ScienceDirect ProcediaScienceDirect Computer Science 00 (2018) 000–000
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Procedia Computer Science 126 (2018) 2137–2152
22nd International Conference on Knowledge-Based and Intelligent Information & Engineering Systems 22nd International Conference on Knowledge-Based and Intelligent Information & Engineering Systems
On Analysis of e-Banking Websites Quality – Comet Application On Analysis of e-Banking Websites Quality – Comet Application Witold Chmielarz*, Marek Zborowski Witold Chmielarz*, Marek Zborowski
Abstract
University of Warsaw, Krakowskie Przedmieście 26,28 Str. 00-927 Warsaw, Poland University of Warsaw, Krakowskie Przedmieście 26,28 Str. 00-927 Warsaw, Poland University of Warsaw, Krakowskie Przedmieście 26,28 Str. 00-927 Warsaw, Poland University of Warsaw, Krakowskie Przedmieście 26,28 Str. 00-927 Warsaw, Poland
Abstract The main goal of this article is to identify the best e-banking websites in Poland in 2017 from the point of view of individual clients. But on the other hand, it is a need to do it by the best method. So, the authors’ research examines the The main goal of this article is to identify the best e-banking websites in Poland in 2017 from the point of view of possibilities of the applications of the modelling using fuzzy sets for an intuitive approach to multi-criteria evaluate eindividual clients. But on the other hand, it is a need to do it by the best method. So, the authors’ research examines the banking websites in Poland. In the present study, the authors used for this purpose the Characteristic Objects METhod possibilities of the applications of the modelling using fuzzy sets for an intuitive approach to multi-criteria evaluate e(COMET). In order to obtain the data for the analysis, the authors’ created an electronic spread-sheet of evaluations banking websites in Poland. In the present study, the authors used for this purpose the Characteristic Objects METhod which was made available on the Internet, and the participants for the study were selected with purposeful random (COMET). In order to obtain the data for the analysis, the authors’ created an electronic spread-sheet of evaluations sampling. Subsequently, on the basis of the obtained scores, the authors carried out analyses and presented the findings, which was made available on the Internet, and the participants for the study were selected with purposeful random together with the conclusions and recommendations resulting from the study. The authors’ own contribution to the sampling. Subsequently, on the basis of the obtained scores, the authors carried out analyses and presented the findings, research was the specification of the preferences of the website evaluation criteria as the main determinants of the together with the conclusions and recommendations resulting from the study. The authors’ own contribution to the perception of the websites’ quality, the identification of the best e-banking websites on the basis of the selected research was the specification of the preferences of the website evaluation criteria as the main determinants of the COMET multi-criteria method as well as the formulation of conclusions which could be the starting point for the perception of the websites’ quality, the identification of the best e-banking websites on the basis of the selected creation of a new, relevant solution to be applied in the area. COMET multi-criteria method as well as the formulation of conclusions which could be the starting point for the creation of a new, relevant solution to be applied in the area. © 2018 The Authors. Published by Elsevier Ltd. © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) © 2018 The Authors. Published by Elsevier Ltd. Selection responsibility of KES KES International. International. Selection and and peer-review peer-review under under responsibility of This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review responsibility of KES International. Keywords: electronic banking,under evaluation of the websites, COMET Keywords: electronic banking, evaluation of the websites, COMET
* Witold Chmielarz. Tel.: +48 225-534-002; fax: +48 225-534-001. E-mail address:
[email protected] * Witold Chmielarz. Tel.: +48 225-534-002; fax: +48 225-534-001. E-mail address:
[email protected] 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection peer-review under responsibility of KES International. 1877-0509and © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 1877-0509 © 2018 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Selection and peer-review under responsibility of KES International. 10.1016/j.procs.2018.07.238
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1. Introduction The importance of electronic banking in Poland is evidenced by the constant pace of its development. In relation to the fourth quarter of 2016 the number of individual clients who have potential access to account increased in relation to the fourth quarter of 2017 by over 7%, reaching 35,512 million users (92% of the population), where the number of active individual clients rose by more than 3.5%%, reaching the level of 15,889 million (45% of the population) [1]. It is the fastest growing banking sector – as indicated in the previous publications [2] – nothing seems to interfere with these positive trends. Over the last ten years, the number of customers has increased by more than 25 million. There are almost 45% of active clients among all the customers with electronic access to the account. Thus, it is the sphere, the development of which should be carefully examined and analysed. The studies into bank websites are carried out for the following reasons: to assess the situation on the banking services market from the perspective of the quality of websites of particular banks, to determine which of the banking websites is the best and why, to specify and create as well as to verify the optimal method for the bank websites’ evaluation, to analyse the characteristics of bank websites in order to create recommendations with regard to designing the websites. The authors concentrated on the third point. The problems related to the functioning of websites, in particular, access to e-banking services, are widely discussed in the literature on the subject, and there is no single formula which would allow their unambiguous assessment and the improvement of their quality. Numerous analyses also do not indicate what effect they have on the development of banking in the countries where they are being examined. There is an ongoing process of searching for the method which would best reflect the tendencies in this sphere and at the same time would be most convenient from the point of view of its users. Literature review shows that bank websites may be analysed from the point of view of their usability (sitemap, address catalogue) [3], functionality (search, navigation, content) [4], interactivity (accessibility and responsiveness) [5], visualization (colour scheme, background, graphics, text) [6], reliability [7], cost-effectiveness (costs of purchase, transport, the difference in prices in traditional and online shops) [8]. Most of the evaluation methods of e-banking websites are traditional scoring methods based on specific criteria sets, evaluated according to a fixed scale. Among the criteria which are most frequently applied there are technical and functional criteria. Many of them contain factors which may be evaluated in a highly subjective way: text clarity, the attractiveness of the colour scheme, images and photos, the speed of finding specific functions and using them) etc. In addition, some users do not treat particular criteria sets in an equivalent way. On the other hand, there are also numerous problems with determining preferences and relations between them. These problems – according to relevant literature on the subject – are solved by multi-criteria methods. The article presents a new fuzzy COMET method which helps to eliminate the problem of rank reversal, and it also shows greater accuracy than other multi-criteria decision support methods [9, 10, 11]. In the relevant literature on the subject, the most frequently discussed issues are tasks related to the selection of the strategy (scenario) [12, 13], choice of location [14, 15, 16], selection of a supplier [17, 18,] or performance (usability) evaluation [19, 20, 21]. In order to address the above-described problems, the authors reach for classic methods or their fuzzy extensions. They are mainly methods such as: Analytic Hierarchy Process (AHP) [14, 15], fuzzy AHP (fAHP) [22], Analytic Network Process (ANP) [16], fuzzy ANP (fANP) [18], Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) [15], fuzzy TOPSIS (fTOPSIS) [14, 18, 20, 2], ELimination and Choice Expressing REality (ELECTRE) [19] as well as fuzzy Preference Ranking Organization Method for Enrichment Evaluations (fPROMETHEE) [16]. However, the question arises which method would be the best for analyse of economic problems? The authors will try to get closer to solving this issue.
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2. Research Method and Description of the Sample During the research the following procedure was adopted: defining the criteria for the evaluation of the tools allowing for accessing e-banking services, verifying the comprehensibility and importance of criteria sets, their modification and verification of additional questions, adopting the methodology and evaluation criteria scale, placing the verified survey questionnaires on the university servers and generating invitations for users to complete them, carrying out calculations by means of the scoring method, the scoring method with preferences and the TOPSIS method, analysis and discussion of the findings, conclusions and recommendations concerning the usability of banking websites. The research in this paper has been conducted using the authors’ own criteria sets used for electronic access to accounts of particular banks. The criteria sets were applied since 2006 and they were created on the basis of relevant literature and verified following consultations with the experts. The evaluation criteria were established during an internet discussion conducted with the participation of scientists and researchers representing leading universities dealing with electronic banking in Poland, based on the literature on the subject. At the moment of economic crisis of 2008, a set of anti-crisis criteria, i.e. the selected measures which – in the experts’ opinion – were supposed to counteract the potential effects of the banking crisis [22] - was added to the set of evaluation criteria used to assess the access to banking services. The second modification took place in 2017 where the authors verified the correctness, comprehensibility and importance of the selected criteria for the users with the participation of 244 respondents. Finally, after this verification and consideration of users’ comments, the criteria adopted in the studies into the evaluation of banking websites were divided into three main groups: economic criteria, technical, visualisation and security criteria, anti-crisis measures. The respondents evaluated their preferences with regard to criteria groups as well as individual criteria. Specific criteria with preferences calculated as an arithmetic mean of the scores are presented in Table 1. Ci
Table 1. Clients’ preferences (C1-C20) concerning particular evaluation criteria for evaluation of e-banking website by users’ evaluation Evaluation of particular features
Average
Economic
61.72%
C1
The average nominal interest rate on a current account and an associated savings account
6.77%
C2
Account maintenance PLN/month (the average of current and savings account)
7.71%
C3
Fee for a regular electronic transfer to a bank where the user holds a bank account
5.94%
C4
Fee for an electronic transfer to another bank
6.10%
C5
Payment order (the right to access the account of a debtor and collect the amount of money indicated by the creditor)
3.84%
C6
Fee for issuing a debit card
4.12%
C7
The monthly fee for a card PLN/month (below the required limit for free transactions)
6.12%
C8
The annual average interest rate on savings accounts in PLN
5.63%
C9
Annual interest rate on deposits of PLN 10,000-20,000
4.80%
C10 Annual interest rate on loans of PLN 10,000-20,000
4.51%
C11 Fees for deposits and withdrawals from ATMs/cash deposit machines in Poland
6.18%
Technical, visualisation and security
32.43%
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Ci
Evaluation of particular features
Average
C12 Additional services (e.g. insurance, investment funds, foreign currency account, cross-border transfer, top-up phone payments, the number of available ATMs/cash deposit machines, others, e.g. Blik payment),
4.30%
C13 Access channels (bank branch, Internet-website, Internet-mobile application, call centre, SMS, helpline)
4.84%
C14
Security (token, ID and password, list of one-time passwords, list of one-time codes, SSL protocol, SMS with a code)
5.89%
C15 Visualisation
3.10%
C16 Navigation
3.15%
C17 Clarity and user-friendliness
3.75%
C18 Functionality
3.35%
C19 User-friendliness of mobile banking (website, application)
4.05%
Anti-crisis measures
5.85%
C20 Dynamics of the changes in interest rates on deposits, loans last year, the average place from the rankings, increase/decrease in the number of clients, the stability of pricing policy),
5.85%
Among the groups, the most important set were economic criteria which obtained on average a 62% score (including the most important criterion – account maintenance PLN/month (average: checking and savings account) – nearly 8%), subsequently, technical and security criteria – on average 32% (the most important security measures 6%) as well as anti-crisis measures, on average - 6%. In order to evaluate particular criteria in the banks which were selected by the clients, the authors used a standardised, simplified Likert scale [33], in which lack of a particular quality is represented by the value equal to zero, its complete fulfilment is equal to one, average fulfilment of the feature – 0.5 and intermediary values such as good fulfilment is equal to 0.75; and sufficient fulfilment amounts to 0.25. 3. The Characteristic of Objects METhod (COMET) 3.1. Fuzzy Set Theory: preliminaries Modelling using Fuzzy sets has proven to be an effective way of formulating multi-criteria decision problems [32]. The basic definitions of notions and concepts of Fuzzy Set Theory are presented as following [9, 10, 11]: Definition 1 Fuzzy set and membership function. The characteristic function A of a crisp set A X assigns a value either 0 or 1 to each member in X inasmuch as
crisp sets only allow full membership ( A ( x) 1) or non-membership at all ( A ( x) 0) . This function can be generalized to a function A~ such that the value assigned; to the element of the universal set X fall within a specified range, i.e., A~ : X [0,1] . The assigned value indicates the membership grade of the element in the set
~ A. The function A~ is called the membership function and the set A {( x, A~ ( x))} , where
A~ ( x) for each
x X
by
is called a fuzzy set [9, 24, 26].
Definition 2 Triangular fuzzy number (TFN).
~
x X , defined
~
A fuzzy set A , defined on the universal set of real numbers , is said to be a triangular fuzzy number A( a, m, b) if its membership function has the following form (1) [9, 11]:
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0, x a xa , axm m a A~ ( x, a, m, b) 1, x m bx , m xb b m 0, x a
(1)
and the following characteristics (2, 3): x1 , x 2 [a, b] x 2 x1 A~ ( x 2 ) A~ ( x1 )
(2)
x1 , x 2 [b, c] x 2 x1 A~ ( x 2 ) A~ ( x1 )
(3)
~
Definition 3 The support of a TFN A
~
~
This is the crisp subset of the set A whose all elements have non-zero membership values in the set A (4): ~ S ( A) {x : A~ ( x) 0} [a, b]
(4)
~
Definition 4 The core of a TFN A This is the singleton (one-element fuzzy set) with the membership value equal to one (5): ~ C ( A) {x : A~ ( x) 1} m
(5)
Definition 5 The fuzzy rule. The single fuzzy rule can be based on tautology Modus Ponens [10]. The reasoning process uses logical connectives IF-THEN, OR and AND. Definition 6 The rule base. The rule base consists of logical rules determining causal relationships existing in the system between fuzzy sets of its inputs and output [27]. Definition 7 T-norm operator: product The t-norm operator is a function T modelling the intersection operation AND of two or more fuzzy numbers, e.g.
~ ~ A and B . In this paper, only product is used as t-norm operator [23]:
A~ ( x) AND B~ ( y) A~ ( x) B~ ( y)
(6)
3.2. The COMET algorithm All The COMET is a very intuitive approach, but to be able to understand this, the basic knowledge on the Fuzzy Sets is necessary [9, 10 11]. The formal concept and notation of the COMET method can be presented by using the following five steps [11], where the fuzzy model is created in the result: Step 1: Define the space of the problem as follows:
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An expert determines the dimensionality of the problem by selecting number r of criteria, C1 , C 2 ,...,C r .
~ ~
~
Subsequently, the set of triangular fuzzy numbers for each criterion Ci is selected, i.e., Ci1 , Ci 2 ,...Cici . These numbers represent characteristic values in the considered domain. In this way, the following result is obtained (7): ~ ~ ~ C1 {C11 ,C12 ,...,C 1c1 } ~ ~ ~ C 2 {C 21 ,C 22 ,...,C 2c2 } (7) . ~ ~ ~ C r {C r1 ,C r2 ,...,C rcr } where c1 , c 2 ,...,cr are numbers of the fuzzy numbers for all criteria. Step 2: Generate the characteristic objects The characteristic objects (CO) are obtained by using the Cartesian Product of triangular fuzzy numbers cores for each criterion as follows (8):
CO C (C1 ) C (C2 ) ... C (Cr )
(8)
As the result of this, the ordered set of all CO is obtained (9): ~ ~ ~ CO1 {C (C11 ), C (C 21 ),...,C (C r1 )} ~ ~ ~ CO 2 {C (C11 ), C (C 21 ),...,C (C r 2 )} . ~ ~ ~ COt {C (C1c1 ), C (C 2c2 ),...,C (C rcr )}
(9)
where t is the number of CO (10): r
t ci i 1
(10)
Step 3: Rank and evaluate the characteristic objects. Determine the Matrix of Expert Judgment (MEJ). This is a result of the comparison of the characteristic objects by the knowledge of the expert. The MEJ structure is as follows (11):
11 21 MEJ ... t1 CO1
12 ... 1t CO1 22 ... 2t CO2 ...
t 2
CO2
... ... ... tt COt ... COt ...
(11)
where ij is a result of comparing COi and CO j by the expert. The more preferred characteristic object gets one point and the second object gets a null point. If the preferences are balanced, both objects get a half point. It depends solely on the knowledge and opinion of the expert and can be presented as (12):
Author name / Procedia Computer Science 00 (2018) 000–000 Witold Chmielarz et al. / Procedia Computer Science 126 (2018) 2137–2152
0.0, f exp (COi ) f exp (CO j ) ij f (COi , CO j ) 0.5, f exp (COi ) f exp (CO j ) 1.0, f (CO ) f (CO ) exp exp i j
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(12)
where f exp is an expert judgment function. The most important properties are described by the formulas (13) and (14):
ii f (COi , COi ) 0.5 ji 1 ij
(13) (14)
On the basis of formulas (13) and (14), the number of comparisons is reduced from t 2 cases to p cases (15): t t (t 1) p 2 2
(15)
Afterwards, we obtain a vertical vector of the summed Judgments (SJ) as follows (16): t
SJ i ij j 1
(16)
The last step assigns to each characteristic object the approximate value of the preference. In the result, we obtain a vertical vector P, where i-th row contains the approximate value of preference for COi . This algorithm is presented as a fragment of pseudo code: 1: k = length(unique(SJ)); 2: P = zeros(t,1); 3: for i = 1:k 4: ind = find(SJ == max(SJ)); 5: P(ind) = (k - i) / (k - 1); 6: SJ(ind) = 0; 7: end In line 1, we obtain number k as a number of unique value of the vector SJ. In line 2, we create vertical vector P of zeros (with identical size as vector SJ). In line 4, we obtain index with the maximum value of vector SJ. This index is used to assign the value of the preference to an adequate position in vector P (based on the principle of insufficient reason). In line 6, the maximum value of the vector SJ is reset. Step 4: The rule base. Each one characteristic object and value of preference is converted to a fuzzy rule as follows, general form (17) and detailed form (18):
IF COi THAN Pi
~ ~ IF C (C1i ) AND C (C 2i ) AND… THAN Pi
In this way, the complete fuzzy rule base is obtained, which can be presented as (19):
(17) (18)
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IF CO1 THAN
P1
IF CO 2
P2
THAN
..................................... IF COt
THAN
(19)
Pt
Step 5: Inference in a fuzzy model and final ranking. Each one alternative is a set of crisp number, which corresponding with criteria C1 , C 2 ,...,C r . It can be presented as follows (20):
Ai {a1i , a2i ,...,ari }
(20)
where condition (21) must be satisfied.
~ ~ a1i [C (C11 ), C (C1c1 )] ~ ~ a1i [C (C 21 ), C (C 2c2 )] ..................................... ~ ~ a ri [C (C r1 ), C (C rcr )]
(21)
Each one alternative activates the specified number of fuzzy rules, where for each one is determined the fulfilment degree of the conjunctive complex premise. Fulfilment degrees of all activated rules sum to one. The preference of alternative is computed as the sum of the product of all activated rules, as their fulfilment degrees, and their values of the preference. The final ranking of alternatives is obtained by sorting the preference of alternatives. 4. Case Study: e-Banking Websites Assessment The COMET method is characterised by unique properties, which are rare in the field of multi-criteria decisionmaking methods. First, it is important to note at this point the property related to resistance to the rank reversal paradox. This feature results from the fact that the COMET method evaluates alternatives using a model identified on the basis of characteristic objects which are independent of the set of the assessed decision variants. This means that, unlike many other methods of multi-criteria decision-making analysis, in this method, there is no comparison between the examined decision-making variants, and the result of their assessment is only proposed on the basis of the obtained model. Therefore, if we use the same decision model, then the values for the alternatives will not change, and thus the above-mentioned paradox will not occur [27]. The decision model defines the evaluation model for all decision variants in a particular problem space, which may be compared to measuring the length of the object by means of the previously defined model and not comparisons between the measured objects. Additionally, the identification of a decision model allows evaluating any set of alternatives in the considered numerical space without the need to engage an expert again in the assessment process, due to the fact that the identified object is in a continuous space. In such situations, other competitive methods most frequently require the entire identification and calculation procedure to be repeated from the very beginning, due to the fact that they identify only the assessment values for the currently considered set of alternatives, not for the entire problem state space [25]. In addition, the COMET method allows relatively easy identification of both linear and non-linear human decision-making functions, which allows increasing the scope of its application to include both linear and non-linear problems [25]. In the first step of the process of identifying the decision-making model with the application of the COMET method, an expert defines the perception of the state of the problem being solved. This defines the dimensionality of the problem, i.e. the set of 20 linguistic variables, where each linguistic variable is assigned one single component of
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decision criterion. These variables will be designated as: C1, C2, C3,... They are presented in details in Table 1 (section 2). The final effect of the first stage is a set of 20 linguistic variables representing the relevant criteria together with the defined sets of triangular fuzzy numbers in the form presented in Fig. 1.
Fig. 1. The set of two triangular numbers (Ci1 – “low level” and Ci2 – “high level” for a criterion Ci, where i = 1:20
Tables 2 and 3 present the set of examined alternatives, based on which the authors determine the values and the values of their properties in relation to the examined criteria. Ci C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20
A1 3.523 4.115 4.444 4.282 4.085 4.166 3.789 3.362 3.259 3.276 3.967 3.999 4.363 4.198 4.115 3.999 4.101 4.161 4.342 3.749
Ci C1 C2 C3 C4 C5 C6 C7
A11 3.182 3.636 4.727 4.818 3.909 4.182 3.636
A2 3.570 4.149 4.562 4.380 4.231 4.347 3.843 3.488 3.421 3.281 4.223 3.901 4.322 4.174 4.066 3.934 4.091 4.157 4.306 3.678
A12 3.786 4.071 4.357 4.500 4.000 4.357 3.929
Table 2. The efficiency of decision alternatives in relation to the examined criteria
A3 3.143 4.143 4.000 3.929 3.857 4.143 3.429 3.286 2.929 2.857 3.571 3.786 4.286 4.214 3.786 3.500 3.571 3.714 3.643 3.500
A4 3.174 3.565 4.130 3.826 3.565 3.783 3.435 3.130 3.087 3.087 3.478 3.217 3.435 3.565 3.348 3.391 3.478 3.348 3.435 3.391
A5 2.842 3.947 4.474 4.263 4.316 4.263 3.474 2.895 3.000 2.947 3.526 3.526 4.526 4.316 3.842 3.737 4.053 4.000 4.053 3.737
A6 3.300 4.043 4.329 4.029 4.000 3.914 3.657 2.971 3.000 2.971 3.914 3.671 4.129 3.914 3.671 3.671 3.900 3.886 3.929 3.457
A7 3.368 3.921 4.500 4.368 3.947 4.211 3.974 3.132 3.105 3.184 3.974 3.658 4.211 4.000 3.816 3.947 4.053 3.816 3.974 3.658
Table 3. The criteria (C1 – C20) for e-banking websites assessment
A13 3.522 4.130 4.424 4.293 4.174 4.250 3.717
A14 3.481 4.136 4.461 4.331 4.097 4.195 3.779
A15 3.613 4.452 4.387 4.161 4.161 4.323 4.419
A16 3.800 4.700 4.800 4.600 4.200 4.700 4.300
A17 3.519 4.060 4.308 4.135 3.925 3.955 3.744
A18 3.714 4.000 4.143 4.214 3.929 3.929 3.786
A8 4.000 4.000 4.444 4.222 3.556 4.111 3.333 3.889 4.000 3.889 3.667 3.667 4.000 4.222 3.667 3.444 3.444 3.667 3.778 4.000
A19 3.816 4.368 4.500 4.211 4.158 4.053 3.842
A9 3.267 4.000 4.167 3.800 3.867 4.100 3.700 2.933 3.167 3.033 3.767 3.533 4.100 3.600 3.300 3.500 3.367 3.833 3.767 3.200
A20 3.304 4.000 4.435 4.261 4.000 4.087 3.783
A10 3.452 3.613 3.968 3.774 3.935 4.097 3.677 3.194 3.129 3.161 3.774 3.774 4.065 3.806 3.581 3.742 3.645 3.806 3.645 3.484
A21 3.182 4.182 4.455 4.364 4.000 4.636 4.091
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C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20
3.545 3.364 3.364 4.000 3.909 4.000 3.909 4.091 4.182 4.091 4.273 4.091 3.909
3.643 3.143 3.000 3.786 3.786 4.143 4.143 4.000 3.714 3.714 3.786 4.000 3.643
3.543 3.217 3.283 3.870 4.022 4.370 4.087 4.315 4.163 4.217 4.239 4.348 3.728
3.305 3.221 3.299 3.760 4.052 4.422 4.188 4.240 4.162 4.227 4.214 4.442 3.766
3.677 3.516 3.226 4.194 3.387 3.742 3.645 3.613 3.806 4.032 3.903 3.968 3.581
3.200 2.800 2.900 4.500 3.700 4.200 4.100 4.400 4.600 4.300 4.200 4.300 3.500
3.293 3.135 3.248 3.917 4.045 4.346 4.233 4.038 3.902 3.985 4.113 4.278 3.805
3.500 3.143 3.000 3.500 3.571 3.786 3.929 3.429 3.571 3.643 3.786 3.786 3.786
3.632 3.500 3.684 4.000 3.974 4.132 3.895 4.053 4.079 4.026 4.000 4.026 3.868
3.435 2.913 2.957 3.435 3.609 3.913 3.957 3.783 3.696 3.783 3.957 4.000 3.304
3.545 3.364 3.545 4.000 4.000 3.909 4.182 4.182 4.000 4.273 4.000 3.455 3.818
Based on the previously identified linguistic variables, the authors will determine the characteristic objects. They are created as the Cartesian Product of the sets where a single set contains the characteristic values of one linguistic variable. The next step consists in determining the Matrix of Expert Judgment (MEJ), which is created by comparing the pairs of all characteristic objects. In this case, this is a matrix of 1048576 rows and 1048576 columns. Subsequently, the vectors for summed judgements (SJ) points and preferences (P) are calculated. Using these values, a basis of fuzzy rules is created, which describes the model by means of 1048576 rules. In the next step, each characteristic object and its performance was converted to a fuzzy rule with (6). A sample rule is presented below (22): 𝑅𝑅1 : 𝐼𝐼𝐼𝐼 𝐶𝐶1 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶2 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶3 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶4 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶5 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶6 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶7 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶8 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶9 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶10 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶11 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶12 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶13 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶14 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶15 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶16 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶17 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶18 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶19 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶20 ~2 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑃𝑃~0.00
𝑅𝑅2 : 𝐼𝐼𝐼𝐼 𝐶𝐶1 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶2 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶3 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶4 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶5 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶6 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶7 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶8 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶9 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶10 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶11 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶12 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶13 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶14 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶15 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶16 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶17 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶18 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶19 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶20 ~5 𝑇𝑇𝑇𝑇𝐸𝐸𝑁𝑁 𝑃𝑃~0.05
𝑅𝑅3 : 𝐼𝐼𝐼𝐼 𝐶𝐶1 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶2 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶3 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶4 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶5 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶6 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶7 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶8 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶9 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶10 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶11 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶12 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶13 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶14 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶15 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶16 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶17 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶18 ~2 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶19 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶20 ~2 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑃𝑃~0.05
(22)
⋯⋯⋯⋯⋯⋯⋯
𝑅𝑅1048576: 𝐼𝐼𝐼𝐼 𝐶𝐶1 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶2 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶3 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶4 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶5 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶6 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶7 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶8 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶9 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶10 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶11 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶12 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶13 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶14 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶15 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶16 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶17 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶18 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶19 ~5 𝐴𝐴𝐴𝐴𝐴𝐴 𝐶𝐶20 ~5 𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑃𝑃~1
In the last step of the model creation, each alternative was presented as a set of crisp numbers corresponding to the C1 – C20 criteria. Mamdani’s fuzzy inference method was used to compute the preference Pi of each of the alternatives. The obtained P vertical vector, along with the resulting ranks of the alternatives, are presented in Table 6. According to the ranking generated by the COMET method, the A16 alternative (i.e. Orange Finance) is the best choice. However, the second place gets an A2 alternative, which was smaller only about 1.67% point.
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The influence of every criterion is different in each of the examined cases. On the basis of the COMET method, it is possible to identify particular relevance levels (local weights of criteria relevance). The results are presented in Tables 4 and 5. For example, criterion no. 1 was the most relevant in the assessment of the A18 alternative. The relevance level amounted to 0.0551. The lowest relevance level for this alternative was indicated for the A3 alternative and it reached 0.0401. Thus, the relative difference between these two relevance levels was 30.42%. The experiment shows that the relevance level of the criteria is not constant. Contrary to many common views, the relevance weights may change depending on the value of the remaining parameters. Ci C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19 C20
A1 0.0513 0.0506 0.0505 0.0505 0.0511 0.0497 0.0503 0.0505 0.0513 0.0518 0.0516 0.0533 0.0528 0.0522 0.0531 0.0520 0.0525 0.0527 0.0544 0.0516
Ci C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12 C13 C14 C15 C16 C17 C18 C19
A2 0.0519 0.0509 0.0517 0.0515 0.0527 0.0517 0.0509 0.0521 0.0536 0.0517 0.0546 0.0520 0.0523 0.0518 0.0524 0.0511 0.0522 0.0525 0.0538 0.0506
A12 0.0521 0.0477 0.0473 0.0507 0.0476 0.0496 0.0495 0.0516 0.0466 0.0446 0.0468 0.0480 0.0479 0.0491 0.0491 0.0460 0.0453 0.0457 0.0478
Table 5. Local relevance levels of particular criteria for specific alternatives
A3 0.0401 0.0459 0.0410 0.0417 0.0432 0.0445 0.0403 0.0433 0.0400 0.0391 0.0413 0.0451 0.0469 0.0473 0.0437 0.0405 0.0407 0.0420 0.0408 0.0427
A4 0.0404 0.0389 0.0422 0.0403 0.0396 0.0403 0.0402 0.0409 0.0421 0.0423 0.0400 0.0377 0.0369 0.0394 0.0381 0.0390 0.0394 0.0374 0.0382 0.0411
A5 0.0403 0.0473 0.0495 0.0489 0.0524 0.0495 0.0448 0.0422 0.0457 0.0451 0.0446 0.0458 0.0533 0.0522 0.0482 0.0473 0.0504 0.0493 0.0495 0.0499
A6 0.0470 0.0487 0.0482 0.0466 0.0490 0.0458 0.0475 0.0437 0.0462 0.0459 0.0498 0.0480 0.0491 0.0478 0.0465 0.0468 0.0489 0.0482 0.0483 0.0466
A7 0.0461 0.0457 0.0486 0.0489 0.0468 0.0477 0.0498 0.0440 0.0457 0.0470 0.0489 0.0461 0.0485 0.0472 0.0466 0.0486 0.0491 0.0458 0.0473 0.0475
A8 0.0523 0.0445 0.0461 0.0453 0.0400 0.0445 0.0395 0.0522 0.0563 0.0548 0.0429 0.0440 0.0439 0.0477 0.0426 0.0401 0.0395 0.0418 0.0428 0.0496
A9 0.0477 0.0492 0.0474 0.0450 0.0484 0.0489 0.0491 0.0443 0.0499 0.0481 0.0490 0.0473 0.0497 0.0451 0.0430 0.0458 0.0435 0.0486 0.0474 0.0444
Table 6. Local relevance levels of particular criteria for specific alternatives - cont.
A13 0.0499 0.0496 0.0492 0.0495 0.0509 0.0496 0.0481 0.0516 0.0492 0.0504 0.0491 0.0523 0.0517 0.0497 0.0543 0.0528 0.0527 0.0524 0.0532
A14 0.0469 0.0476 0.0476 0.0479 0.0479 0.0469 0.0466 0.0457 0.0466 0.0479 0.0455 0.0504 0.0502 0.0487 0.0511 0.0505 0.0506 0.0499 0.0522
A15 0.0504 0.0527 0.0481 0.0474 0.0501 0.0497 0.0562 0.0527 0.0528 0.0486 0.0524 0.0435 0.0438 0.0438 0.0449 0.0477 0.0497 0.0476 0.0480
A16 0.0496 0.0528 0.0500 0.0495 0.0476 0.0512 0.0516 0.0425 0.0385 0.0401 0.0532 0.0444 0.0463 0.0462 0.0516 0.0544 0.0500 0.0482 0.0490
A17 0.0470 0.0464 0.0457 0.0454 0.0455 0.0438 0.0458 0.0451 0.0449 0.0467 0.0471 0.0500 0.0491 0.0490 0.0483 0.0470 0.0473 0.0483 0.0499
A18 0.0551 0.0502 0.0481 0.0507 0.0502 0.0480 0.0513 0.0536 0.0508 0.0489 0.0468 0.0489 0.0471 0.0500 0.0456 0.0477 0.0479 0.0491 0.0487
A19 0.0523 0.0510 0.0486 0.0472 0.0493 0.0459 0.0481 0.0511 0.0516 0.0545 0.0492 0.0501 0.0475 0.0459 0.0495 0.0502 0.0488 0.0480 0.0479
A10 0.0456 0.0407 0.0415 0.0409 0.0452 0.0450 0.0445 0.0432 0.0443 0.0449 0.0449 0.0461 0.0454 0.0434 0.0422 0.0445 0.0427 0.0442 0.0419 0.0436
A20 0.0465 0.0477 0.0489 0.0487 0.0485 0.0473 0.0485 0.0496 0.0442 0.0450 0.0433 0.0466 0.0461 0.0477 0.0473 0.0466 0.0469 0.0486 0.0487
A11 0.0413 0.0405 0.0494 0.0522 0.0444 0.0455 0.0435 0.0476 0.0472 0.0473 0.0472 0.0473 0.0442 0.0442 0.0480 0.0495 0.0476 0.0493 0.0467 0.0486
A21 0.0463 0.0512 0.0504 0.0512 0.0498 0.0548 0.0538 0.0527 0.0525 0.0554 0.0517 0.0530 0.0473 0.0517 0.0536 0.0517 0.0543 0.0504 0.0435
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C20
0.0475
0.0500
0.0481
0.0473
0.0431
0.0483
0.0531
0.0502
0.0440
0.0522
The results of the comparison of global preferences and local average relevance for each alternative (i.e. a particular bank) obtained with the application of the COMET method are presented in Table 6. They show a relatively greater discrepancy between the places reached in the ranking in both evaluations than, for instance, the scores obtained with the use of the TOPSIS method (equal, with preferences). The TOPSIS method, in turn, pointed to greater similarity of the scores to those obtained using simple scoring methods (for a homogenous bank assessment set) [28]. Comparing the first five places established with the application of the highest preferences (with the following order of banks: Orange Finance, Bank Millennium SA, ING Bank Śląski SA, Raiffeisen Bank Polska SA, mBank), then after calculating the local average relevance, among the first five positions there were only two banks: Bank Millennium SA (first place – all Ci>0.05)) and Bank Śląski SA (the fourth position – 7 Ci>0.05, excellent visualization). This was caused by relatively high local indices of the Ci relevance in relation to their counterparts in other banks. The second place in the ranking was taken by Alior Bank (19 Ci> 0.05), with the highest score for using m-banking services, even higher than in the case of mBank that dropped from the 5th position to the 8th place. The third position was occupied by Volkswagen Bank Polska owing to the best score obtained for interest rates on loans (16 ratings >0.05). However, the bank obtained low scores for mobile banking, access channels and the average nominal interest rate on a personal account and an associated savings account. The last place among the five top positions was taken by PKO Bank Polski SA (INTELIGO) with the highest C20 index (the dynamics of changes in interests rates on deposits and loans in the previous year, average position in the rankings, increase/decrease in the number of clients, stability of pricing policy) as well as 9 Ci>0.05, which received low scores for relatively high fees charged for basic services (deposits, withdrawals from ATMs, fees for transfers, etc.). The shift with regard to this bank was the most spectacular change in the ranking in the case of comparison with global preferences: it has moved by 12 positions upwards. The bank which experienced the greatest fall was Orange Bank: it has moved from the first position to the distant 9 th place in the global ranking. The bank has received only six Ci>0,05 (two = 0,05). In this case, the lowest interest rate on deposits and the highest rates on credits turned out to be very important aspects for clients, and thus, in comparison to other offers, these aspects were rated low. Table 6. The global preferences and local average relevance for alternatives (A1-A21) in e-banking services assessment (COMET) Alternative Ai
Bank
Global preferences
Rank
Local average relevance
Rank
A1
Alior Bank SA
5.09%
6
5.17%
2
A2
Bank Millennium SA
5.20%
2
5.21%
1
A3
Bank Ochrony Środowiska SA
4.31%
19
4.25%
20
A4
Bank Pocztowy SA
3.74%
21
3.97%
21
A5
Bank Polska Kasa Opieki SA
4.63%
14
4.78%
11
A6
Bank Zachodni WBK SA
4.45%
16
4.74%
12
A7
BGŻ BNP Paribas SA (BNP)
4.77%
13
4.73%
13
A8
BGŻ Optima
4.79%
12
4.55%
18
A9
Credit Agricole Bank Polska SA
4.14%
20
4.71%
14
A10
Deutsche Bank Polska SA
4.32%
18
4.37%
19
A11
Euro Bank SA
5.03%
8
4.66%
17
A12
Getin Noble Bank SA
4.86%
11
4.80%
9
A13
ING Bank Śląski SA
5.17%
3
5.08%
4
A14
mBank
5.15%
5
4.84%
8
A15
Nest Bank
4.90%
10
4.89%
7
A16
Orange Finance
5.41%
1
4.80%
10
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Alternative Ai
Bank
Global preferences
Rank
2149
Local average relevance
Rank
A17
PKO Bank Polski SA (iPKO)
4.92%
9
4.70%
16
A18
PKO Bank Polski SA (INTELIGO)
4.42%
17
4.96%
5
A19
Raiffeisen Bank Polska SA
5.16%
4
4.93%
6
A20
T-Mobile Usługi Bankowe
4.48%
15
4.70%
15
A21
Volkswagen Bank Polska SA
5.07%
7
5.14%
3
The analysis of the last five positions in the ranking does not produce such spectacular findings. The three last positions remained largely the same. The move of Credit Agricole Bank Polska SA (due to high scores obtained for the aspects such as access channels and fees for account maintenance) from the penultimate position to the 14th place, resulted in the fact that Deutsche Bank Polska SA and Bank Ochrony Środowiska SA moved to two last positions in the ranking. In the case of Deutsche Bank Polska SA, the survey participants assigned relatively good scores for additional banking services (yet still below 0.05). The lowest scores were obtained in the case of account maintenance. None of Ci reached the level of 0.05, and all the scores fell in the range of 0.04. A similar phenomenon was observed in the case of Bank Ochrony Środowiska SA., where the index related to the interest rate on loans was rated below 0.04. The last position was taken by Bank Pocztowy SA with 10 indices below 0.04, and one of the worst scores for interest rates on loans. The results of the local relevance indices were presented in Tables 4 and 5. The comparison of global preference indices and local average relevance indices are shown in Table 6. The figure presented below (Fig. 2) indicates the variability of the criterion weight of wc8 in relation to the considered decision alternatives. This shows the variability of the average criterion weight for the examined alternatives in comparison to the computed global preferences and is an illustration of the previously presented discussion.
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Orange Finance Bank Millennium SA ING Bank Śląski SA Raiffeisen Bank Polska SA mBank Alior Bank SA Volkswagen Bank Polska SA Euro Bank SA PKO Bank Polski SA (iPKO) Nest Bank Local average relevance
Getin Noble Bank SA
Global preferences
BGŻ Optima BGŻ BNP Paribas SA (BNP) Bank Polska Kasa Opieki SA T-Mobile Usługi Bankowe Bank Zachodni WBK SA PKO Bank Polski SA (INTELIGO) Deutsche Bank Polska SA Bank Ochrony Środowiska SA Credit Agricole Bank Polska SA Bank Pocztowy SA 0%
1%
2%
3%
4%
5%
6%
Fig. 2. Variability of average criterion weight for the examined alternatives in comparison to the calculated global preferences
Conclusions The analyses which were carried out and the discussion of their findings indicate significant differences between the application possibilities and the results of using different research methods to assess the quality of e-banking websites. Undoubtedly, the simplest methods are different variants of scoring evaluations. In addition, the interpretation of the findings is easy and convincing from the point of view of potential designers. As it is frequently claimed, even with specific mass scale surveys (e.g. carried out in the banking sphere), the problem still consists in a high level of subjectivism of the evaluations. For a number of years many researchers have tried to solve this problem applying the evaluation methods which due to their specific objectivity of the calculated preferences appeared to be better and more useful than traditional methods. The development of these methods moved towards the application of multi-criteria, fuzzy, probabilistic, etc. methods, which was presented in Section 1. The authors of the study conducted numerous practical experiments [29, 30, 31] related to the application of various methods to evaluate websites, including the AHP/ANP, ELECTRE, PROMETHEE and TOPSIS methods. The application of multi-criteria methods was associated with numerous drawbacks pertaining to data collection (e.g. in the AHP/ANP group), or the determination of particular indices (e.g. veto threshold in the ELECTRA method), which were incomprehensible for the users. Moreover, the results of some methods are difficult to interpret – we obtain an optimal result which may depend, for instance, on the order of the listed criteria. The COMET method, as was discovered, eliminates these inconveniences. Moreover, the interpretation of its findings is relatively easy. Thus, the first limitation of this study is the problem of comparing its results with the findings obtained with the application of other methods which involved the same research sample.
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A second, specific limitation of the present study was only partially random selection of the sample. The respondents were selected among the homogeneous population of university students. However, one should bear in mind that this particular group includes the most active users of the latest IT solutions, and this is the group which may best observe and indicate the tendencies with regard to future changes in electronic banking websites as well as offer recommendations in this regard. Considering all the above, there arises a need to carry out the research which would allow comparing the findings resulting from the use of the COMET with findings of TOPSIS, AHP/ANP method and the results obtained with the application of traditional evaluation methods on the same research sample for finding the optimal method of assessment e-banking services solution. References [1] NETB@nk, 2016, NETB@nk Raport Bankowość internetowa i płatności bezgotówkowe. 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