information and attract potential clients via dedicated websites. This study proposes a hybrid fuzzy MCDM framework considering various quality characteristics under a fuzzy environment for effectively ranking website quality of the top-four CPA firms in Taiwan. In this hybrid approach, the relative weights of evaluation criteria are determined by fuzzy ANP method and the ratings of CPA firm websites are assessed in linguistic terms by fuzzy VIKOR. The results of fuzzy ANP show that the top-five priorities of the 12 criteria for website quality are ‘‘richness,’’ ‘‘understandability,’’ ‘‘assurance,’’ ‘‘relevance,’’ and ‘‘reliability.’’ Moreover, the findings from fuzzy VIKOR show that ‘‘Delitte’’ website is the best website and that ‘‘KPMG’’ website is the worst one. The worst website performs poorly in terms of ‘‘understandability,’’ ‘‘richness,’’ ‘‘relevance,’’ ‘‘currency,’’ and ‘‘assurance.’’ These five criteria should be regard as the improvement items with higher priority because they have more opportunities to rapidly close to the gaps. The fuzzy ANP method, which combines the ANP with fuzzy set theory, not only can offer a more precise analysis by integrating interdependent relationships, but also can use triangular numbers to represent the vague and imprecise judgment of human. In addition, the fuzzy VIKOR method helps evaluators achieve an acceptable compromise of the maximum group utility for the ‘‘majority’’ and the minimum of the individual regret for the ‘‘opponent.’’ The empirical study has demonstrated the combined fuzzy ANP-VIKOR approach is an effective tool for evaluating website quality of the CPA firms. The results could help CPAs identify the strengths and weaknesses of their own websites and in comparison with those of their competitors. Thus, the hybrid fuzzy MCDM approach takes Ahn, T., Ryu, S., & Han, I. (2007). The impact of Web quality and playfulness on user acceptance of online retailing. Information and Management, 44(3), 263–275. Aladwani, A. M., & Palvia, P. C. (2002). 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