Expert Systems with Applications 38 (2011) 5967–5973
Contents lists available at ScienceDirect
Expert Systems with Applications
journal homepage: www.elsevier.com/locate/eswa
A Fuzzy DEMATEL framework for modeling cause and effect relationships
of strategy map
Javad Jassbi a, Farshid Mohamadnejad a,⇑, Hossein Nasrollahzadeh b
a
b
Department of Industrial Management, Faculty of Management and Economics, Science & Research Branch, Islamic Azad University, Tehran, Islamic Republic of Iran
Department of Management, Imam Sadiq University, Tehran, Islamic Republic of Iran
a r t i c l e
i n f o
Keywords:
Strategy map
Structural modeling
Cause and effect relationships
Fuzzy DEMATEL
a b s t r a c t
The Balanced Scorecard (BSC) is a widely adopted performance management framework first introduced
in the early 1990s. More recently, it has been proposed as the basic for a strategic management system.
Strategy mapping is the most important task in building a Balanced Scorecard system. Strategy mapping
is the process for visually making cause and effect relationships between all possible strategic objectives
in an organization. The process for building and constructing a strategy map is a human centric activity
which could be considered as the combination and integration of all knowledge and preferences of the
managerial boards. From the view point of strategic decision making in an organization, the process
for building a strategy map could be viewed in a general body of a unified group decision making context.
If we see the strategy map, as a structural modeling framework for making the cause and effect relationships among the strategic objectives, it is possible to deploy Decision Making Trial and Evaluation Laboratory (DEMATEL) as a framework for structural modeling approach subject to the problem. The
DEMATEL method gathers collective knowledge to capture the causal relationships between strategic criteria. The model is especially practical and useful for visualizing the structure of complicated causal relationships with matrices or digraphs. Generally speaking, because in building any strategy map, the
assigned preferences between the objectives are not crisp necessarily, and experts’ domain knowledge
could be extracted in a fuzzy environment, then the extended fuzzy DEMATEL is proposed to deal with
the ambiguities inherent of such the judgments.
Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction
The Balanced Scorecard (BSC) is a widely adopted performance
management framework first described in the early 1990s. More
recently, it has been proposed as the basic for a strategic management system (Cobbold & Lawrie, 2002). Balanced Scorecard methodology and framework is becoming a widely used performance
measurement and management system for today’s successful organizations (Kaplan & Norton, 2008). By implementation of Balanced
Scorecard system, organizations seek to translate their vision into
operational goals, communicate their vision and link it to individual performance, plan their businesses, and receive feedbacks and
learn from their underlying operational activities then adjusting
their strategy accordingly (Kaplan & Norton, 1996). It is most noted
that that Balanced Scorecard can be best characterized as a ‘‘strategic management system’’ that claims to integrate all quantitative
and abstract measures of true importance to the enterprise in an
integrated total system called ‘‘close-lope management system’’
⇑ Corresponding author. Tel.: +98 21 448 67241 3; fax: +98 21 448 67251.
E-mail address: [email protected] (F. Mohamadnejad).
0957-4174/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.eswa.2010.11.026
(Kaplan & Norton, 2008). At the strategic point of view, the Balanced Scorecard provides managers with the instrumentation
needed to navigate to future competitive success. Indeed, BSC
could be considered as support decision making at the strategic
management level, which improves the satisfaction of the strategic
objectives (Bobillo, Delgado, & Gómez-Rom, 2009). It must be
noted that BSC helps managers to focus their attention on strategic
issues and implementation management of the strategy. Simultaneously, it can be the best applicable tool for providing more comprehensive view of a business, which in turn helps organizations
act in their best long-term interests (Niven, 2006).
Strategy mapping is the most important task in building a Balanced Scorecard system, and so must be the first of the sequential
stepwise processes for BSC system design (Makhijani & Creelman,
2008). Strategy map is visual representation of cause and effect
relationships in any BSC management system. The managerial
board of organization, as the body of decision making team, starts
by their combination and assimilation of their knowledge and
experiences, to build logical relationships among the strategic
objectives. On the other hand, as the process of building the strategy map shows, it is a human centric process in which all executives’ preferences, experiences and knowledge are in place to
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J. Jassbi et al. / Expert Systems with Applications 38 (2011) 5967–5973
reach to a uniform consensus. But many experiences show that the
managerial boards, through set of high level management sessions
and based on a formal general agreement, make relationships between strategic objectives.
The authors believe that by proposing a proper framework for
structuring the process of strategy mapping, there would be possible to follow the procedure in a more stepwise procedure. From the
decision making methodologies and algorithms point of view, the
general process of constituting a strategy map could be considered
as a uniform group decision making process, through which the
preferences of decision makers (executives or managerial boards)
must be integrated to reach to the set of final decisions (making
which objects must be linked to which one). Indeed, it is possible
to put an equivalency between the process of strategy mapping
and the group decision making algorithms.
In this paper, we propose a Fuzzy Decision Making Trial and
Error Laboratory (Lin & Wu, 2004) framework, as a powerful
group decision making model to build the structural relationships
among the strategic objectives for a strategy map. Decision
Making Trial and Error Laboratory (DEMATEL) (Fontela & Gabus,
1976) can clear see the cause-effect relationship of criteria when
measuring a problem. It is most noted that in building any strategy map, the assigned preferences between the objectives are
not crisp necessarily, and experts’ domain knowledge could be extracted in a fuzzy environment, then the extended fuzzy DEMATEL
is proposed to deal with the ambiguities inherent of such the
judgments.
The rest of the paper is organized as follows. In Section 2, we
overview the related works conducted to propose frameworks for
modeling Balanced Scorecard system, particularly in fuzzy environments. In Sections 3–5, the process of modeling a strategy
map, as group decision making process, is discussed and the essence of using DEMATEL as structural modeling framework to
model the process is presented. Section 6 presents the test of
our proposed framework through a real case of Saipa Yadak
Trading Company strategy map. In Section 7, we argue two
dissections through which the proposed framework could be
more effective and logically been architected. Finally, conclusion
is presented.
2. An overview of related works
A Balanced Scorecard is more than a business model because it
moves performance measurement to performance management
(Köppen et al., 2007). The multidimensionality of the framework
and broad functionalities the system provides necessitated different researches and practitioners to study and analyze Balanced
Scorecard from different point of views. As the literature shows,
the scientists and practitioners working in the field of Balanced
Scorecard have different backgrounds and interests. Indeed, models and frameworks proposed for advancement and improvement
of BSC are very broad in nature (Linard & Yoon, 2000).
However, the idea of extending BSC with fuzzy logic is not completely new. Kardaras and Mentzas (1997) used fuzzy cognitive
maps to model and analyze business performance assessment.
Haase (2000) proposed a fuzzy balance scorecard and implemented its proposal in the ActiveScoreCard system. Chou and Liang
(2001) applied a fuzzy BSC to shipping companies. Su, Liang, Liu,
and Chou (2003) also worked with ports performance. Pochert
(2005) considered an alternative model for fuzzy BSC. Nissen
(2006) also considered a fuzzy balance scorecard, analyzed the
new modeling process and presented a prototypical implementation. Wu, Tsai, Shih, and Fu (2010) evaluated government performance based on balanced scorecard methodology using fuzzy
linguistic labels which can be considered as national project in
the related domain. Köppen et al. (2007) proposed a functional
model for estimating relations in a balanced scorecard system
which appeared under the topic of machine learning and intelligence. Chytas (2008) offered a proactive fuzzy cognitive balanced
scorecard which sounds a novelty in the stream. And more recently, Bobillo et al. (2009) provided a fuzzy expert system for balanced scorecard system which covers the general body of BSC and
deals with the all perspectives.
As all the works show, they are not specifically intending to propose a framework for strategy map, rather they focused on the general framework of the balanced scorecard. But many of these
authors are attempting to produce any kind of decision support
for the field. As it has been emphasized, designing the strategy
maps with clearly established causal links leads to cascade the
understanding of strategy down through the organization. Therefore, all employees are aware of strategic intent and the impact
of operational activities upon its delivery (Evans, 2007). Then, it
is worth to note that any decision support for the strategy map
could be the very first and important step for construction a general BSC system. In the next sections, we will discuss our proposed
model derived on Fuzzy DEMATEL framework and show that the
proposed model tries to extract a framework for cause and effect
relationships of the strategy map.
3. Modeling cause and effect relationships of strategy map
Although the question of what continues the core of BSC is still
under great considerations and attracted many scientific and practical researches (Bukh & Malmi, 2005), it has been accepted in a
general view that the causality of hypothesis between strategic
objectives is the main body and constitution of a Balanced Scorecard system, which is coming under the strategy map (Kaplan &
Norton, 2004). Strategy map is a tool for constructing linkages between strategic objectives among perspectives of a balanced scorecard system and depicts objectives in multiple perspectives with
their corresponding cause-effect relationship(s).
The strategy map enables managers at each level of the organization to specify scorecards that describe the strategy as a set of
cause-and-effect relationships that can be tested and adjusted
(Achterbergh, Beeres, & Vriens, 2003). It has been emphasized that
designing the strategy maps with clearly established causal links
leads to cascade the understanding of strategy down through the
organization. Therefore, all employees are aware of strategic intent
and the impact of operational activities upon its delivery Evans,
2007). Strategy mapping is the most important task in building a
Balanced Scorecard system. Get the map right and it becomes
much simpler to select meaningful measures, targets and initiatives. Unfortunately, many companies stymie their scorecard efforts because they make basic mistakes in mapping (Makhijani &
Creelman, 2008).
Strategy mapping is the process for visually making cause and
effect relationships between all possible strategic objectives in an
organization. By selecting and filtering their strategic objectives,
organizations, based on combination and assimilation of their
managerial board knowledge, start to build logical relationships
among the objectives. In the other word, it is been noted that in
any formal procedure for extracting the strategy maps, based on
the general managers’ knowledge and experiences, they have been
asked to set the relationships between strategic objectives. Indeed,
through a set of session at the strategic level of organization and
with the combination and assimilation of their knowledge, they
will set casual relationship between the objectives (Niven, 2006).
As the process of building the strategy map shows, it is a human
centric process in which all executives’ preferences, experiences
and knowledge are in place to reach to a uniform consensus.
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J. Jassbi et al. / Expert Systems with Applications 38 (2011) 5967–5973
As noted earlier, in this paper we observe the process for building a strategy map as a group decision making processes in which
the preferences of decision makers (executives) must be integrated
to reach to the set of decisions. Indeed, any causal relationships
would be considered as the combination of all preferences of managerial boards or experts as the decision makers in a unified group
decision making problem. The map construction could be burden
by many human judgmental streams which fully filled with errors
and unexpected missed judgments.
4. DEMATEL as a group decision making method for strategy
mapping
The Decision Making Trial and Evaluation Laboratory (DEMATEL) method is presented in 1973 (Fontela & Gabus, 1976), as a
kind of structural modeling approach about a problem. It can
clearly see the cause-effect relationship of criteria when measuring
a problem. The DEMATEL method gathers collective knowledge to
capture the causal relationships between strategic criteria. The
model is especially practical and useful for visualizing the structure of complicated causal relationships with matrices or digraphs.
The matrices or digraph portrays a contextual relation between the
elements of the system, in which a numeral represents the
strength of influence. Hence, the DEMATEL method can convert
the relationship between the causes and effects of criteria into an
intelligible structural model of the system (Lin & Wu, 2004). As
many strategy maps could, in their general form of construction,
be considered as structural modeling by its own nature, then DEMATEL could be best suited for strategy map building and design.
To establish a structural model of the strategy map, executives’
judgments for deciding the relationship between objectives of the
organizations are usually derived based on a process group decision making procedure. It is quite considerable that, due to the human judgmental characteristics of strategy mapping, the boards of
executives assign their preferences and importance to any relationships among the selected strategic objectives with actually crisp
values. But these crisp values are inadequate in the real world. Indeed, these human judgments with preferences in the process of
decision making in general are often unclear and hard to estimate
by exact numerical values has created the need for fuzzy logic (Lin
& Wu, 2004).
As it is clear the general manager(s) decides about the weight of
causality between the objectives by his/her own knowledge and
experiences, this is a human centric activity and certainly is processed in uncertain environments. Therefore, enabling the DEMATEL method to be suitable for solving multi-person and multicriteria decision-making problems in fuzzy environments, it is
needed to build an extended crisp DEMATEL method by applying
linguistic variables (Lin & Wu, 2004). Indeed, to deal with the
ambiguity of human assessments, the preferences of decision makers’ (general managers) are extended to fuzzy numbers by adopting fuzzy linguistic scale. On the other word, a more sensible
approach is to use linguistic assessments instead of numerical values, in which all assessments of strategic objectives of strategy
map are evaluated by means of linguistic variables.
By adopting a fuzzy triangular number, a fuzzy DEMATEL exertion will be in place by expressing different degrees of influences or
causalities in crisp DEMATEL, with five linguistic terms as {Very
high, High, Low, Very low, No} and their corresponding positive triangular fuzzy numbers (Lin & Wu, 2004). These linguistic terms are
shown in Table 1.
At the next step (Lin & Wu, 2004) subject to the fuzzy linguistic
scale and due to extracted strategy map, every general manager is
asked to make pair wise relationships between each pair of objectives O = {Oi|i = 1, 2, . . . , n}. On the other hand, if he/she says objective O10 has Very High Influence (VH) on O5, he/she indicates his/
her preferences for the casual relationship between these two strategic objectives. Indeed, in this process, any individual preferences
and assessment about the causality between each pair of the strategic objectives are measured through a fuzzy number assigning.
Normally this will be a fuzzy matrix which is shown by ~zp and
called Assessment Data Fuzzy Matrix. The same table will be filled
out by all members (executives or managers) who have an essential role in establishing a strategy map in an organization. Indeed,
there are p fuzzy matrices which p = {1, 2, . . . , k} is the number of
managerial boards or group of experts, denoting all preferences
and assigned casualties with triangular fuzzy numbers as its elements. As an example of i strategic objectives for a general manager is depicted in Table 2.
Next (Lin & Wu, 2004), it must acquire and average the assessment of executives’ preferences using
~z ¼
ð~z1 ~z2 ~zp Þ
:
p
ð1Þ
5. Fuzzy DEMATEL as a basis for strategy map architecture
In this section, we first discuss the process of deploying fuzzy
DEMATEL algorithms for constituting the strategy map. In the next
section, through Saipa Yadak Trading Company empirical data, we
illustrate the proposed framework in a real case study.
Following the Balanced Scorecard methodology, as the first step
for building any strategy map, the general managers of the organization prepare the draft list of strategic goals which extracted
based on the their strategic planning. Then, through the committee
of basic Executive Teams, by filtering and refining the general strategic objectives, the key ones will be selected and identified. Then,
the list will be final set of objectives by which the casual linkages
must be architected. As it is clear, this list will be the decision set
for the algorithm. It is suggested that the Executive Team locate all
these strategic objectives into the formal perspectives of strategy
map in order to make the steps of DEMATEL algorithms more
viable.
Following the stepwise procedures of group decision making
algorithms, the general managers then are asked through a questioner to specify which strategic objective receives a link from its
predecessor(s).
Table 1
The correspondence of linguistic terms and linguistic
values.
Linguistic terms
Linguistic value
Very High Influence (VH)
High Influence (H)
Low Influence (L)
Very Low Influence (VL)
No Influence (No)
(0.75, 1.0, 1.0)
(0.5, 0.75, 1.0)
(0.25, 0.5, 0.75)
(0, 0.25, 0.5)
(0, 0, 0.25)
Table 2
The assessment data fuzzy matrix of a general manager.
O1
O2
O3
...
Oi2
Oi1
Oi
O1
O2
O3
...
Oi2
Oi1
Oi
–
VH
VH
H
VH
VH
VH
H
–
H
H
VH
L
VH
No
H
–
H
VH
VH
VH
No
H
VH
–
VH
VH
VH
No
L
VH
VH
–
VH
H
No
H
VH
VH
H
–
H
H
H
VH
VH
No
VH
–
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Then, fuzzy matrix ~z is produced which is shown as
2
0
6 ~z
6 21
~z ¼ 6
6 ..
4 .
~zn1
~z12
3
~zln
0 ~z2n 7
7
..
.. 7
7:
.
. 5
...
0
..
.
~zn2
ð2Þ
0
which is called initial direct-relation fuzzy matrix. In this matrix,
~zij ¼ ðlij ; mij :uij Þ are triangular fuzzy numbers and ~zii ði ¼ 1; 2; . . . ; nÞ
will be regarded as triangular fuzzy number (0, 0, 0) whenever is
necessary.
Then, by normalizing initial direct-relation fuzzy matrix, we ace by using
quire normalized direct-relation fuzzy matrix X
2
~x11
6 ~x
6 21
e ¼6
X
6 ..
4 .
~xn1
3
. . . ~xln
0 ~x2n 7
7
..
.. 7
7;
.
. 5
. . . ~xnn
~x12
~x21
..
.
~xn2
ð3Þ
Saipa Yadak Trading Company founded in early 1992, as the
provider of after sale services to the customers of Saipa Automobile
Manufacturing Group (the first car manufacturing among Iran).
The main mission of the company is providing suitable commercial
technical grounds, by which the consumers of Saipa Company’s
products could receive best services at all times and remain satisfied with their choice of Saipa products. The first conduct of an
opinion center in auto industry among the country has been set
up by Saipa Yadak Trading Company in 1996. The center is in a
continuous and direct contact with owners of Saipa Vehicles in order to receive their suggestions and assess their satisfaction with
the company’s products. The development of this modern computer network is aimed to achieve maximum customer satisfaction. In order to provide better services all over the country and
facilitate the response to customer’s needs, the company increased
the number of its authorized dealers to more than 270 by 2008.
Moreover, several mobile service providers in various areas within
where
~xij ¼
~zij
lij mij nij
¼
;
;
r
r r r
ð4Þ
Strategic objectives
and
r ¼ maxlin
n
X
!
uij :
ð5Þ
j¼1
P
It is assumed at least one i such that nj¼1 uij < r.
After computing the above matrices, the total-relation fuzzy
e is computed. Total-relation fuzzy matrix is defined as
matrix T
(Lin & Wu, 2004)
~1 þ X
~2 þ þ X
~ k Þ:
T~ ¼ lim ðX
k!1
ð6Þ
Then,
2~
t11 ~t12
6 ~t
6 21 ~t21
T~ ¼ 6
6 ..
...
4 .
~t n1 ~t n2
~t ln 3
0 ~t 2n 7
7
7
..
. 7:
.
. . 5
. . . ~t nn
Table 3
The list of strategic objectives of Saipa Yadak Trading Company.
O1. Economical and financial growth
O2. Increasing annual profit
O3. Increasing market share of accessories
O4. Strong branding
O5. Increasing customer loyalty
O6. Increasing customer satisfaction
O7. Increasing agents loyalty to the company
O8. Developing outsourcing process
O9. Benchmarking through the rivals
O10. JIT Based services and repairs
O11. On time demanding and real time grantee
O12. Accessibility to the learning and agile service network
O13. Customized supportive system based on new technologies
O14. Upgrading service network toward customer preferences and predefined standardization
O15. Learning human capital, aligned with the company’s policies
...
ð7Þ
Table 4
Saipa Yadak Trading Company strategy map draft.
Perspectives
00
In which ~t ij ¼ ðlij ; m00ij ; u00ij Þ and
00
1
00
00
½lij ¼ X l ðI X 1
1 Þ; ½mij ¼ X l ðI X m Þ; ½uij ¼ X l ðI X 1
u Þ:
Objectives
Financial
O2. Increasing
Annual Profit
O1. Economical and
Financial Growth
ð8Þ
~ then it is calculated D
~i þ R
~ i and D
~i R
~ i in
By producing matrix T,
~ i and R
~ i are the sum of row and the sum of columns of T~
which D
respectively.
~i þ R
~ i and D
~i R
~ i are
To finalize the procedure, all calculated D
defuzified through suitable defuzification method. Then, there
~i þ R
~ i Þdef which shows how
would be two sets of numbers: ðD
~i R
~ i Þdef which shows
important the strategic objectives are, and ðD
which strategic objective is cause and which one is effect. Gener~i R
~ i Þdef is positive, the objectives belong to
ally, if the value ðD
~i R
~ i Þdef is negative, the objecthe cause group, and if the value ðD
tives belong to the effect group.
O3. Increasing Market
Share of Accessories
Customer
O6. Increasing
Customer Satisfaction
Internal
processes
O8. Developing
Outsourcing Process
O10. JIT Based
Services and Repairs
O12. Accessibility to the
Learning and Agile
Service Network
6. Case study: Saipa Yadak Trading Company strategy map with
fuzzy DEMATEL framework
As a case study, Saipa Yadak Trading Company’s real data are
considered to illustrate the capability of introduced model in order
to construct Company Strategy Map.
O4. Strong Branding
Learning and
growth
O14. Upgrading Service
Network toward Customer
Preferences and Pre Defined
Standardization
O5. Increasing
Customer Loyalty
O7. Increasing Agents
Loyalty to the Company
O9. Benchmarking
through the Rivals
O11. On Time
Demanding and Real
Time Grantee
O13. Customized
Supportive System based
on New Technologies
O15. Learning Human
Capital, Aligned with
the Company's Policies
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J. Jassbi et al. / Expert Systems with Applications 38 (2011) 5967–5973
the city are prepared to offer their services to customers. Saipa Yadak has more comprehensive plans underway to secure further
convenience of its clients. It is worth to be noted that the overall
turnover of Iran Auto Industry will be exceeded up to 11 billion
dollars which the share of the company is estimated up to 5 percent by 2009 (http://www.saipayadak.org/aboute.php, 2009).
The authors, through excessive sessions with Saipa Yadak Trading Company CEOs and all general executives, realized and identified the draft list of company’s strategic objectives based on the its
strategic planning. The result will be the first draft of the Company’s strategic objectives as shown in Table 3.
By conducting brainstorming techniques in the sessions, we
placed the extracted strategic objective into the formal perspectives of balanced scorecards. This will be the un-dimensional version of the company strategy map which is depicted on Table 4.
At the next step, subject to the fuzzy linguistic scale and due to
extracted strategy map, every general manager is asked to make
pair wise relationships between each pair of 15 objectives
O ¼ fOi ji ¼ 1; 2; . . . ; 15g. Then, we will have 33 Assessment Data
Fuzzy Matrix in hand. As an example, the assessment data of Engineering Department Management of the Company are depicted in
Table 5.
Table 5
The Assessment Data Fuzzy Matrix of A General Manager.
O1
O2
O3
O4
O5
O6
O7
O8
O9
O10
O11
O12
O13
O14
O15
O1
O2
O3
O4
O5
O6
O7
O8
O9
O10
O11
O12
O13
O14
O15
–
VH
VH
H
VH
VH
VH
H
H
L
VH
VH
H
H
H
H
–
H
H
VH
L
VH
L
H
H
VH
VH
H
H
H
No
H
–
H
VH
VH
VH
H
H
H
VH
VH
H
H
H
No
H
VH
–
VH
VH
VH
H
H
VL
VH
VH
H
H
H
No
L
VH
VH
–
VH
H
H
H
VL
VH
VH
H
VH
VH
No
H
VH
VH
H
–
H
H
H
VL
VH
VH
H
VH
VH
H
H
VH
VH
No
VH
–
H
H
H
VH
VH
H
VH
VH
No
L
L
L
No
No
VH
–
H
VH
VH
VL
L
L
L
H
L
L
L
No
No
L
H
–
VL
L
VL
VL
VL
VL
No
L
L
VH
No
No
No
H
L
–
L
H
H
VL
L
No
L
L
VH
No
No
H
H
H
VH
–
VH
L
VH
L
No
L
VL
H
No
No
L
VH
H
L
L
–
H
L
L
H
H
VL
L
No
No
L
L
H
L
L
L
–
L
L
L
L
No
H
L
H
L
H
H
VH
H
VL
VL
–
L
H
H
H
H
VL
VL
No
H
H
VL
VL
VL
VL
L
–
Table 6
The Initial direct-relation fuzzy matrix ~z.
O1
O2
O3
..
.
O13
O14
O15
O1
O2
O3
...
O13
O14
O15
(0, 0, 0)
(.45, .58, .68)
(.35, .49, .67)
..
.
(.64, .75, .84)
(.18, .25.16)
(.41, .56, .69)
(.55, .68, .73)
(0, 0, 0)
(.18, .25, .36)
..
.
(.33, .38, .44)
(.26, .41, .71)
(.36, .51, .68)
(.46, .58, .63)
(.35, .46, .65)
(0, 0, 0)
..
.
(.51, .59., .66)
(.68, .81, .95)
(.31, .46, .76)
...
...
...
..
.
...
...
...
(.36, .49, .61)
(.55, .65, .75)
..
.
(0, 0, 0)
(.55, .68, .81)
(.29, .46., 76)
(.26, .42, .64)
(.33, .43, .55)
(.21, .29, .34)
..
.
(.35., .44, .59)
(0, 0, 0)
(.42, .49, .58)
(.55, .70, .93)
(.16, .31, .48)
(.45, .50, .65)
..
.
(.22, .33, .46)
(.12, .29., 46)
(0, 0, 0)
Table 7
e
The normalized initial direction-relation fuzzy matrix X.
O1
O2
O3
..
.
O13
O14
O15
O1
O2
O3
...
O13
O14
O15
(0, 0, 0)
(.05, .06, .07)
(.04, .05, .07)
..
.
(.07, .08, .09)
(.02, .03, .03)
(.05, .06, .07)
(.06, .07, .07)
(0, 0, 0)
(.02, .03, .04)
..
.
(.03, .04, .05)
(.03, .05, .07)
(.05, .06, .07)
(.05, .06, .06)
(.04, ..05, .07)
(0, 0, 0)
..
.
(.05, .06., .07)
(.07, .08, .09)
(.04, .05, .07)
...
...
...
..
.
...
...
...
(.04, .05, .07)
(.05, .06, .07)
..
.
(0, 0, 0)
(.06, .07, .08)
(.05, .06., 07)
(.03, .05, .07)
(.03, .04, .05)
(.03, .04, .05)
..
.
(.04., .05, .06)
(0, 0, 0)
(.05, .05, .06)
(.06, .07, .01)
(.02, .03, .04)
(.05, .06, .07)
..
.
(.03, .04, .05)
(.02, .03., 05)
(0, 0, 0)
O1
O2
O3
...
O13
O14
O15
(.07, .14, .33)
(.15, .24, .33)
(.11, .20, .42)
..
.
(.17, .15, .39)
(.12, .23.33)
(.08, .15, .22)
(.06, .07, .07)
(.05, .15, .25)
(.09, .18, .24)
..
.
(.13, .20, .35)
(.15, .18, .27)
(.15, .26, .37)
(.10, .21, .31)
(.02, .04, .06)
(.19, .12, .29)
..
.
(.15, .26., .35)
(.19, .14, .20)
(.05, .10, .17)
...
...
...
..
.
...
...
...
(.32, .25, .47)
(.15, .26, .37)
(.13, .25, .36)
(.06, .14, .19)
(.33, .24, .28)
..
.
(.14., .19, .26)
(.14, .24, .33)
(.05, .05, .06)
(.05, .17, .21)
(.21, .31, .43)
(.09, .16, .27)
..
.
(.06, .10, .19)
(.21, .13., 26)
(.35, .22, .49)
Table 8
e.
The total-relation fuzzy matrix T
O1
O2
O3
..
.
O13
O14
O15
..
.
(.16, .14, .25)
(.16, .07, .08)
(.05, .06., 07)
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J. Jassbi et al. / Expert Systems with Applications 38 (2011) 5967–5973
Table 9
e i; D
ei þ R
ei ; D
ei R
ei ; ðD
ei þ R
e i Þdef ; ð D
ei R
e i Þdef .
ei ; D
The values of R
O1
O2
O3
..
.
O13
O14
O15
Di + Ri
Di Ri
(Di + Ri)def
(Di Ri)def
(1.65, 1.54, 2.43)
(1.55, 1.44, 2.45)
(1.71, 1.45, 2.52)
..
.
(.94, 1.15, 2.55)
(1.72, 1.54, 2.65)
(1.58, 1.55, 2.78)
(2.46,1.47, 2.42)
(2.75, 1.75, 2.15)
(2.79, 1.98, 2.56)
..
.
(2.43, 1.25, 2.55)
(2.45, 1.54, 2.56)
(2.55, 1.68, 2.76)
3.25
3.12
3.03
..
.
3.56
3.85
3.46
0.68
0.57
0.59
..
.
-0.25
-0.17
-0.26
common that an objective can be a cause for many others as the
weighs of its relationships are produced through the model. In order to solve this problem, we believe managerial board interpretations, as one suitable way, are highly required. They can choose the
relationships they believe are most robust and omit the rest or set
of scenarios for any analytical reasoning. Next possible way could
be to propose further enhanced methodology or algorithm for optimal weightening in a way that unnecessary casual relationships
could be visualized less important.
8. Conclusion
Using (1) to average all these assessments matrices, we will
have initial-direct fuzzy matrix ~z. Our partial results are shown
in Table 6. Then, using (4), the normalized direct-relation fuzzy
~ will be produced. The partial results of our case study
matrix X
are depicted in Table 7.
Following (8), we will acquire the total-relation fuzzy matrix
which will be the last step for transforming crisp data into the fuzzy environments. Our matrix partially depicted on Table 8.
To access the casual relationships between strategic objectives,
~i þ R
~ i Þ and ðD
~i R
~ i Þ in which D
~ i and R
~ i are the
we will calculate ðD
sum of row and the sum of columns of our total-relation fuzzy matrix respectively. Our partial results are shown in Table 9.
To finalize the procedure, all calculated Di þ Ri and Di Ri are
defuzified through COG (center of gravity) defuzification method.
Then, we have two sets of numbers: ðDi þ Ri Þdef which shows the
importance of all strategic objectives by aggregation of all managers’ preferences and ðDi Ri Þdef which assign strategic objectives
into cause and effect groups.
As the shown in Table 9, the strategic objectives are divided into
two groups. The first is cause group which implies O15, O14, O12,
O13, O9, and O8 and effect group which implies the rest of the
objectives.
Strategy mapping is the very important first step in any Balanced Scorecard system. Strategy maps in a general term could
be viewed as the structural modeling systems. The process of
building a strategy map is a group decision making process by its
nature and needs managerial board or experts’ value assignments.
Then, we proposed a fuzzy DEMATEL methodology, as a very powerful structural decision making systems, for modeling cause and
effect relationships of the strategy map. It is possible to build
and deploy any other structural modeling frameworks/algorithms
as the extension of work and compare the weaknesses and
strengths of the mythologies.
Acknowledgement
The authors thank Mr Amoozadeh, President of Saipa Yadak
Trading Company, Mr Postindooz and Mr Daftari, Vice Presidents,
Mr Khorampoor, International Supply Executive, Mr Tarahomi,
Financial Executive, Mr Rezaie, Human Resource Executive, Mr
Sharif, Central Services Executive, Mr Ghandi, Information Technology Executive, Mr Roozbahani, Technical Engineering Executive,
Mr Carafi, Training Executive, and all other executives and managers of the company for their valuable help and patience.
7. Discussions and remarks
References
The authors believe two indications exit for discussion and revision of the methodology proposed in this paper. As it has been
noted earlier, the procedure of DEMATEL method utilizes the pair
wise comparisons between the criteria/objectives. Then, it is observed that by this judgmental value assigning, it is most common
that two (or maybe more) criteria/objectives produce values such
the way that we observe any recursive cause and effect relationships. On the other hand, we may see (in the case of the strategy
map) that one object from upper perspective (say Financial Perspective for example) produces negative value; hence, it would
be a cause objective, whereas the formal methodology of the strategy maps indicate that the prior perspectives must contain cause
effects for posteriors. The authors believe that, in such a situation,
by using the proposed technique which gathers and unifies collective experts’ knowledge to capture the causal relationships, this reverse causality must be granted by the executive boards in order to
set forth analytical scenarios for understanding and diagnosis the
reversed relationships.
The second point deals with the multiplicity of cause and effect
relationships. It is clear that by the very compact group mangers or
experts who are supposed to design the strategy map, it is most
common to reach to a general consensus. By any type of discussion,
they set priorities and build casual relationships. The group human
processing based on the organizational experiences, indeed will
connect cause and effect objectives by any means. But by collecting
the experts’ preferences, it is most happening to produce values
that may show different possibilities, or better say weights, for
any relationships between objectives. On the other hand, it is very
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