An integrated model for extending brand based on fuzzy ARAS and ANP methods.
Zamani, Mahmoud ; Rabbani, Arefeh ; Yazdani-Chamzini, Abdolreza 等
Introduction
Brand extension, defined as the use of an established brand name
for new-product categories, is one of the most common strategies used in
developing an existing brand, which can reduce risk and increase
investment by enhancing consumer perception. Brand extension strategies
are beneficial because they reduce new product introduction costs, and
perceived risk of the new product, hence increasing the chances of
success (Aaker 1990; Keller 1998). Approximately 80% of new products
introduced each year are brand extensions (Keller 1998). This is due to
the fact that launching a new product is not only time consuming; but
also, needs a big budget to create awareness and to promote a
product's benefits (Tauber 1981). On the other hand, a victorious
brand can help a company to more easily launch new products in novel
categories.
Generally, two main advantages of brand extensions could be
underlined: the ability to facilitate new-product acceptance; and
provide positive feedback to the parent brand and company (1).
Therefore, it is important for marketing researchers and brand managers
to understand how consumers evaluate them (Estes et al. 2012). A
successful brand message strategy relies on a congruent communication
and a clear brand image (Sjodin, Torn 2006).
Although there are significant benefits in brand extension
strategies, there are also significant risks, resulting in a diluted or
severely damaged brand image. Poor choices for brand extension may
dilute and deteriorate the core brand and damage the brand equity (Aaker
1990). In spite of the positive impact of brand extension, negative
association and wrong communication strategy do harm to the parent brand
and even the brand family (Tauber 1981; Aaker 1990). Therefore, for
propose of decreasing the level of risk in the process of brand
extension, it is necessary to take into account both qualitative and
quantitative parameters influencing the problem in order to get the
deeper insight into the problem area. This helps an organisation to
properly model the problem of brand extension.
On the other hand, the merit of using multi-criteria decision
making (MCDM) techniques is to model a complex and sophisticated problem
by applying a well-organised and systematic approach. The MCDM methods
provide tools for considering both tangible and intangible parameters
involved in the process of modelling in order to make a proper and
accurate decision. These methods are strongly recommended as helpful in
reaching important decisions that cannot be determined in a
straightforward manner (Wu et al. 2010; Fouladgar et al. 2012).
Different MCDM techniques have been developed to solve multi criteria
problems. These methods can be classified into three main categories
(Belton, Stewart 2002): (i) value measurement model such as analytical
hierarchy process (AHP), (ii) outranking models such as Preference
Ranking Organisation METHod for Enrichment Evaluation (PROMETHEE), and
(iii) goal aspiration and reference level models such as Technique to
Order Preference by Similarity to Ideal Solution (TOPSIS) and Additive
Ratio Assessment Method (ARAS).
ARAS, first introduced by Zavadskas and Turskis (2010), is a branch
of the MCDM techniques that solve a complex problem by using simple
relative comparisons. This method uses the basic concept of degree of
optimality for selecting the best alternative among a pool of
alternatives by calculating the ratio of the sum of normalized and
weighted criteria scores to the sum of the values of normalized and
weighted criteria. The ARAS method is employed by different researchers
to rank the possible alternatives in order to select the best ones
(Zavadskas et al. 2010; Zavadskas, Turskis 2010; Bakshi, Sarkar 2011;
Bakshi, Sinharay 2011; Dadelo et al. 2012; Zavadskas et al. 2012; Kutut
et al. 2013). This is due to the fact that the ARAS method has several
advantages: (i) the computations defined in the process of modelling a
decision making problem are straightforward, (ii) the concepts have a
profound logic (iii) this method contains a simple mathematical form in
the pursuit of the best alternative, and (iv) the relative weights are
incorporated into the comparison procedures.
However, ARAS is not capable of facing the vagueness and
uncertainty derived from subjective judgments and/or lack of information
and/or incomplete data; so that failure to consider the inherent
uncertainty and/or imprecision of the elements could result in
unreliable and unrealistic assessment. The merit of using fuzzy logic is
to take the existing uncertainty into account. This technique uses a
linguistic variable instead of the traditional quantitative expression,
which is a very helpful concept for dealing with the unknown and complex
situations (Zadeh 1965). The combination of fuzzy logic and ARAS
technique, known as fuzzy ARAS, is a strategic methodology used for
solving the aforementioned problems. Since the fuzzy ARAS contains
simple and fast computations, logical process, and tolerating the
uncertainty, is recently employed for formulating different aspects of
priority problems (Turskis, Zavadskas 2010; Turskis et al. 2012).
However, the main limitation of the fuzzy ARAS method is in
formulating a decision making problem without taking into account the
interdependency among the evaluation criteria. In the system of
real-life problems, the evaluation criteria are strongly interdependent.
To take the interrelationship among the elements into account, different
models have been developed. Analytic network process (ANP) is one of the
most popular techniques in formulating the mutual relationship among the
elements. This technique interprets the interrelationship between
weights of relationship. This method is employed by a large number of
researchers owing to its particular strengths. The reasons for using an
ANP-based decision analysis approach are: (1) ANP can measure all
tangible and intangible criteria in the model (Saaty 1996), (2) ANP is a
relatively simple, intuitive approach that can be accepted by managers
and other decision-makers (Presley, Meade 1999), (3) ANP allows for a
more complex relationship between the decision levels and attributes as
it does not require a strict hierarchical structure (Yazgan et al.
2010), and (4) ANP is more adapted to real world problems (Fouladgar et
al. 2012).
On the other hand, in the case of complex problems, it is usually
better to use opinions of a group of experts because it is difficult for
a single person to possess knowledge and experience in all details of
the problem (Sotirov, Krasteva 1994).
The main objective of the current study is to model a brand
extension problem as a MCDM problem and provide a three-step decision
support framework to accurately evaluate the possible alternatives. For
achieving the aim, after defining the problem under consideration and
identifying the evaluation criteria and feasible alternatives, the ANP
method is employed for obtaining the relative weights of the evaluation
criteria but not the entire evaluation process to reduce the large
number of pairwise comparison. For this reason, fuzzy ARAS is used to
calculate the performance of alternatives, and to prioritize the
feasible strategies in terms of their overall performance on evaluation
main and sub-criteria.
The paper is organized as follows. Section 1 presents a brief
overview of the ANP methodology. Section 2 explains the basic concepts
of fuzzy logic and the uncertainty involved in the process of decision
making. This section also goes one step beyond and examines the steps of
the fuzzy ARAS technique. The proposed model is clearly presented in
section 3. An application of the proposed model is illustrated in
section 4. Finally, conclusions are discussed in the last section.
1. Analytic network process (ANP)
The Analytic network process (ANP), firstly introduced by Saaty
(1996), is a generalization of the AHP technique. The AHP technique
models a complex problem by decomposing the problem into a hierarchical
structure, in which the elements of decision are independent and the
relationship between the levels of decision are linear; so that, it
ignores interrelationships among the elements. Figure 1 illustrates the
difference between hierarchy and network structures. As shown in Figure
1, a hierarchy is a linear top down structure and network is a
non-linear structure that spreads out in all directions. An ANP system
uses arcs to show the relationships among elements, where the directions
of arcs signify directional dependence (Chung et al. 2005). The ANP
technique extends the AHP to facilitate the process of formulating the
problems with feed-back and dependence (Fouladgar et al. 2012). This
method replaces the hierarchy in the AHP with a network to equip the ANP
for modelling the interrelationships among decision elements in order to
solve the problems that are nonlinear and more complex. Thus, the ANP
produces priorities or relative importance of elements in a complex
network model with consideration of inter-dependency among elements (Lee
et al. 2012).
Like with AHP, pairwise comparison in ANP is performed in the
framework of a matrix, and a local priority vector can be derived as an
estimate of the relative importance associated with the elements (or
clusters) being compared by solving the following equation (Yuksel,
Dagdeviren 2007):
A x w = [[lambda].sub.max] x w, (1)
where A is the matrix of pairwise comparison, w is the eigenvector,
and [[lambda].sub.max] is the largest eigenvalue of A.
In this paper, the hierarchy and network model proposed for
modelling the mutual relationships among the benefit, opportunity, cost,
and risk (BOCR) parameters including four levels (see Fig. 2).
In the first level, the optimum brand extension strategy (the goal)
is located, the BOCR parameters (main criteria) and the BOCR sub-factors
(sub-criteria) are situated in the second and third levels,
respectively, and the brand extension strategies (alternatives) are
located in the last level. The structure of a supermatrix--a matrix of
the influences among the elements--for the BOSR network with four levels
can be defined as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)
where [W.sub.1] is a matrix that reflects the impact of the overall
purpose (selecting the optimal brand extension strategy) on the main
criteria (BOCR factors); [W.sub.2] is the matrix that represents the
impact of each of the main criteria on each other or inner independence
of the BOCR factors; [W.sub.3] is the vector that shows the impact of
the main criteria (BOCR factors) on each of the sub-criteria (BOCR
sub-criteria); [W.sub.4] is the matrix that reflects the impact of the
sub-criteria (BOCR sub-criteria) on each of the alternatives; and I is
the identity matrix.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
In order to perform the ANP methodology for obtaining the
importance weights of the BOCR factors, the algorithm employed is
stepwise as follows:
Step 1. Define the problem and identify the factors having an inner
dependency with each other.
Step 2. Without taking into account the dependence among the BOCR
factors; calculate the importance weights of the factors with a
Saaty's (1-9) scale (Saaty 1980). This means that the process of
this step leads to [W.sub.1] be acquired.
Step 3. Calculate the inner dependence matrix of each BOCR factor
with respect to the other factors with a 1-9 scale. This means that this
step calculates the [W.sub.2] matrix.
Step 4. Measure the interdependent priorities of the BOCR factors.
Calculating [W.sub.factors] = [W.sub.1] x [W.sub.2] is performed in this
step.
Step 5. Calculate the local importance weights of the BOCR
sub-factors with a 1-9 scale. [W.sub.sub-factors (local)] is obtained in
this step.
Step 6. Measure the global importance weights of the BOCR
sub-factors by multiplying the values of steps 4 and 5
([W.sub.sub-factors (global)] = [W.sub.factors] x [W.sub.sub-factors
(local)]).
2. Fuzzy ARAS technique
Additive Ratio Assessment (ARAS), introduced by Zavadskas and
Turskis (2010), is based on the concept that the phenomena of
complicated world could be understood by using simple relative
comparisons (Turskis, Zavadskas 2010). The ARAS method not only
determines the performance of alternatives, but also calculates ratio of
each alternative to the ideal alternative.
According to the basic concepts of the ARAS method, decision team
assigns the relative importance of the evaluation criteria and ratings
of the feasible alternatives with respect to the criteria under
consideration by using numerical values. In real world problems, it is
often difficult for a decision maker to determine precise weights for
criteria and alternatives with respect to the criteria under
consideration (Yazdani-Chamzini, Yakhchali 2012). The merit of using a
fuzzy approach is to determine the importance or preference of criteria
and alternatives using fuzzy numbers instead of crisp numbers to be more
adapted to the real world cases. Therefore, fuzzy logic and ARAS
technique are combined in the form of the fuzzy ARAS method to formulate
the real world problems more accurately. The fuzzy ARAS technique helps
the decision team to conduct a comprehensive analysis for prioritizing
the preference of the alternatives in presence of vague or imprecise
information. The procedure of fuzzy ARAS can be defined as follows.
Step 1. Choose the linguistic rating, [[??].sub.ij]: i= 1, 2, ...,
m; j= 1, 2, ..., n for alternatives with respect to criteria under
consideration. The values given in Table 1 and Figure 2 present the
linguistic ratings applied for alternatives.
Step 2. Form the fuzzy decision matrix. Fuzzy ARAS solves a problem
with m alternatives evaluated based on n dimensions. In order to
construct the fuzzy ARAS matrix, first a judgment matrix is established
as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)
where [[??].sub.ij] is fuzzy value representing the preference of
the i alternative in terms of the j criterion; [[??].sub.0j] is the
optimal value of the j criterion.
Step 3. Aggregate the ratings of alternatives respect to each
criterion ([[??].sub.ij]). In order to aggregate the ratings of
alternatives versus each criterion, the arithmetic mean is applied.
Let the fuzzy ratings of all decision makers be Triangular Fuzzy
Numbers (TFNs) [[??].sub.ijk] = ([a.sub.ijk], [b.sub.ijk], [c.sub.ijk]),
k = 1, 2, ..., K, which [[??].sub.ijk] represents the value of the i-th
alternative respect to the j-th criterion by k-th decision maker. Then
the aggregated fuzzy rating can be define as:
[[??].sub.ij] = ([a.sub.ij], [b.sub.ij], [c.sub.ij]), k = 1, 2,
..., K, (4)
where
[a.sub.ij] = 1/K [K.summation over (k=1)] [a.sub.ijk], [b.sub.ij] =
1/K [K.summation over (k=1)] [b.sub.ijk], [c.sub.ij] = 1/K [K.summation
over (k=1)] [c.sub.ijk]. (5)
Step 4. Calculate the optimal value of j criterion. It's
optimal value is unknown, then it can be obtained by using the following
equations:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; The larger,
the better type, (6)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; The smaller,
the better type. (7)
Step 5. Normalize the decision matrix. The ratio to the optimal
value is used to avoid the difficulties caused by different dimensions
of the criteria. Several algorithms are developed for calculating the
ratio to the optimal value. However, the values are usually transferred
into the closed interval 0 and 1. The matrix resulted from the
normalization process can be defined as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)
The criteria, whose preferable values are maxima, are normalized as
follows (Turskis, Zavadskas 2010):
[[??].sub.ij] = [[??].sub.ij]/[m.summation over (i=0)]
[[??].sub.ij] (9)
The criteria, whose preferable values are minima, are normalized
using a two-stage procedure:
[[??].sub.ij] = 1/[[??].sup.*.sub.ij]; [[??].sub.ij] =
[[??].sub.ij]/[m.summation over (i=0)] [[??].sub.ij]. (10)
After normalizing the values, the dimensionless values of the
criteria are comparable. Step 6. Calculate the weighted normalized
decision matrix. The weighted normalized value is calculated by
multiplying the weights of the criteria under consideration ([w.sub.j])
with the normalized fuzzy decision matrix derived from the previous
step. The weighted normalized decision matrix is calculated by the
following relations:
[[??].sub.ij] = [[??].sub.ij] [w.sub.j]. (11)
Step 7. Measure the optimality function. The following equation is
employed for determining the values of optimality function of i-th
alternative (Turskis, Zavadskas 2010):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)
The biggest value for [[??].sub.i] is the best, and the least one
is the worst.
Step 8. Defuzzify the values of optimality function. The output
obtained for each alternative is a fuzzy number. Therefore, it is
necessary to convert fuzzy numbers into crisp numbers by defuzzification
in order to compare the rank of dimensions. The procedure of
defuzzification is to locate the Best Nonfuzzy Performance (BNP) value.
Methods of such defuzzified fuzzy ranking generally include mean of
maximal (MOM), centre of area (COA), and a-cut (Chen et al. 2011). In
this study, the authors employ the centre of area (COA) method to
prioritize the order of importance of each dimension. This method is a
simple and practical without the need to bring in the preferences of any
evaluators (Wu et al. 2009). The BNP value for the fuzzy number
[[??].sub.i] = (L[[??].sub.i], M[[??]S.sub.i], U[[??].sub.i]) can be
found by using the following equation:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (13)
Step 9. Calculate the degree of the alternative utility by making a
comparison with the optimum one [S.sub.0]. The utility degree of an
alternative can be calculated by the following Equation:
[K.sub.i] = [S.sub.i]/[S.sub.0]. (14)
From the mathematical point of view, the values acquired for
[K.sub.i] belong to the range of [0, 1].
Step 10. Rank the alternatives according to [K.sub.i] in descending
order and select the alternative with maximum value of [K.sub.i].
3. The proposed model
The proposed model can be defined as presented in the following
steps:
Step 1: Identify the evaluation criteria and classify them based on
the BOCR factors.
Step 2: Construct the pairwise comparison matrices based on the
scale given in Table 1 for calculating the importance weights of the
main and sub-factors. Assume that there is no dependence among the BOCR
factors (i.e. construct the AHP model). The local weights of sub-factors
arise from this step.
Step 3: Form the pairwise comparison matrices for measuring the
relative weights of the BOCR factors (i.e. construct the ANP model). The
interdependent weights of the factors are derived from this step.
Step 4: Calculate the global weights of the evaluation indicators
by multiplying the weights of the sub-factors obtained in Step 2 with
those of the factors to which it belongs and that is acquired in the
previous step.
Step 5: Define a linguistic scale for describing the preference
ratings of the alternatives.
Step 6: Aggregate the fuzzy values resulting from the previous
step.
Step 7: Obtain the preference ratings of the alternatives by using
the fuzzy ARAS technique based on the global weights yielded in Step 4
and the ratings obtained from the previous step.
Step 8: Prioritize the brand extension strategies in descending
order and select the highest rank as the first choice.
The schematic diagram of the proposed model for selecting the
optimal brand extension strategy is provided in Figure 3.
[FIGURE 3 OMITTED]
4. An application of the proposed method in food industry
A manufacturing company desires to select the most appropriate new
product to extend its brand into a wide range of new categories and earn
money. In order to show the potential application of the proposed model,
a stepwise demonstration of methodology is given to exemplify how
ANP-ARAS method under fuzzy environment can be used for the evaluation
and assessment of the brand extension of food industry in Iran's
market. The example is based on a real-world decision problem. Dairy
food industry in Iran has been in business for fifty years and has more
than 400 sales representatives in the country. From the point of view of
production, this company is considered as one of the most important
producers. Dairy food industry has a large number of labour force in
industrial agricultural, commercial and service sections. Therefore,
this industry is chosen for the case study.
For achieving the aim, a team of seven evaluators was established,
including experts with at least five years of experience in the field of
marketing and brand extension. This helps the authorities to
appropriately analyse the group decisions (Robbins 1994). The proposed
model is described below as a stepwise procedure, based on the steps
defined in the previous section.
The priority weights of the evaluation criteria for extending brand
are calculated by using the process of the algorithm described in the
previous section. After synthesizing the literature review from previous
studies, preliminary screening, and a number of face to face interviews
with the evaluator team, the four BSC criteria including thirteen
sub-criteria, and five feasible alternatives are considered to be
involved in the process of the evaluation (see Fig. 4). The four
perspectives of the BSC model are applied as a framework of the analysis
to help in the definition of the indicators.
In this study, the importance weights of the main and sub-criteria
are investigated by distributing questionnaires designed in the format
of AHP questionnaire (i.e. pairwise comparisons) and conducting
face-to-face interviews with the expert team. The evaluators are asked
to determine the importance of the elements in each level with respect
to their relative importance toward their upper criterion. Each decision
maker evaluates the criteria under consideration by using two-by-two
comparisons. In order to make a comparison between two components,
Saaty's (1-9) scale (Saaty 1980) is employed, where 1 represents no
difference between the two components and 9 represents overwhelming
dominance of the component under consideration (row component) over the
comparison component (column component). Likewise, the reverse
comparison between the components is routinely determined by a
reciprocal value. An example of the pairwise comparison matrix for the
main criteria (BOCR factors) is depicted in Table 2.
[FIGURE 4 OMITTED]
Since different decision makers have a different background, they
look at the problem from divergent angles; consequently, their judgments
are be dissimilar. After gathering information with the help of a
questionnaire, the pair-wise comparison matrices are aggregated into the
final aggregated matrices by using the geometric mean technique. This
method can be used to aggregate different judgments from several experts
as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)
where [a.sub.ijh] is an element of the decision matrix evaluated by
decision maker h; [a.sub.ij(gp)] is the geometric mean of the values
determined by the expert team; and H is the total number of evaluators.
Table 3 shows the final matrix for main and sub-criteria. In order to
valid the matrices, the group consistency index (GCI) is calculated and
then the group consistency ratio (GCR) is computed as indicated in the
last column of Table 3.
The GCI can be mathematically defined as:
GCI = ([[lambda].sub.max] - n)/n , (16)
where [[lambda].sub.max] is the largest eigenvalue; and n is the
number of the criteria under consideration. The GCR is obtained as:
GCR = GCI/RCI. (17)
The Random Consistency Index (RCI), derived from a randomly
generated square matrix, is shown in Table 4. The group judgment is
consistent provided that the GCR is less than 0.1.
To show how interdependency among the main-criteria can influence
the difference of priority weights, the impact of each criterion on
every other factor using pairwise comparison process is carried out.
According to the aforementioned process, pairwise comparison matrices
based on group decision making using the geometric mean technique are
formed for the BOCR factors as depicted in Tables 5-8.
The relative weights of the BOCR factors are listed in the last row
of Tables 5-8. The inner dependence matrix is formed as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Using the inner dependence weights resulted from this step and the
dependence weights derived from the previous step, the priority weights
for the BOCR factors is yielded as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
The results change from 0.453 to 0.35, 0.109 to 0.167, 0.286 to
0.274, and 0.151 to 0.209 for the priority values of factors B, O, C and
R, respectively. From the above matrix, it can be obvious that the
results are significantly different from when the interdependent weights
are not taken into account. It can be seen that the largest changes are
in "O" and "R" criteria. Without considering the
dependency among the criteria, "B" has the highest intensity
among all criteria. However, when taking the interdependency into
account, the intensity of "B" is completely different. The
"B" criterion became the most important factor for evaluating
brand extension strategies because "B" criterion influences
other criteria more significantly.
Therefore, the priority weights for main and sub-criteria are
computed as listed in Table 9.
[FIGURE 5 OMITTED]
Based on the results derived from the model, "C1" is
weighted more heavily (0.158) than the other criteria. The results also
reveal that the criterion "R3" (0.031) is less important than
the other criteria. The assessment results for the priority weights of
the evaluation criteria under consideration are decreasingly depicted in
Figure 5.
In the next step of the proposed model, evaluators are asked to
build the decision matrix by comparing the alternatives under each
criterion by using the scale given in Table 1 and Figure 2. For the
evaluation indicators under benefit and opportunity factors (B1, B2, B3,
B4, O1, O2, and O3), the higher the score, the better the performance of
the brand extension strategy is. Whereas, for the indicators under cost
and risk factors (C1, C2, C3, R1, R2, R3, and R4), the higher the score,
the worse the performance of the brand extension strategy is. A sample
of the fuzzy decision matrix evaluated by one of the experts is depicted
in Table 10. Then, the aggregated fuzzy performance ratings of the
feasible alternatives with respect to each criterion are computed by Eq.
(4) and the results are presented in Table 11. By multiplying the
normalized decision matrix and the weights derived from the ANP
technique, the weighted normalized decision matrix is obtained as shown
in Table 12.
After calculating the weighted normalized decision matrix, the
values of optimality function for the brand extension strategies must be
determined by using Eq. (12) as presented in Table 13.
In order to make a comparison between the performances of the
alternatives, the values resulting from optimality function are
transferred into crisp value by using the defuzzification process.
Finally, after calculating the utility degree of each alternative by
using Eq. (14), the alternatives are ranked in descending order and the
alternative with maximum value of Ki is selected as the best choice.
According to Ki values, the ranking of the alternatives in descending
order are A2, A3, A4, and A1. The proposed model indicates that ice
cream (A2) is the best method with Ki value of 0.808. Rankings of the
alternatives according to Ki values are listed in the last row of Table
13.
Conclusions
Group decision making under fuzzy environment provides a powerful
tool for evaluating and prioritizing the feasible alternatives under
their preference with respect to the criteria being often in conflicting
with each other. This paper proposes a new integrated model based on ANP
and fuzzy ARAS methods that is capable of handling both subjective
judgment and objective information in the process of formulating a
decision making problem. However, according to the inherent complexity
and less of information in real world problems, the output of the
proposed model is more adapted with real world terms. The proposed model
integrates ANP and fuzzy ARAS models under the group decision making.
The first is used to interpret the interrelationship into weights of
relationship. The latter is based on the concept that the phenomena of
complicated world could be understood by using simple relative
comparisons for solving the MCDM problems with multi-judges in the term
of vagueness. In the system of the proposed model, the ANP technique is
utilized to calculate the relative weights of the evaluation indicators
and fuzzy ARAS is used to obtain the performance ratings of the feasible
alternatives by using linguistic terms. In order to prove the validity
and suitability of the proposed model, a real case study is illustrated
for the brand extension strategy selection in the food industry.
Although the proposed model is employed for the strategic decisions, it
can be applied for making the best decision in any other area of
engineering and management.
doi:10.3846/16111699.2014.923929
Caption: Fig. 1. Difference between a hierarchy (A) and a network
(B) (Azimi et al. 2011)
Caption: Fig. 2. Membership function of linguistic variables for
preference rating
Caption: Fig. 3. The outline of the proposed model
Caption: Fig. 4. Structure of the brand extension problem
Caption: Fig. 5. Final ranking of the criteria
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Received 06 November 2013; accepted 09 May 2014
Mahmoud Zamani (1), Arefeh Rabbani (2), Abdolreza Yazdani-Chamzini
(3), Zenonas Turskis (4)
(1,2) Young Researchers Club, Central Tehran Branch, Islamic Azad
University, Teheran, Iran
(3) Young Researchers Club, South Tehran Branch, Islamic Azad
University, Teheran, Iran
(4) Department of Construction Technology and Management, Faculty
of Civil Engineering, Vilnius Gediminas Technical University, Sauletekio
al. 11, LT-10223 Vilnius, Lithuania
E-mails: (1)
[email protected]; (2)
[email protected];
(3)
[email protected]; (4)
[email protected]
(corresponding author)
(1) www.citeman.com
Mahmoud ZAMANI is a PhD student in innovation at The University of
Teheran Management School, Teheran, Iran. He is the author of more than
5 research papers. His interests include innovation, technology
strategy, marketing and MCDM methods.
Arefeh RABBANI graduated with MSc from the management and
accounting faculty at Allame Tabatabaee University, Teheran, Iran in
2013. Her interests include innovation, human resource management (HRM),
organization learning and Strategy.
Abdolreza YAZDANI-CHAMZINI. Master of Science in the Department of
Mining Engineering, research assistant of Teheran University,
Teheran-Iran. Author of more than 46 research papers. In 2011, he
graduated from the Science and Engineering Faculty at Tarbiat Modares
University, Teheran-Iran. His research interests include decision
making, forecasting, modelling, and optimization.
Zenonas TURSKIS. Professor, senior research fellow at the
Construction Technology and Management Laboratory of Vilnius Gediminas
Technical University, Lithuania. His research interests include building
technology and management, decision-making theory, computer-aided design
and expert systems. Author of more than 90 research papers.
Table 1. Linguistic variables for the rating of alternatives
Linguistic variables Triangular fuzzy number
Very poor (VP) (0, 0.15, 0.3)
Poor (P) (0.2, 0.35, 0.5)
Fair (F) (0.4, 0.5, 0.6)
Good (G) (0.5, 0.65, 0.8)
Very good (VG) (0.7, 0.85, 1)
Table 2. A sample of comparison matrix for the BOCR factors
BOCR factors B O C R
B 1 4 2 3
O 0.25 1 0.33 0.5
C 0.5 3 1 2
R 0.33 2 0.5 1
Table 3. Final matrix for the main-criteria
BOCR B O C R GCI
criteria
B 1.00 3.26 2.21 2.79 0.0165
O 0.31 1.00 0.31 0.67
C 0.45 3.23 1.00 2.12
R 0.36 1.49 0.47 1.00
Sub- B1 B2 B3 B4 O1 O2 O3 C1 C2
criteria
B
B1 1.00 1.67 1.45 2.32
B2 0.60 1.00 0.78 1.84
B3 0.69 1.28 1.00 2.13
B4 0.43 0.54 0.47 1.00
O
O1 1.00 0.87 1.23
O2 1.15 1.00 1.65
O3 0.81 0.61 1.00
C
C1 1.00 2.43
C2 0.41 1.00
C3 0.28 0.40
R
R1
R2
R3
R4
Sub- C3 R1 R2 R3 R4
criteria
B
B1 0.0032
B2
B3
B4
O
O1 0.0015
O2
O3
C
C1 3.56 0.019
C2 2.51
C3 1.00
R
R1 1.00 2.34 2.27 3.78 0.01
R2 1.00 1.31 1.23
R3 1.00 0.88
R4 1.00
Table 4. The Random Consistency Index (Saaty 1980)
n 3 4 5 6 7 8 9 10
RCI 0.58 0.90 1.12 1.24 1.32 1.41 1.45 1.49
n 11 12 13 14 15
RCI 1.51 1.48 1.56 1.57 1.59
Table 5. The inner dependence matrix of the BOCR factors
with respect to "B"
B O C R Relative importance weights
O 1 0.64 0.87 0.271
C 1.56 1 1.04 0.388
R 1.15 0.96 1 0.341
GCR = 0.005
Table 6. The inner dependence matrix of the BOCR factors with
respect to "O"
O B C R Relative importance weights
B 1 1.23 1.64 0.410
C 0.81 1 1.57 0.352
R 0.61 0.64 1 0.237
GCR = 0.002
Table 7. The inner dependence matrix of the BOCR factors
with respect to "C"
C B O R Relative importance weights
B 1 2.43 1.78 0.505
O 0.81 1 0.67 0.202
R 0.61 0.64 1 0.293
GCR = 0.0005
Table 8. The inner dependence matrix of the BOCR factors
with respect to "R"
R B O C Relative importance weights
B 1 1.33 1.13 0.380
O 0.81 1 0.96 0.297
C 0.61 0.64 1 0.323
GCR = 0.001
Table 9. Priority weights for the main and sub-criteria
BOCR criteria Sub-criteria Local weights Global weights
B 0.35 --
B1 0.362 0.127
B2 0.226 0.079
B3 0.275 0.096
B4 0.136 0.048
O 0.167 --
O1 0.335 0.056
O2 0.406 0.068
O3 0.259 0.043
C 0.274 --
C1 0.576 0.158
C2 0.286 0.078
C3 0.137 0.038
R 0.209 --
R1 0.503 0.105
R2 0.198 0.041
R3 0.146 0.031
R4 0.153 0.032
Table 10. A sample of fuzzy evaluation matrix evaluated
by one of the experts
A1 A2 A3 A4
B1 F VG G P
B2 G G VP F
B3 G VG G F
B4 VG G F G
O1 VG VG G G
O2 F F G VG
O3 G F F F
C1 VG G F F
C2 F VG G G
C3 F G F G
R1 VG F G G
R2 G F F P
R3 P G F G
R4 VG F VP P
Table 11. Aggregated evaluation matrix
A0 A1 A2
B1 (1,1,1) (0.34,0.49,0.64) (0.59,0.74,0.89)
B2 (1,1,1) (0.46,0.61,0.76) (0.47,0.62,0.77)
B3 (1,1,1) (0.51,0.66,0.81) (0.62,0.77,0.92)
B4 (1,1,1) (0.62,0.77,0.92) (0.42,0.57,0.72)
O1 (1,1,1) (0.58,0.73,0.88) (0.61,0.76,0.91)
O2 (1,1,1) (0.41,0.56,0.71) (0.36,0.51,0.66)
O3 (1,1,1) (0.48,0.63,0.78) (0.29,0.44,0.59)
C1 (0.29,0.29,0.29) (0.57,0.72,0.87) (0.46,0.61,0.76)
C2 (0.32,0.32,0.32) (0.32,0.47,0.62) (0.62,0.77,0.92)
C3 (0.38,0.38,0.38) (0.41,0.56,0.71) (0.45,0.6,0.75)
R1 (0.36,0.36,0.36) (0.63,0.78,0.93) (0.36,0.51,0.66)
R2 (0.23,0.23,0.23) (0.47,0.62,0.77) (0.41,0.56,0.71)
R3 (0.13,0.13,0.13) (0.13,0.28,0.43) (0.52,0.67,0.82)
R4 (0.17,0.17,0.17) (0.65,0.8,0.95) (0.37,0.52,0.67)
A3 A4
B1 (0.53,0.68,0.83) (0.24,0.39,0.54)
B2 (0.12,0.27,0.42) (0.37,0.52,0.67)
B3 (0.43,0.58,0.73) (0.33,0.48,0.63)
B4 (0.36,0.51,0.66) (0.46,0.61,0.76)
O1 (0.44,0.59,0.74) (0.51,0.66,0.81)
O2 (0.48,0.63,0.78) (0.64,0.79,0.94)
O3 (0.32,0.47,0.62) (0.38,0.53,0.68)
C1 (0.37,0.52,0.67) (0.29,0.44,0.59)
C2 (0.46,0.61,0.76) (0.45,0.6,0.75)
C3 (0.38,0.53,0.68) (0.49,0.64,0.79)
R1 (0.41,0.56,0.71) (0.51,0.66,0.81)
R2 (0.33,0.48,0.63) (0.23,0.38,0.53)
R3 (0.38,0.53,0.68) (0.46,0.61,0.76)
R4 (0.17,0.32,0.47) (0.27,0.42,0.57)
Table 12. Weighted normalized decision matrix
A0 A1 A2
B1 (0.010,0.010,0.010) (0.005,0.007,0.009) (0.008,0.010,0.012)
B2 (0.007,0.007,0.007) (0.004,0.005,0.006) (0.004,0.005,0.007)
B3 (0.008,0.008,0.008) (0.005,0.007,0.008) (0.006,0.008,0.010)
B4 (0.004,0.004,0.004) (0.003,0.004,0.005) (0.002,0.003,0.004)
O1 (0.005,0.005,0.005) (0.003,0.004,0.005) (0.004,0.005,0.005)
O2 (0.006,0.006,0.006) (0.003,0.004,0.005) (0.003,0.004,0.005)
O3 (0.004,0.004,0.004) (0.002,0.003,0.004) (0.001,0.002,0.003)
C1 (0.009,0.009,0.009) (0.002,0.005,0.007) (0.004,0.007,0.009)
C2 (0.004,0.004,0.004) (0.003,0.004,0.006) (0.001,0.002,0.003)
C3 (0.002,0.002,0.002) (0.001,0.002,0.002) (0.001,0.002,0.002)
R1 (0.006,0.006,0.006) (0.001,0.002,0.004) (0.004,0.006,0.007)
R2 (0.003,0.003,0.003) (0.001,0.002,0.002) (0.001,0.002,0.003)
R3 (0.002,0.002,0.002) (0.002,0.002,0.003) (0.001,0.001,0.002)
R4 (0.002,0.002,0.002) (0.000,0.001,0.001) (0.001,0.002,0.002)
A3 A4
B1 (0.007,0.009,0.011) (0.003,0.005,0.007)
B2 (0.001,0.002,0.004) (0.003,0.004,0.006)
B3 (0.004,0.006,0.008) (0.003,0.005,0.006)
B4 (0.002,0.003,0.003) (0.002,0.003,0.004)
O1 (0.003,0.004,0.004) (0.003,0.004,0.005)
O2 (0.004,0.005,0.006) (0.005,0.006,0.007)
O3 (0.001,0.002,0.003) (0.002,0.002,0.003)
C1 (0.006,0.008,0.011) (0.007,0.009,0.012)
C2 (0.002,0.003,0.005) (0.002,0.003,0.005)
C3 (0.001,0.002,0.003) (0.001,0.001,0.002)
R1 (0.003,0.005,0.007) (0.002,0.004,0.006)
R2 (0.002,0.002,0.003) (0.002,0.003,0.003)
R3 (0.001,0.002,0.002) (0.001,0.001,0.002)
R4 (0.002,0.002,0.003) (0.001,0.002,0.003)
Table 13. Final ranking of the brand extension strategies
A0 A1
[[??].sub.i] (0.071,0.071,0.071) (0.036,0.052,0.068)
[MATHEMATICAL EXPRESSION 0.071 0.052198
NOT REPRODUCIBLE IN
ASCII]
[K.sub.i] 1 0.7373
Rank 4
A2 A3
[[??].sub.i] (0.041,0.057,0.073) (0.039,0.055,0.071)
[MATHEMATICAL EXPRESSION 0.0572 0.055163
NOT REPRODUCIBLE IN
ASCII]
[K.sub.i] 0.808 0.779
Rank 1 2
A4
[[??].sub.i] (0.038,0.054,0.070)
[MATHEMATICAL EXPRESSION 0.05408
NOT REPRODUCIBLE IN
ASCII]
[K.sub.i] 0.764
Rank 3
