Description
Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS
Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS
Saeed Rouhani
?
, Mehdi Ghazanfari, Mostafa Jafari
Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
a r t i c l e i n f o
Keywords:
Business intelligence
Evaluation model
Fuzzy TOPSIS
Enterprise systems
a b s t r a c t
Evaluation of business intelligence for enterprise systems before buying and deploying them is of vital
importance to create decision support environment for managers in organizations. This study aims to
propose a new model to provide a simple approach to assess enterprise systems in business intelligence
aspects. This approach also helps the decision-maker to select the enterprise system which has suitable
intelligence to support managers’ decisional tasks. Using wide literature review, 34 criteria about busi-
ness intelligence speci?cations are determined. A model that exploits fuzzy TOPSIS technique has been
proposed in this research. Fuzzy weights of the criteria and fuzzy judgments about enterprise systems
as alternatives are employed to compute evaluation scores and ranking. This application is realized to
illustrate the utilization of the model for the evaluation problems of enterprise systems. On this basis,
organizations will be able to select, assess and purchase enterprise systems which make possible better
decision support environment in their work systems.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Nowadays, the individual-system approach applied to decision-
support such as decision support systems (DSS) has been substi-
tute by a new environmental approach. In the past, DSS were inde-
pendent systems in an organization and had a frail relationship
with other systems (island systems). However, now enterprise sys-
tems are the foundation of an organization. And practitioners de-
sign and implement business intelligence as umbrella concept
create a decision-support environment for management in enter-
prise systems (Alter, 2004). The increasing trend to use intelligent
tools in business systems has increased the need for BI evaluation
of enterprise systems.
There are some delimited efforts to evaluate BI, but always they
consider BI as tools or separated systems to enterprise systems.
Lönnqvist and Pirttimäki (2006) designed BI performance model
to measure BI. To this aim, the measurement and the evaluation
in BI ?led was restricted to prove BI investment worth and BI val-
ues. Elbashir, Collier, and Davern (2008) have discussed about
measuring the effects of business intelligence systems on business
process, and have presented model for effect measures. Also Lin,
Tsai, Shiang, Kuo, and Tsai (2009) have developed performance
assessment model for business intelligence systems using ANP,
but they have considered BI as separated systems again.
Although organizations usually utilize functional and non-func-
tional requirements to evaluate and select enterprise systems, the
novel idea create question as follow:
1.1. How could organizations evaluate the BI for enterprise systems?
To ?ll the gap between use of enterprise system; ef?cient sup-
port decision and BI integrated in work systems; this research has
been done to present fuzzy evaluation model. This model can be
applied to evaluate and rank candidate enterprise systems like
Enterprise Recourse Planning (ERP), Supply Chain Management
(SCM), Customer Relationship Management (CRM), and Accounting
and Of?ce Automation system. In this regard, organization can
choose in a better way for designing, selecting, evaluating and buy-
ing enterprise systems with criteria that help them to have better
decision support enjoinment in their work systems.
The rest of this paper is prearranged as follows: Section 2 is
about past researches attempt to de?ne business intelligence and
wide-ranging literature review about BI and decision support crite-
ria to evaluate enterprise systems is summarized in Section 2 too.
Section 3 explains general TOPSIS method and stages of new fuzzy
TOPSIS method which customized in this paper evaluation model
are described in Section 4. The proposed evaluation model based
on fuzzy TOPSIS method and evaluation procedures for ?ve enter-
prise systems with thirty for criteria are illustrated in Section 5. Fi-
nally, Section 6 concludes the research work, its ?ndings and
proposed future research.
0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2011.09.074
?
Corresponding author. Address: 43, Reyhani Pamchi Allay, Allameh Amini St,
West Mobarez St, Abouzar Blv, Pirouzi Ave, Tehran 17789-14361, Iran. Tel.: +98
9122034980; fax: +98 21 77936752.
E-mail address: [email protected] (S. Rouhani).
Expert Systems with Applications 39 (2012) 3764–3771
Contents lists available at SciVerse ScienceDirect
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j our nal homepage: www. el sevi er . com/ l ocat e/ eswa
2. Business intelligence
BI refers to a management philosophy and tool that help orga-
nizations to manage and re?ne business information to make
effective decisions (Ghoshal & Kim, 1986). The term can be used
when referring to the following concepts (Lönnqvist & Pirttimäki,
2006):
1. Related information and knowledge of the organization, which
describe the business environment, the organization itself, the
conditions of market, customers and competitors and economic
issues;
2. A systemic and systematic process by which organizations
obtain, analyze and distribute the information for making deci-
sions about business operations.
The purpose of BI is to help control the resources and the infor-
mation ?ows of the business, which exist in and around the orga-
nization. BI makes a large contribution to the required intelligence
and knowledge of the organizations’ management by identifying
and processing data in order to explain their hidden meanings (Az-
off & Charlesworth, 2004).
BI is the process through which organizations take advantage of
virtual and digital technology to collect, manage and analyze struc-
tural or non-structural data. In other words, the technology and
commercial processing procedures in the decision-making are sup-
ported through the extraction, integration and analysis of data.
Business intelligence is an instrument of analysis providing auto-
mated decision-making about business conditions, sales, customer
demand and product preference and so on. It uses huge-database
(data-warehouse) analysis, as well as mathematical, statistical,
arti?cial intelligence, data mining and on-line analysis processing
(OLAP). Eckerson Wayne (2005) understood that BI must be able
to provide the following tools: production reporting tools, end-user
query and reporting tools, OLAP, dashboard/screen tools, data min-
ing tools and planning and modeling tools. Literature review was
done on business intelligence speci?cations or criteria that a sys-
tem should have to cover BI de?nitions. These criteria are listed
in Table 1.
3. The TOPSIS method
One of the popular methods applied to multiple criteria
decision-making is technique for order preference by similarity
(TOPSIS). For example, this method has been used by Abo-Sinna
and Amer (2005), Cheng, Chan, and Huang (2003), Feng and Wang
(2000, 2001), Jee and Kang (2000), Liao (2003), Olson (2004),
Opricovic and Tzeng (2004), Tzeng et al. (2005). Also, this method
has been used as fuzzy MCDM problem solving.
TOPSIS method which was proposed by Hwang and Yoon
(1981) is a technique for order preference by similarity to ideal
solution. The ideal solution (also called positive ideal solution) is
a solution that maximizes the bene?t criteria/attributes and mini-
mizes the cost criteria/attributes, while the negative ideal solution
(also called anti-ideal solution) maximizes the cost criteria/attri-
butes and minimizes the bene?t criteria/ attributes. The best alter-
native is the one, which is closest to the ideal solution and farthest
from the negative ideal solution (Wang & Elhag, 2006).
Table 1
BI evaluation criteria.
Criteria
ID
Criteria name Related studies
C1 Group Sorting tools and methodology
(Groupware)
Shim et al. (2002), Reich and Kapeliuk (2005), Damart et al. (2007), Marinoni et al. (2009)
C2 Group decision-making Eom (1999), Evers (2008), Yu et al. (2009)
C3 Flexible models Reich and Kapeliuk (2005), Zack (2007), Lin et al. (2009)
C4 Problem clustering Reich and Kapeliuk (2005), Loebbecke and Huyskens (2007), Lamptey et al. (2008)
C5 Optimization technique Lee and Park (2005), Nie et al. (2008), Shang et al. (2008), Azadivar et al. (2009), Delorme et al. (2009)
C6 Learning technique Power and Sharda (2007), Ranjan (2008), Li et al. (2009), Zhan et al. (2009)
C7 Import data from other systems O
¨
zbayrak and Bell (2003), Alter (2004), Shang et al. (2008), Quinn (2009)
C8 Export reports to other systems O
¨
zbayrak and Bell (2003), Shi et al. (2007), Shang et al. (2008)
C9 Simulation models Power and Sharda (2007), Shang et al. (2008), Quinn (2009), Zhan et al. (2009)
C10 Risk simulation Evers (2008), Galasso and Thierry (2008)
C11 Financial analyses tools Santhanam and Guimaraes (1995), Raggad (1997), Gao and Xu (2009)
C12 Visual graphs Noori and Salimi (2005), Kwon et al. (2007), Power and Sharda (2007), Li et al. (2008), Azadivar et al. (2009)
C13 Summarization Bolloju et al. (2002), Hemsley-Brown (2005), Power and Sharda (2007), Power (2008)
C14 Evolutionary prototyping model Fazlollahi and Vahidov (2001), Bolloju et al. (2002), Gao and Xu (2009), Zhang et al. (2009)
C15 Dynamic model prototyping Koutsoukis et al. (2000), Bolloju et al. (2002), Goul and Corral (2007), González et al. (2008), Pitty et al. (2008)
C16 Backward & forward reasoning Gottschalk (2006), Evers (2008), Zhang et al. (2009)
C17 Knowledge reasoning O
¨
zbayrak and Bell (2003), Plessis and Toit (2006), Evers (2008)
C18 Alarms and warning Power (2008), Ross, Dena, and Mahfouf (2009), Zhang et al. (2009)
C19 Dashboard/Recommender Nemati et al. (2002), Hedgebeth (2007), Bose (2009)
C20 Combination of experiments Courtney (2001), Nemati et al. (2002), Gottschalk (2006), Gonnet et al. (2007), Ross et al. (2009), Hewett
et al. (2009)
C21 Situation awareness modeling Raggad (1997), Plessis and Toit (2006), Feng et al. (2009)
C22 Environmental awareness Phillips-Wren et al. (2004), Koo et al. (2008), Güngör Sen et al. (2008)
C23 Fuzzy decision Metaxiotis et al. (2003), Zack (2007), Makropoulos et al. (2008), Wadhwa et al. (2009), Yu et al. (2009)
C24 OLAP Tan et al. (2003), Lau et al. (2004), Rivest et al. (2005), Shi et al. (2007), Berzal et al. (2008), Lee et al. (2009)
C25 Data mining techniques Bolloju et al. (2002), Shi et al. (2007), Berzal et al. (2008), Cheng et al. (2009)
C26 Data warehouses Tan et al. (2003), Tseng and Chou (2006), March and Hevner (2007), Nguyen et al. (2007)
C27 Web channel Tan et al. (2003), Oppong et al. (2005), Anderson et al. (2007), Power (2008)
C28 Mobile channel Power (2008), Wen et al. (2008), Cheng et al. (2009)
C29 E-mail channel Granebring and Re’vay (2007), Baars and Kemper (2008), Wen et al. (2008)
C30 Intelligent agent Gao and Xu (2009), Lee et al. (2009), Yu et al. (2009)
C31 Multi agent Bui and Lee (1999), Xu and Wang (2002), Granebring and Re’vay (2007)
C32 MCDM tools Hung et al. (2007), Yang (2008), Marinoni et al. (2009), Tansel Iç and Yurdakul (2009)
C33 Stakeholders’ satisfaction Goodhuea et al. (2000), Lönnqvist and Pirttimäki (2006), Evers (2008), González et al. (2008)
C34 Reliability and accuracy of analysis Gregg et al. (2002), Lönnqvist and Pirttimäki (2006), Phillips-Wren et al. (2007), Zack (2007),
González et al. (2008), Power (2008)
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3765
If a MCDM problem has nalternatives (A
1
, . . . ,A
n
) and m decision
criteria (C
1
, . . . , C
m
), each alternative is assessed concerning to m
criteria. Matrix X = (x
ij
)
nÂm
show all values that assigned to the
alternatives concerning to each criteria. The related weight of each
criteria has been shown by W = (w
1
, . . . , w
m
).
The steps of TOPSIS method are as a follow:
1. Normalize the decision matrix X = (x
ij
)
nÂm
using the equation
below:
r
ij
¼
x
ij
?????????????????
n
k¼1
x
2
kj
_ ; i ¼ 1; . . . ; n; j ¼ 1; . . . ; m ð1Þ
2. Calculate the weighted normalized decision matrix V = (v
ij
)
nÂm
:
v
ij
¼ w
j
r
ij
; i ¼ 1; . . . ; n; j ¼ 1; . . . ; m ð2Þ
w
j
is the relative weight of the jth criterion and
m
i¼1
w
j
¼ 1
3. Determination of the ideal and negative-ideal solutions:
A
Ã
¼ v
Ã
1
; . . . ; v
Ã
m
_ _
¼ ðmax
j
v
ij
jj 2 X
b
Þ; ðmin
j
v
ij
jj 2 X
c
Þ
_ _
ð3Þ
A
À
¼ v
À
1
; . . . ; v
À
m
_ _
¼ fðmin
j
v
ij
jj 2 X
b
Þ; ðmax
j
v
ij
jj 2 X
c
Þg ð4Þ
X
b
are the sets of bene?t criteria and X
c
are the sets of cost criteria
4. Calculate the Euclidean distances of each alternative from the
ideal solution and the negative-ideal solution:
D
Ã
i
¼
?????????????????????????????????
m
j¼1
v
ij
Àv
Ã
j
_ _
2
;
¸
¸
¸
_
i ¼ 1; . . . ; n ð5Þ
D
À
i
¼
?????????????????????????????????
m
j¼1
v
ij
Àv
À
j
_ _
2
¸
¸
¸
_
; i ¼ 1; . . . ; n ð6Þ
5. Determination the relative closeness of each alternative to the
ideal solution. The relative closeness of the alternative A
i
con-
cerning to A
?
is characterized as below:
RC
i
¼
D
À
i
D
Ã
i
þ D
À
i
; i ¼ 1; . . . ; n ð7Þ
4. Fuzzy TOPSIS method
In many real examples, the human preference model is uncer-
tain and decision makers might be hesitant or unable to assign
crisp values for judgments (Chan & Kumar, 2007; Shyur & Shih,
2006) and decision-makers often are interested in interval judg-
ments than pointing out their judgments in crisp values (Amiri,
2010). Therefore, one of the problems of traditional TOPSIS is using
crisp values in the evaluation process. Another dif?culty for using
crisp values is that some criteria are dif?cult to measure by crisp
values, so during the evaluation these criteria usually ignored.
The use of fuzzy set theory (Zadeh, 1965) allows the decision-
makers to use qualitative information, incomplete information;
non-obtainable information and somewhat ignorant facts into
decision model (Kulak, Durmusoglu, & Kahraman, 2005).
Thus, fuzzy TOPSIS is developed to solve ranking problems
(Büyükzkan, Feyzioglu, & Nebol, 2008; Chen & Tsao, 2007; Onüt
& Soner, 2007; Wang & Elhag, 2006).
The current research uses triangular fuzzy number for fuzzy
TOPSIS because of ease using a triangular fuzzy number for the
decision-makers to calculate. Furthermore, it has veri?ed that
modeling with triangular fuzzy numbers is an effective way for for-
mulating decision problems where the information available is
subjective and inaccurate (Chang & Yeh, 2002; Chang, Chung, &
Wang, 2007; Kahraman, Beskese, & Ruan, 2004).
Some basic important de?nitions of fuzzy sets are given as be-
low (Amiri, 2010):
1. A triangular fuzzy number ~ a can be de?ned by a triplet
(a
1
, a
2
, a
3
) shown in Fig. 1. The membership function l
~ a
ðxÞ is
de?ned as:
l
~ a
ðxÞ ¼
0 x < a
1
xÀa
1
a
2
Àa
1
a
1
< x < a
2
xÀa
3
a
2
Àa
3
a
2
< x < a
3
0 x < a
3
_
¸
¸
¸
¸
_
¸
¸
¸
¸
_
ð8Þ
Fig. 1. A triangular fuzzy number ~ a.
Forming decision making team
Determining alternatives
Determining the criteria
Structuring fuzzy decision matrix
via decision-making team
Assigning criteria weights via
decision-making team
Computing scores of alternatives
with fuzzy TOPSIS
Determining the final rank
Evaluation results
Stage 1
Stage 2
Stage 3
Fig. 2. Stages of Fuzzy TOPSIS BI Evaluation Model for enterprise systems.
3766 S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771
2. If ~ a and
~
b were two triangular fuzzy numbers which has been
shown by the triplet (a
1
, a
2
, a
3
) and (b
1
, b
2
, b
3
), respectively, then
the operational laws of these two triangular fuzzy numbers are
as follows:
~ aðþÞ
~
b ¼ða
1
; a
2
; a
3
ÞðþÞðb
1
; b
2
; b
3
Þ ¼ða
1
þb
1
; a
2
þb
2
; a
3
þb
3
Þ ð9Þ
~ aðÀÞ
~
b ¼ða
1
; a
2
; a
3
ÞðÀÞðb
1
; b
2
; b
3
Þ ¼ða
1
Àb
1
; a
2
Àb
2
; a
3
Àb
3
Þ ð10Þ
~ aðÂÞ
~
b ¼ða
1
; a
2
; a
3
ÞðÂÞðb
1
; b
2
; b
3
Þ ¼ða
1
Âb
1
; a
2
Âb
2
; a
3
Âb
3
Þ ð11Þ
~ að=Þ
~
b ¼ða
1
; a
2
; a
3
Þð=Þðb
1
; b
2
; b
3
Þ ¼ða
1
=b
3
; a
2
=b
2
; a
3
=b
1
Þ ð12Þ
~ a ¼ðka
1
; ka
2
; ka
3
Þ ð13Þ
3. A linguistic variable which present by words like very low, low,
medium, high, very high use to describe complex condition
(Zadeh, 1975). These linguistic values can also be represented
by fuzzy numbers (Amiri, 2010).
4. If ~ a and
~
b were two triangular fuzzy numbers which has been
shown by the triplet (a
1
, a
2
, a
3
) and (b
1
, b
2
, b
3
), respectively, then
vertex method is used to determine the distance between a and
b:
dð
~
a;
~
bÞ ¼
???????????????????????????????????????????????????????????????????????????????????
1
3
ða
1
À b
1
Þ
2
þ ða
2
À b
2
Þ
2
þ ða
3
À b
3
Þ
2
_ _
_
ð14Þ
5. The weighted normalized fuzzy-decision matrix is made from
below formula:
~ v ¼ ½~ v
ij
?
nÂj
; i ¼ 1; 2; . . . ; n; j ¼ 1; 2; . . . ; m
~ v
ij
¼ ~x
ij
 W
i
ð15Þ
A set of presentation rating of A
j
= (j = 1,2, . . . , m) concerning to
criteria C
i
= (i = 1,2, . . . , n) named ~x ¼ ð~x
ij
; i ¼ 1; 2; . . . ;
n; j ¼ 1; 2; . . . ; mÞ.
Table 2
Linguistic values and fuzzy numbers.
Linguistic variables Fuzzy numbers Fuzzy numbers
Very low (VL) (0, 0, 0.2)
Low (L) (0, 0.2, 0.4)
Medium (M) (0.2, 0.4, 0.6)
High (H) (0.4, 0.6, 0.8)
Very high (VH) (0.6, 0.8, 1)
Excellent (E) (0.8, 1, 1)
Table 3
Fuzzy decision matrix for enterprise systems.
Enterprise systems C1 C2 C3 C4 C5 C6 C7 C8 C9
ES I (0, 0, 0.2) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.8, 1, 1)
ES II (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.8, 1, 1) (0.6, 0.8, 1) (0.4, 0.6, 0.8)
ES III (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6)
ES IV (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1) (0, 0, 0.2)
ES V (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0, 0.2, 0.4) (0, 0, 0.2) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8)
Weight (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.4, 0.6, 0.8)
C10 C11 C12 C13 C14 C15 C16 C17 C18
ES I (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.8, 1, 1) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES II (0, 0.2, 0.4) (0, 0, 0.2) (0.8, 1, 1) (0.4, 0.6, 0.8) (0, 0, 0.2) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.6, 0.8, 1)
ES III (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES IV (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8)
ES V (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.8, 1, 1) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8)
Weight (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.8, 1, 1) (0.6, 0.8, 1) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.6, 0.8, 1)
C19 C20 C21 C22 C23 C24 C25 C26 C27
ES I (0.6, 0.8, 1) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8) (0.8, 1, 1) (0.6, 0.8, 1) (0.8, 1, 1)
ES II (0.8, 1, 1) (0, 0.2, 0.4) (0, 0, 0.2) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.6, 0.8, 1)
ES III (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.8, 1, 1)
ES IV (0.6, 0.8, 1) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.8, 1, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1)
ES V (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.6, 0.8, 1)
Weight (0.8, 1, 1) (0.6, 0.8, 1) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.4, 0.6, 0.8)
C28 C29 C30 C31 C32 C33 C34
ES I (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES II (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4)
ES III (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6)
ES IV (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0, 0.2) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6)
ES V (0.8, 1, 1) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
Weight (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1)
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3767
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Table 4
Weighted normalized fuzzy-decision matrix.
Enterprise systems C1 C2 C3 C4 C5 C6 C7 C8 C9
ES I (0, 0, 0.16) (0, 0.16, 0.4) (0.08, 0.24, 0.48) (0, 0.08, 0.24) (0, 0.12, 0.32) (0.04, 0.16, 0.36) (0.36, 0.64, 1) (0.24, 0.48, 0.8) (0.32, 0.6, 0.8)
ES II (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0, 0.12, 0.32) (0, 0, 0.12) (0, 0, 0.08) (0, 0, 0.12) (0.48, 0.8, 1) (0.36, 0.64, 1) (0.16, 0.36, 0.64)
ES III (0.08, 0.24, 0.48) (0.24, 0.48, 0.8) (0, 0.12, 0.32) (0, 0.08, 0.24) (0, 0.08, 0.24) (0, 0.08, 0.24) (0.24, 0.48, 0.8) (0.24, 0.48, 0.8) (0.08, 0.24, 0.48)
ES IV (0.16, 0.36, 0.64) (0.36, 0.64, 1) (0.08, 0.24, 0.48) (0.04, 0.16, 0.36) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.48, 0.8, 1) (0.48, 0.8, 1) (0, 0, 0.16)
ES V (0.16, 0.36, 0.64) (0.24, 0.48, 0.8) (0, 0.12, 0.32) (0, 0.08, 0.24) (0, 0.04, 0.16) (0, 0, 0.12) (0.36, 0.64, 1) (0.24, 0.48, 0.8) (0.16, 0.36, 0.64)
C10 C11 C12 C13 C14 C15 C16 C17 C18
ES I (0.04, 0.16, 0.36) (0, 0.08, 0.24) (0.64, 1, 1) (0.12, 0.32, 0.6) (0, 0.16, 0.4) (0, 0.08, 0.24) (0, 0.12, 0.32) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8)
ES II (0, 0.08, 0.24) (0, 0, 0.08) (0.64, 1, 1) (0.24, 0.48, 0.8) (0, 0, 0.08) (0, 0, 0.12) (0, 0.12, 0.32) (0, 0.12, 0.32) (0.36, 0.64, 1)
ES III (0.04, 0.16, 0.36) (0, 0.04, 0.16) (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8)
ES IV (0.04, 0.16, 0.36) (0, 0.08, 0.24) (0.48, 0.8, 1) (0.24, 0.48, 0.8) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.16, 0.36, 0.64) (0.24, 0.48, 0.8)
ES V (0.08, 0.24, 0.48) (0, 0.12, 0.32) (0.32, 0.6, 0.8) (0.48, 0.8, 1) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0, 0, 0.16) (0.24, 0.48, 0.8)
C19 C20 C21 C22 C23 C24 C25 C26 C27
ES I (0.48, 0.8, 1) (0, 0, 0.2) (0, 0.04, 0.16) (0, 0, 0.12) (0, 0, 0.16) (0.24, 0.48, 0.8) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.32, 0.6, 0.8)
ES II (0.64, 1, 1) (0, 0.16, 0.4) (0, 0, 0.08) (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0.12, 0.32, 0.6) (0.24, 0.48, 0.8) (0.48, 0.8, 1) (0.24, 0.48, 0.8)
ES III (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0.08, 0.24) (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.32, 0.6, 0.8)
ES IV (0.48, 0.8, 1) (0, 0, 0.2) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.16, 0.36, 0.64) (0.48, 0.8, 1) (0.36, 0.64, 1) (0.64, 1, 1) (0.32, 0.6, 0.8)
ES V (0.32, 0.6, 0.8) (0, 0.16, 0.4) (0, 0.08, 0.24) (0, 0, 0.12) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.24, 0.48, 0.8)
C28 C29 C30 C31 C32 C33 C34
ES I (0.04, 0.16, 0.36) (0, 0, 0.12) (0, 0, 0.2) (0, 0, 0.2) (0.24, 0.48, 0.8) (0.16, 0.4, 0.6) (0.32, 0.6, 0.8)
ES II (0.08, 0.24, 0.48) (0, 0.08, 0.24) (0.24, 0.48, 0.8) (0, 0.16, 0.4) (0, 0.16, 0.4) (0.16, 0.4, 0.6) (0, 0.2, 0.4)
ES III (0.04, 0.16, 0.36) (0.04, 0.16, 0.36) (0, 0.16, 0.4) (0.12, 0.32, 0.6) (0, 0.16, 0.4) (0, 0.2, 0.4) (0.16, 0.4, 0.6)
ES IV (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0, 0.16, 0.4) (0, 0, 0.2) (0.12, 0.32, 0.6) (0.32, 0.6, 0.8) (0.16, 0.4, 0.6)
ES V (0.16, 0.4, 0.6) (0.04, 0.16, 0.36) (0.12, 0.32, 0.6) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.16, 0.4, 0.6) (0.32, 0.6, 0.8)
3
7
6
8
S
.
R
o
u
h
a
n
i
e
t
a
l
.
/
E
x
p
e
r
t
S
y
s
t
e
m
s
w
i
t
h
A
p
p
l
i
c
a
t
i
o
n
s
3
9
(
2
0
1
2
)
3
7
6
4
–
3
7
7
1
5.2. Structuring fuzzy decision matrix and assigning weights of criteria
Based on Linguistic variables (Table 2), alternatives with re-
gards to criteria were assessed by decision making team; also they
assigned appropriate weights to each criterion. Fuzzy decision
averages matrix for enterprise systems was created based on judg-
ment of experts and can be seen in Table 3.
5.3. Evaluate alternatives and determine the ?nal rank
After the fuzzy decision matrix was established, the next step is
to compute the fuzzy weighted decision matrix that is depicted in
Table 4. This matrix is calculated with Eq. (15). Following, by Eqs.
(16) and (17), the fuzzy positive-ideal solution (FPIS, A
?
) and neg-
ative-ideal solution (FNIS, A
À
) were de?ned. Table 5 shows the re-
sults of this step. Then, the Euclidean distance of each alternative
from A
?
and A
À
can be computed by Eqs. (18) and (19). Subse-
quently, the similarities to an ideal solution are solved by Eq.
(20). Finally, the values of each alternative for ?nal ranking have
been illustrated in Table 6. Detailed calculations for FC1 similari-
ties to an ideal solution are as below:
D
Ã
1
¼
????????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:16À0Þ
2
þð0:36À0Þ
2
þð0:64À0:16Þ
2
_ _
_
þ
?????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:36À0Þ
2
þð0:64À0:16Þ
2
þð1À0:4Þ
2
_ _
_
þ. . .
þ
??????????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:32À0:32Þ
2
þð0:6À0:6Þ
2
þð0:8À0:8Þ
2
_ _
_
¼5:465016
D
À
1
¼
??????????????????????????????????????????????????????????????????????????????????
1
3
ð0À0Þ
2
þð0À0Þ
2
þð0:16À0:16Þ
2
_ _
_
þ
??????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0À0Þ
2
þð0:16À0:16Þ
2
þð0:4À0:4Þ
2
_ _
_
þ. . .
þ
????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:32À0Þ
2
þð0:6À0:2Þ
2
þð0:8À0:4Þ
2
_ _
_
¼5:013834
FC
1
¼
D
À
1
D
À
1
þD
Ã
1
¼
4:202188
4:202188þ5:465016
¼0:434685
Comparison of D
Ã
1
; D
Ã
2
; . . . ; D
Ã
5
and D
À
1
; D
À
2
; . . . ; D
À
5
that re?ect BI
capabilities of enterprise systems, strength and weakness, respec-
tively has been shown in Fig. 3. For example, it can be seen that
ES IV has large D
À
i
which shows large distance from negative ideal.
It also proves this enterprise system have appropriate business
intelligence capabilities which enhance decision support in organi-
zation. Ranking and fuzzy ?nal score of evaluated enterprise sys-
tems have been shown in Fig. 4 (ES IV > ES V > ES I > ES II > ES III).
6. Conclusion
The increasing trend to use intelligent tools in work systems has
increased the need for business Intelligence evaluation of enter-
prise systems. In past BI evaluation as a tool or independent system
Table 5
Fuzzy positive and negative ideal solution (FPIS & FNIS).
FPIS & FNIS C1 C2 C3 C4 C5 C6 C7 C8 C9
A
?
(0.16, 0.36, 0.64) (0.36, 0.64, 1) (0.08, 0.24, 0.48) (0.04, 0.16, 0.36) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.32, 0.6, 0.8)
A
À
(0, 0, 0.16) (0, 0.16, 0.4) (0, 0.12, 0.32) (0, 0, 0.12) (0, 0, 0.08) (0, 0, 0.12) (0.24, 0.48, 0.8) (0.24, 0.48, 0.8) (0, 0, 0.16)
C10 C11 C12 C13 C14 C15 C16 C17 C18
A
?
(0.08, 0.24, 0.48) (0, 0.12, 0.32) (0.64, 1, 1) (0.48, 0.8, 1) (0, 0.16, 0.4) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.16, 0.36, 0.64) (0.36, 0.64, 1)
A
À
(0, 0.08, 0.24) (0, 0, 0.08) (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0, 0, 0.16) (0.24, 0.48, 0.8)
C19 C20 C21 C22 C23 C24 C25 C26 C27
A
?
(0.64, 1, 1) (0.12, 0.32, 0.6) (0, 0.08, 0.24) (0.04, 0.16, 0.36) (0.16, 0.36, 0.64) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.64, 1, 1) (0.32, 0.6, 0.8)
A
À
(0.32, 0.6, 0.8) (0, 0, 0.2) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0.12, 0.32, 0.6) (0.24, 0.48, 0.8) (0.32, 0.6, 0.8) (0.24, 0.48, 0.8)
C28 C29 C30 C31 C32 C33 C34
A
?
(0.16, 0.4, 0.6) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.32, 0.6, 0.8)
A
À
(0.04, 0.16, 0.36) (0, 0, 0.12) (0, 0, 0.2) (0, 0, 0.2) (0, 0.16, 0.4) (0, 0.2, 0.4) (0, 0.2, 0.4)
Table 6
Final computation results.
Enterprise systems D
Ã
i
D
À
i
FC
i
ES I 5.465016 4.202188 0.434685
ES II 5.727552 3.960358 0.408794
ES III 5.967252 3.676034 0.381201
ES IV 3.459038 6.211444 0.64231
ES V 5.013834 4.65206 0.481286
2
2.5
3
3.5
4
4.5
5
5.5
6
ES I
ES II
ES III ES IV
ES V
D*
D-
Fig. 3. Evaluation of D
Ã
i
& D
À
i
for enterprise systems.
0.64
0.48
0.43
0.41
0.38
0
0.2
0.4
0.6
0.8
ES IV ES V ES I ES II ES III
Fig. 4. Ranking the evaluated enterprise systems.
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3769
was separated to evaluation of enterprise systems includes Enter-
prise Recourse Planning (ERP), Supply Chain Management (SCM),
Customer Relationship Management (SCM), Accounting and Of?ce
Automation system. In this research, with considering BI as enter-
prise systems non-functional requirements, an evaluation model
for enterprise systems using fuzzy TOPSIS was develop. BI de?ni-
tion and BI evaluation criteria were gathered by large literature re-
view in BI researches. After describing general TOPSIS method, a
new customized fuzzy TOPSIS method with detailed stages was de-
scribed. With following proposed evaluation model, ?ve enterprise
systems with those 34 criteria was assessed by decision-making
team and fuzzy positive and negative ideal solution were deter-
mined. After that by computing ?nal fuzzy score for each enter-
prise system and comparing them, the ranking of evaluated
enterprise systems was presented.
Applyingother MCDMmethods infuzzyenvironment toevaluate
enterprise systems by considering BI criteria, comparing these
methods and developing expert systemto select best enterprise sys-
tem with high intelligence level are recommended for future re-
search. The authors believe that after this research, organization
can decide in a better way for designing, selecting, evaluating and
buying enterprise systems with criteria and model that help them
to have better decision support environment in their work systems.
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S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3771
doc_190262320.pdf
Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS
Evaluation model of business intelligence for enterprise systems using fuzzy TOPSIS
Saeed Rouhani
?
, Mehdi Ghazanfari, Mostafa Jafari
Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran
a r t i c l e i n f o
Keywords:
Business intelligence
Evaluation model
Fuzzy TOPSIS
Enterprise systems
a b s t r a c t
Evaluation of business intelligence for enterprise systems before buying and deploying them is of vital
importance to create decision support environment for managers in organizations. This study aims to
propose a new model to provide a simple approach to assess enterprise systems in business intelligence
aspects. This approach also helps the decision-maker to select the enterprise system which has suitable
intelligence to support managers’ decisional tasks. Using wide literature review, 34 criteria about busi-
ness intelligence speci?cations are determined. A model that exploits fuzzy TOPSIS technique has been
proposed in this research. Fuzzy weights of the criteria and fuzzy judgments about enterprise systems
as alternatives are employed to compute evaluation scores and ranking. This application is realized to
illustrate the utilization of the model for the evaluation problems of enterprise systems. On this basis,
organizations will be able to select, assess and purchase enterprise systems which make possible better
decision support environment in their work systems.
Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction
Nowadays, the individual-system approach applied to decision-
support such as decision support systems (DSS) has been substi-
tute by a new environmental approach. In the past, DSS were inde-
pendent systems in an organization and had a frail relationship
with other systems (island systems). However, now enterprise sys-
tems are the foundation of an organization. And practitioners de-
sign and implement business intelligence as umbrella concept
create a decision-support environment for management in enter-
prise systems (Alter, 2004). The increasing trend to use intelligent
tools in business systems has increased the need for BI evaluation
of enterprise systems.
There are some delimited efforts to evaluate BI, but always they
consider BI as tools or separated systems to enterprise systems.
Lönnqvist and Pirttimäki (2006) designed BI performance model
to measure BI. To this aim, the measurement and the evaluation
in BI ?led was restricted to prove BI investment worth and BI val-
ues. Elbashir, Collier, and Davern (2008) have discussed about
measuring the effects of business intelligence systems on business
process, and have presented model for effect measures. Also Lin,
Tsai, Shiang, Kuo, and Tsai (2009) have developed performance
assessment model for business intelligence systems using ANP,
but they have considered BI as separated systems again.
Although organizations usually utilize functional and non-func-
tional requirements to evaluate and select enterprise systems, the
novel idea create question as follow:
1.1. How could organizations evaluate the BI for enterprise systems?
To ?ll the gap between use of enterprise system; ef?cient sup-
port decision and BI integrated in work systems; this research has
been done to present fuzzy evaluation model. This model can be
applied to evaluate and rank candidate enterprise systems like
Enterprise Recourse Planning (ERP), Supply Chain Management
(SCM), Customer Relationship Management (CRM), and Accounting
and Of?ce Automation system. In this regard, organization can
choose in a better way for designing, selecting, evaluating and buy-
ing enterprise systems with criteria that help them to have better
decision support enjoinment in their work systems.
The rest of this paper is prearranged as follows: Section 2 is
about past researches attempt to de?ne business intelligence and
wide-ranging literature review about BI and decision support crite-
ria to evaluate enterprise systems is summarized in Section 2 too.
Section 3 explains general TOPSIS method and stages of new fuzzy
TOPSIS method which customized in this paper evaluation model
are described in Section 4. The proposed evaluation model based
on fuzzy TOPSIS method and evaluation procedures for ?ve enter-
prise systems with thirty for criteria are illustrated in Section 5. Fi-
nally, Section 6 concludes the research work, its ?ndings and
proposed future research.
0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2011.09.074
?
Corresponding author. Address: 43, Reyhani Pamchi Allay, Allameh Amini St,
West Mobarez St, Abouzar Blv, Pirouzi Ave, Tehran 17789-14361, Iran. Tel.: +98
9122034980; fax: +98 21 77936752.
E-mail address: [email protected] (S. Rouhani).
Expert Systems with Applications 39 (2012) 3764–3771
Contents lists available at SciVerse ScienceDirect
Expert Systems with Applications
j our nal homepage: www. el sevi er . com/ l ocat e/ eswa
2. Business intelligence
BI refers to a management philosophy and tool that help orga-
nizations to manage and re?ne business information to make
effective decisions (Ghoshal & Kim, 1986). The term can be used
when referring to the following concepts (Lönnqvist & Pirttimäki,
2006):
1. Related information and knowledge of the organization, which
describe the business environment, the organization itself, the
conditions of market, customers and competitors and economic
issues;
2. A systemic and systematic process by which organizations
obtain, analyze and distribute the information for making deci-
sions about business operations.
The purpose of BI is to help control the resources and the infor-
mation ?ows of the business, which exist in and around the orga-
nization. BI makes a large contribution to the required intelligence
and knowledge of the organizations’ management by identifying
and processing data in order to explain their hidden meanings (Az-
off & Charlesworth, 2004).
BI is the process through which organizations take advantage of
virtual and digital technology to collect, manage and analyze struc-
tural or non-structural data. In other words, the technology and
commercial processing procedures in the decision-making are sup-
ported through the extraction, integration and analysis of data.
Business intelligence is an instrument of analysis providing auto-
mated decision-making about business conditions, sales, customer
demand and product preference and so on. It uses huge-database
(data-warehouse) analysis, as well as mathematical, statistical,
arti?cial intelligence, data mining and on-line analysis processing
(OLAP). Eckerson Wayne (2005) understood that BI must be able
to provide the following tools: production reporting tools, end-user
query and reporting tools, OLAP, dashboard/screen tools, data min-
ing tools and planning and modeling tools. Literature review was
done on business intelligence speci?cations or criteria that a sys-
tem should have to cover BI de?nitions. These criteria are listed
in Table 1.
3. The TOPSIS method
One of the popular methods applied to multiple criteria
decision-making is technique for order preference by similarity
(TOPSIS). For example, this method has been used by Abo-Sinna
and Amer (2005), Cheng, Chan, and Huang (2003), Feng and Wang
(2000, 2001), Jee and Kang (2000), Liao (2003), Olson (2004),
Opricovic and Tzeng (2004), Tzeng et al. (2005). Also, this method
has been used as fuzzy MCDM problem solving.
TOPSIS method which was proposed by Hwang and Yoon
(1981) is a technique for order preference by similarity to ideal
solution. The ideal solution (also called positive ideal solution) is
a solution that maximizes the bene?t criteria/attributes and mini-
mizes the cost criteria/attributes, while the negative ideal solution
(also called anti-ideal solution) maximizes the cost criteria/attri-
butes and minimizes the bene?t criteria/ attributes. The best alter-
native is the one, which is closest to the ideal solution and farthest
from the negative ideal solution (Wang & Elhag, 2006).
Table 1
BI evaluation criteria.
Criteria
ID
Criteria name Related studies
C1 Group Sorting tools and methodology
(Groupware)
Shim et al. (2002), Reich and Kapeliuk (2005), Damart et al. (2007), Marinoni et al. (2009)
C2 Group decision-making Eom (1999), Evers (2008), Yu et al. (2009)
C3 Flexible models Reich and Kapeliuk (2005), Zack (2007), Lin et al. (2009)
C4 Problem clustering Reich and Kapeliuk (2005), Loebbecke and Huyskens (2007), Lamptey et al. (2008)
C5 Optimization technique Lee and Park (2005), Nie et al. (2008), Shang et al. (2008), Azadivar et al. (2009), Delorme et al. (2009)
C6 Learning technique Power and Sharda (2007), Ranjan (2008), Li et al. (2009), Zhan et al. (2009)
C7 Import data from other systems O
¨
zbayrak and Bell (2003), Alter (2004), Shang et al. (2008), Quinn (2009)
C8 Export reports to other systems O
¨
zbayrak and Bell (2003), Shi et al. (2007), Shang et al. (2008)
C9 Simulation models Power and Sharda (2007), Shang et al. (2008), Quinn (2009), Zhan et al. (2009)
C10 Risk simulation Evers (2008), Galasso and Thierry (2008)
C11 Financial analyses tools Santhanam and Guimaraes (1995), Raggad (1997), Gao and Xu (2009)
C12 Visual graphs Noori and Salimi (2005), Kwon et al. (2007), Power and Sharda (2007), Li et al. (2008), Azadivar et al. (2009)
C13 Summarization Bolloju et al. (2002), Hemsley-Brown (2005), Power and Sharda (2007), Power (2008)
C14 Evolutionary prototyping model Fazlollahi and Vahidov (2001), Bolloju et al. (2002), Gao and Xu (2009), Zhang et al. (2009)
C15 Dynamic model prototyping Koutsoukis et al. (2000), Bolloju et al. (2002), Goul and Corral (2007), González et al. (2008), Pitty et al. (2008)
C16 Backward & forward reasoning Gottschalk (2006), Evers (2008), Zhang et al. (2009)
C17 Knowledge reasoning O
¨
zbayrak and Bell (2003), Plessis and Toit (2006), Evers (2008)
C18 Alarms and warning Power (2008), Ross, Dena, and Mahfouf (2009), Zhang et al. (2009)
C19 Dashboard/Recommender Nemati et al. (2002), Hedgebeth (2007), Bose (2009)
C20 Combination of experiments Courtney (2001), Nemati et al. (2002), Gottschalk (2006), Gonnet et al. (2007), Ross et al. (2009), Hewett
et al. (2009)
C21 Situation awareness modeling Raggad (1997), Plessis and Toit (2006), Feng et al. (2009)
C22 Environmental awareness Phillips-Wren et al. (2004), Koo et al. (2008), Güngör Sen et al. (2008)
C23 Fuzzy decision Metaxiotis et al. (2003), Zack (2007), Makropoulos et al. (2008), Wadhwa et al. (2009), Yu et al. (2009)
C24 OLAP Tan et al. (2003), Lau et al. (2004), Rivest et al. (2005), Shi et al. (2007), Berzal et al. (2008), Lee et al. (2009)
C25 Data mining techniques Bolloju et al. (2002), Shi et al. (2007), Berzal et al. (2008), Cheng et al. (2009)
C26 Data warehouses Tan et al. (2003), Tseng and Chou (2006), March and Hevner (2007), Nguyen et al. (2007)
C27 Web channel Tan et al. (2003), Oppong et al. (2005), Anderson et al. (2007), Power (2008)
C28 Mobile channel Power (2008), Wen et al. (2008), Cheng et al. (2009)
C29 E-mail channel Granebring and Re’vay (2007), Baars and Kemper (2008), Wen et al. (2008)
C30 Intelligent agent Gao and Xu (2009), Lee et al. (2009), Yu et al. (2009)
C31 Multi agent Bui and Lee (1999), Xu and Wang (2002), Granebring and Re’vay (2007)
C32 MCDM tools Hung et al. (2007), Yang (2008), Marinoni et al. (2009), Tansel Iç and Yurdakul (2009)
C33 Stakeholders’ satisfaction Goodhuea et al. (2000), Lönnqvist and Pirttimäki (2006), Evers (2008), González et al. (2008)
C34 Reliability and accuracy of analysis Gregg et al. (2002), Lönnqvist and Pirttimäki (2006), Phillips-Wren et al. (2007), Zack (2007),
González et al. (2008), Power (2008)
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3765
If a MCDM problem has nalternatives (A
1
, . . . ,A
n
) and m decision
criteria (C
1
, . . . , C
m
), each alternative is assessed concerning to m
criteria. Matrix X = (x
ij
)
nÂm
show all values that assigned to the
alternatives concerning to each criteria. The related weight of each
criteria has been shown by W = (w
1
, . . . , w
m
).
The steps of TOPSIS method are as a follow:
1. Normalize the decision matrix X = (x
ij
)
nÂm
using the equation
below:
r
ij
¼
x
ij
?????????????????
n
k¼1
x
2
kj
_ ; i ¼ 1; . . . ; n; j ¼ 1; . . . ; m ð1Þ
2. Calculate the weighted normalized decision matrix V = (v
ij
)
nÂm
:
v
ij
¼ w
j
r
ij
; i ¼ 1; . . . ; n; j ¼ 1; . . . ; m ð2Þ
w
j
is the relative weight of the jth criterion and
m
i¼1
w
j
¼ 1
3. Determination of the ideal and negative-ideal solutions:
A
Ã
¼ v
Ã
1
; . . . ; v
Ã
m
_ _
¼ ðmax
j
v
ij
jj 2 X
b
Þ; ðmin
j
v
ij
jj 2 X
c
Þ
_ _
ð3Þ
A
À
¼ v
À
1
; . . . ; v
À
m
_ _
¼ fðmin
j
v
ij
jj 2 X
b
Þ; ðmax
j
v
ij
jj 2 X
c
Þg ð4Þ
X
b
are the sets of bene?t criteria and X
c
are the sets of cost criteria
4. Calculate the Euclidean distances of each alternative from the
ideal solution and the negative-ideal solution:
D
Ã
i
¼
?????????????????????????????????
m
j¼1
v
ij
Àv
Ã
j
_ _
2
;
¸
¸
¸
_
i ¼ 1; . . . ; n ð5Þ
D
À
i
¼
?????????????????????????????????
m
j¼1
v
ij
Àv
À
j
_ _
2
¸
¸
¸
_
; i ¼ 1; . . . ; n ð6Þ
5. Determination the relative closeness of each alternative to the
ideal solution. The relative closeness of the alternative A
i
con-
cerning to A
?
is characterized as below:
RC
i
¼
D
À
i
D
Ã
i
þ D
À
i
; i ¼ 1; . . . ; n ð7Þ
4. Fuzzy TOPSIS method
In many real examples, the human preference model is uncer-
tain and decision makers might be hesitant or unable to assign
crisp values for judgments (Chan & Kumar, 2007; Shyur & Shih,
2006) and decision-makers often are interested in interval judg-
ments than pointing out their judgments in crisp values (Amiri,
2010). Therefore, one of the problems of traditional TOPSIS is using
crisp values in the evaluation process. Another dif?culty for using
crisp values is that some criteria are dif?cult to measure by crisp
values, so during the evaluation these criteria usually ignored.
The use of fuzzy set theory (Zadeh, 1965) allows the decision-
makers to use qualitative information, incomplete information;
non-obtainable information and somewhat ignorant facts into
decision model (Kulak, Durmusoglu, & Kahraman, 2005).
Thus, fuzzy TOPSIS is developed to solve ranking problems
(Büyükzkan, Feyzioglu, & Nebol, 2008; Chen & Tsao, 2007; Onüt
& Soner, 2007; Wang & Elhag, 2006).
The current research uses triangular fuzzy number for fuzzy
TOPSIS because of ease using a triangular fuzzy number for the
decision-makers to calculate. Furthermore, it has veri?ed that
modeling with triangular fuzzy numbers is an effective way for for-
mulating decision problems where the information available is
subjective and inaccurate (Chang & Yeh, 2002; Chang, Chung, &
Wang, 2007; Kahraman, Beskese, & Ruan, 2004).
Some basic important de?nitions of fuzzy sets are given as be-
low (Amiri, 2010):
1. A triangular fuzzy number ~ a can be de?ned by a triplet
(a
1
, a
2
, a
3
) shown in Fig. 1. The membership function l
~ a
ðxÞ is
de?ned as:
l
~ a
ðxÞ ¼
0 x < a
1
xÀa
1
a
2
Àa
1
a
1
< x < a
2
xÀa
3
a
2
Àa
3
a
2
< x < a
3
0 x < a
3
_
¸
¸
¸
¸
_
¸
¸
¸
¸
_
ð8Þ
Fig. 1. A triangular fuzzy number ~ a.
Forming decision making team
Determining alternatives
Determining the criteria
Structuring fuzzy decision matrix
via decision-making team
Assigning criteria weights via
decision-making team
Computing scores of alternatives
with fuzzy TOPSIS
Determining the final rank
Evaluation results
Stage 1
Stage 2
Stage 3
Fig. 2. Stages of Fuzzy TOPSIS BI Evaluation Model for enterprise systems.
3766 S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771
2. If ~ a and
~
b were two triangular fuzzy numbers which has been
shown by the triplet (a
1
, a
2
, a
3
) and (b
1
, b
2
, b
3
), respectively, then
the operational laws of these two triangular fuzzy numbers are
as follows:
~ aðþÞ
~
b ¼ða
1
; a
2
; a
3
ÞðþÞðb
1
; b
2
; b
3
Þ ¼ða
1
þb
1
; a
2
þb
2
; a
3
þb
3
Þ ð9Þ
~ aðÀÞ
~
b ¼ða
1
; a
2
; a
3
ÞðÀÞðb
1
; b
2
; b
3
Þ ¼ða
1
Àb
1
; a
2
Àb
2
; a
3
Àb
3
Þ ð10Þ
~ aðÂÞ
~
b ¼ða
1
; a
2
; a
3
ÞðÂÞðb
1
; b
2
; b
3
Þ ¼ða
1
Âb
1
; a
2
Âb
2
; a
3
Âb
3
Þ ð11Þ
~ að=Þ
~
b ¼ða
1
; a
2
; a
3
Þð=Þðb
1
; b
2
; b
3
Þ ¼ða
1
=b
3
; a
2
=b
2
; a
3
=b
1
Þ ð12Þ
~ a ¼ðka
1
; ka
2
; ka
3
Þ ð13Þ
3. A linguistic variable which present by words like very low, low,
medium, high, very high use to describe complex condition
(Zadeh, 1975). These linguistic values can also be represented
by fuzzy numbers (Amiri, 2010).
4. If ~ a and
~
b were two triangular fuzzy numbers which has been
shown by the triplet (a
1
, a
2
, a
3
) and (b
1
, b
2
, b
3
), respectively, then
vertex method is used to determine the distance between a and
b:
dð
~
a;
~
bÞ ¼
???????????????????????????????????????????????????????????????????????????????????
1
3
ða
1
À b
1
Þ
2
þ ða
2
À b
2
Þ
2
þ ða
3
À b
3
Þ
2
_ _
_
ð14Þ
5. The weighted normalized fuzzy-decision matrix is made from
below formula:
~ v ¼ ½~ v
ij
?
nÂj
; i ¼ 1; 2; . . . ; n; j ¼ 1; 2; . . . ; m
~ v
ij
¼ ~x
ij
 W
i
ð15Þ
A set of presentation rating of A
j
= (j = 1,2, . . . , m) concerning to
criteria C
i
= (i = 1,2, . . . , n) named ~x ¼ ð~x
ij
; i ¼ 1; 2; . . . ;
n; j ¼ 1; 2; . . . ; mÞ.
Table 2
Linguistic values and fuzzy numbers.
Linguistic variables Fuzzy numbers Fuzzy numbers
Very low (VL) (0, 0, 0.2)
Low (L) (0, 0.2, 0.4)
Medium (M) (0.2, 0.4, 0.6)
High (H) (0.4, 0.6, 0.8)
Very high (VH) (0.6, 0.8, 1)
Excellent (E) (0.8, 1, 1)
Table 3
Fuzzy decision matrix for enterprise systems.
Enterprise systems C1 C2 C3 C4 C5 C6 C7 C8 C9
ES I (0, 0, 0.2) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.8, 1, 1)
ES II (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.8, 1, 1) (0.6, 0.8, 1) (0.4, 0.6, 0.8)
ES III (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6)
ES IV (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1) (0, 0, 0.2)
ES V (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0, 0.2, 0.4) (0, 0, 0.2) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8)
Weight (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.4, 0.6, 0.8)
C10 C11 C12 C13 C14 C15 C16 C17 C18
ES I (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.8, 1, 1) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES II (0, 0.2, 0.4) (0, 0, 0.2) (0.8, 1, 1) (0.4, 0.6, 0.8) (0, 0, 0.2) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.6, 0.8, 1)
ES III (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES IV (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8)
ES V (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.8, 1, 1) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8)
Weight (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.8, 1, 1) (0.6, 0.8, 1) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.4, 0.6, 0.8) (0.6, 0.8, 1)
C19 C20 C21 C22 C23 C24 C25 C26 C27
ES I (0.6, 0.8, 1) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8) (0.8, 1, 1) (0.6, 0.8, 1) (0.8, 1, 1)
ES II (0.8, 1, 1) (0, 0.2, 0.4) (0, 0, 0.2) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.6, 0.8, 1)
ES III (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.8, 1, 1)
ES IV (0.6, 0.8, 1) (0, 0, 0.2) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0.8, 1, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1)
ES V (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.4, 0.6, 0.8) (0.6, 0.8, 1)
Weight (0.8, 1, 1) (0.6, 0.8, 1) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.4, 0.6, 0.8)
C28 C29 C30 C31 C32 C33 C34
ES I (0.2, 0.4, 0.6) (0, 0, 0.2) (0, 0, 0.2) (0, 0, 0.2) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
ES II (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4)
ES III (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0.2, 0.4, 0.6) (0, 0.2, 0.4) (0, 0.2, 0.4) (0.2, 0.4, 0.6)
ES IV (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0, 0.2, 0.4) (0, 0, 0.2) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8) (0.2, 0.4, 0.6)
ES V (0.8, 1, 1) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.2, 0.4, 0.6) (0.4, 0.6, 0.8)
Weight (0.2, 0.4, 0.6) (0.2, 0.4, 0.6) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.6, 0.8, 1) (0.8, 1, 1) (0.8, 1, 1)
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3767
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Table 4
Weighted normalized fuzzy-decision matrix.
Enterprise systems C1 C2 C3 C4 C5 C6 C7 C8 C9
ES I (0, 0, 0.16) (0, 0.16, 0.4) (0.08, 0.24, 0.48) (0, 0.08, 0.24) (0, 0.12, 0.32) (0.04, 0.16, 0.36) (0.36, 0.64, 1) (0.24, 0.48, 0.8) (0.32, 0.6, 0.8)
ES II (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0, 0.12, 0.32) (0, 0, 0.12) (0, 0, 0.08) (0, 0, 0.12) (0.48, 0.8, 1) (0.36, 0.64, 1) (0.16, 0.36, 0.64)
ES III (0.08, 0.24, 0.48) (0.24, 0.48, 0.8) (0, 0.12, 0.32) (0, 0.08, 0.24) (0, 0.08, 0.24) (0, 0.08, 0.24) (0.24, 0.48, 0.8) (0.24, 0.48, 0.8) (0.08, 0.24, 0.48)
ES IV (0.16, 0.36, 0.64) (0.36, 0.64, 1) (0.08, 0.24, 0.48) (0.04, 0.16, 0.36) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.48, 0.8, 1) (0.48, 0.8, 1) (0, 0, 0.16)
ES V (0.16, 0.36, 0.64) (0.24, 0.48, 0.8) (0, 0.12, 0.32) (0, 0.08, 0.24) (0, 0.04, 0.16) (0, 0, 0.12) (0.36, 0.64, 1) (0.24, 0.48, 0.8) (0.16, 0.36, 0.64)
C10 C11 C12 C13 C14 C15 C16 C17 C18
ES I (0.04, 0.16, 0.36) (0, 0.08, 0.24) (0.64, 1, 1) (0.12, 0.32, 0.6) (0, 0.16, 0.4) (0, 0.08, 0.24) (0, 0.12, 0.32) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8)
ES II (0, 0.08, 0.24) (0, 0, 0.08) (0.64, 1, 1) (0.24, 0.48, 0.8) (0, 0, 0.08) (0, 0, 0.12) (0, 0.12, 0.32) (0, 0.12, 0.32) (0.36, 0.64, 1)
ES III (0.04, 0.16, 0.36) (0, 0.04, 0.16) (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8)
ES IV (0.04, 0.16, 0.36) (0, 0.08, 0.24) (0.48, 0.8, 1) (0.24, 0.48, 0.8) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.16, 0.36, 0.64) (0.24, 0.48, 0.8)
ES V (0.08, 0.24, 0.48) (0, 0.12, 0.32) (0.32, 0.6, 0.8) (0.48, 0.8, 1) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0, 0, 0.16) (0.24, 0.48, 0.8)
C19 C20 C21 C22 C23 C24 C25 C26 C27
ES I (0.48, 0.8, 1) (0, 0, 0.2) (0, 0.04, 0.16) (0, 0, 0.12) (0, 0, 0.16) (0.24, 0.48, 0.8) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.32, 0.6, 0.8)
ES II (0.64, 1, 1) (0, 0.16, 0.4) (0, 0, 0.08) (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0.12, 0.32, 0.6) (0.24, 0.48, 0.8) (0.48, 0.8, 1) (0.24, 0.48, 0.8)
ES III (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0.08, 0.24) (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.32, 0.6, 0.8)
ES IV (0.48, 0.8, 1) (0, 0, 0.2) (0, 0.04, 0.16) (0, 0.08, 0.24) (0.16, 0.36, 0.64) (0.48, 0.8, 1) (0.36, 0.64, 1) (0.64, 1, 1) (0.32, 0.6, 0.8)
ES V (0.32, 0.6, 0.8) (0, 0.16, 0.4) (0, 0.08, 0.24) (0, 0, 0.12) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.24, 0.48, 0.8)
C28 C29 C30 C31 C32 C33 C34
ES I (0.04, 0.16, 0.36) (0, 0, 0.12) (0, 0, 0.2) (0, 0, 0.2) (0.24, 0.48, 0.8) (0.16, 0.4, 0.6) (0.32, 0.6, 0.8)
ES II (0.08, 0.24, 0.48) (0, 0.08, 0.24) (0.24, 0.48, 0.8) (0, 0.16, 0.4) (0, 0.16, 0.4) (0.16, 0.4, 0.6) (0, 0.2, 0.4)
ES III (0.04, 0.16, 0.36) (0.04, 0.16, 0.36) (0, 0.16, 0.4) (0.12, 0.32, 0.6) (0, 0.16, 0.4) (0, 0.2, 0.4) (0.16, 0.4, 0.6)
ES IV (0.04, 0.16, 0.36) (0.08, 0.24, 0.48) (0, 0.16, 0.4) (0, 0, 0.2) (0.12, 0.32, 0.6) (0.32, 0.6, 0.8) (0.16, 0.4, 0.6)
ES V (0.16, 0.4, 0.6) (0.04, 0.16, 0.36) (0.12, 0.32, 0.6) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.16, 0.4, 0.6) (0.32, 0.6, 0.8)
3
7
6
8
S
.
R
o
u
h
a
n
i
e
t
a
l
.
/
E
x
p
e
r
t
S
y
s
t
e
m
s
w
i
t
h
A
p
p
l
i
c
a
t
i
o
n
s
3
9
(
2
0
1
2
)
3
7
6
4
–
3
7
7
1
5.2. Structuring fuzzy decision matrix and assigning weights of criteria
Based on Linguistic variables (Table 2), alternatives with re-
gards to criteria were assessed by decision making team; also they
assigned appropriate weights to each criterion. Fuzzy decision
averages matrix for enterprise systems was created based on judg-
ment of experts and can be seen in Table 3.
5.3. Evaluate alternatives and determine the ?nal rank
After the fuzzy decision matrix was established, the next step is
to compute the fuzzy weighted decision matrix that is depicted in
Table 4. This matrix is calculated with Eq. (15). Following, by Eqs.
(16) and (17), the fuzzy positive-ideal solution (FPIS, A
?
) and neg-
ative-ideal solution (FNIS, A
À
) were de?ned. Table 5 shows the re-
sults of this step. Then, the Euclidean distance of each alternative
from A
?
and A
À
can be computed by Eqs. (18) and (19). Subse-
quently, the similarities to an ideal solution are solved by Eq.
(20). Finally, the values of each alternative for ?nal ranking have
been illustrated in Table 6. Detailed calculations for FC1 similari-
ties to an ideal solution are as below:
D
Ã
1
¼
????????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:16À0Þ
2
þð0:36À0Þ
2
þð0:64À0:16Þ
2
_ _
_
þ
?????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:36À0Þ
2
þð0:64À0:16Þ
2
þð1À0:4Þ
2
_ _
_
þ. . .
þ
??????????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:32À0:32Þ
2
þð0:6À0:6Þ
2
þð0:8À0:8Þ
2
_ _
_
¼5:465016
D
À
1
¼
??????????????????????????????????????????????????????????????????????????????????
1
3
ð0À0Þ
2
þð0À0Þ
2
þð0:16À0:16Þ
2
_ _
_
þ
??????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0À0Þ
2
þð0:16À0:16Þ
2
þð0:4À0:4Þ
2
_ _
_
þ. . .
þ
????????????????????????????????????????????????????????????????????????????????????????????
1
3
ð0:32À0Þ
2
þð0:6À0:2Þ
2
þð0:8À0:4Þ
2
_ _
_
¼5:013834
FC
1
¼
D
À
1
D
À
1
þD
Ã
1
¼
4:202188
4:202188þ5:465016
¼0:434685
Comparison of D
Ã
1
; D
Ã
2
; . . . ; D
Ã
5
and D
À
1
; D
À
2
; . . . ; D
À
5
that re?ect BI
capabilities of enterprise systems, strength and weakness, respec-
tively has been shown in Fig. 3. For example, it can be seen that
ES IV has large D
À
i
which shows large distance from negative ideal.
It also proves this enterprise system have appropriate business
intelligence capabilities which enhance decision support in organi-
zation. Ranking and fuzzy ?nal score of evaluated enterprise sys-
tems have been shown in Fig. 4 (ES IV > ES V > ES I > ES II > ES III).
6. Conclusion
The increasing trend to use intelligent tools in work systems has
increased the need for business Intelligence evaluation of enter-
prise systems. In past BI evaluation as a tool or independent system
Table 5
Fuzzy positive and negative ideal solution (FPIS & FNIS).
FPIS & FNIS C1 C2 C3 C4 C5 C6 C7 C8 C9
A
?
(0.16, 0.36, 0.64) (0.36, 0.64, 1) (0.08, 0.24, 0.48) (0.04, 0.16, 0.36) (0, 0.12, 0.32) (0.12, 0.32, 0.6) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.32, 0.6, 0.8)
A
À
(0, 0, 0.16) (0, 0.16, 0.4) (0, 0.12, 0.32) (0, 0, 0.12) (0, 0, 0.08) (0, 0, 0.12) (0.24, 0.48, 0.8) (0.24, 0.48, 0.8) (0, 0, 0.16)
C10 C11 C12 C13 C14 C15 C16 C17 C18
A
?
(0.08, 0.24, 0.48) (0, 0.12, 0.32) (0.64, 1, 1) (0.48, 0.8, 1) (0, 0.16, 0.4) (0, 0.08, 0.24) (0.08, 0.24, 0.48) (0.16, 0.36, 0.64) (0.36, 0.64, 1)
A
À
(0, 0.08, 0.24) (0, 0, 0.08) (0.32, 0.6, 0.8) (0.12, 0.32, 0.6) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0, 0, 0.16) (0.24, 0.48, 0.8)
C19 C20 C21 C22 C23 C24 C25 C26 C27
A
?
(0.64, 1, 1) (0.12, 0.32, 0.6) (0, 0.08, 0.24) (0.04, 0.16, 0.36) (0.16, 0.36, 0.64) (0.48, 0.8, 1) (0.48, 0.8, 1) (0.64, 1, 1) (0.32, 0.6, 0.8)
A
À
(0.32, 0.6, 0.8) (0, 0, 0.2) (0, 0, 0.08) (0, 0, 0.12) (0, 0, 0.16) (0.12, 0.32, 0.6) (0.24, 0.48, 0.8) (0.32, 0.6, 0.8) (0.24, 0.48, 0.8)
C28 C29 C30 C31 C32 C33 C34
A
?
(0.16, 0.4, 0.6) (0.08, 0.24, 0.48) (0.24, 0.48, 0.8) (0.12, 0.32, 0.6) (0.36, 0.64, 1) (0.32, 0.6, 0.8) (0.32, 0.6, 0.8)
A
À
(0.04, 0.16, 0.36) (0, 0, 0.12) (0, 0, 0.2) (0, 0, 0.2) (0, 0.16, 0.4) (0, 0.2, 0.4) (0, 0.2, 0.4)
Table 6
Final computation results.
Enterprise systems D
Ã
i
D
À
i
FC
i
ES I 5.465016 4.202188 0.434685
ES II 5.727552 3.960358 0.408794
ES III 5.967252 3.676034 0.381201
ES IV 3.459038 6.211444 0.64231
ES V 5.013834 4.65206 0.481286
2
2.5
3
3.5
4
4.5
5
5.5
6
ES I
ES II
ES III ES IV
ES V
D*
D-
Fig. 3. Evaluation of D
Ã
i
& D
À
i
for enterprise systems.
0.64
0.48
0.43
0.41
0.38
0
0.2
0.4
0.6
0.8
ES IV ES V ES I ES II ES III
Fig. 4. Ranking the evaluated enterprise systems.
S. Rouhani et al. / Expert Systems with Applications 39 (2012) 3764–3771 3769
was separated to evaluation of enterprise systems includes Enter-
prise Recourse Planning (ERP), Supply Chain Management (SCM),
Customer Relationship Management (SCM), Accounting and Of?ce
Automation system. In this research, with considering BI as enter-
prise systems non-functional requirements, an evaluation model
for enterprise systems using fuzzy TOPSIS was develop. BI de?ni-
tion and BI evaluation criteria were gathered by large literature re-
view in BI researches. After describing general TOPSIS method, a
new customized fuzzy TOPSIS method with detailed stages was de-
scribed. With following proposed evaluation model, ?ve enterprise
systems with those 34 criteria was assessed by decision-making
team and fuzzy positive and negative ideal solution were deter-
mined. After that by computing ?nal fuzzy score for each enter-
prise system and comparing them, the ranking of evaluated
enterprise systems was presented.
Applyingother MCDMmethods infuzzyenvironment toevaluate
enterprise systems by considering BI criteria, comparing these
methods and developing expert systemto select best enterprise sys-
tem with high intelligence level are recommended for future re-
search. The authors believe that after this research, organization
can decide in a better way for designing, selecting, evaluating and
buying enterprise systems with criteria and model that help them
to have better decision support environment in their work systems.
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