A new hybrid model for evaluating the working strategies: case study of construction company.
Fouladgar, Mohammad Majid ; Yazdani-Chamzini, Abdolreza ; Zavadskas, Edmundas Kazimieras 等
1. Introduction
Companies require managing their organizational resources to be
equipped in facing with an ever-increasingly competitive and changeable
environment. The process of working strategy refers to the procedures
which can be used to develop working strategies in future. For this
reason, companies should determine the pattern of strategic decisions
and actions which set the role, objectives and activities of developing
in the future. Therefore, the appropriate working strategy plays a
significant role in increasing benefit, promoting the sustainability of
company, minimizing risk, improving credibility and as a result
achieving organizational goals and objectives. For achieving the aim,
various strategic alternatives should be evaluated to the best ones be
selected. This process is complex and challenging because various
qualitative and quantitative criteria may affect each other mutually
(Vahdani, Hadipour 2010).
The merit of using multicriteria decision making (MCDM) methods is
their ability to solve complex and sophisticated problems. The MCDM
methods provide powerful tools for determining the best alternative
among the feasible alternatives according to the evaluation criteria.
These methods are recommended as being helpful in reaching important
decisions that cannot be determined in a straightforward manner (Wu et
al. 2010).
The complexity of working systems makes it difficult to
comprehensively manage such system by the help of a single set of
guidelines. Application of a suitable decision process can help decision
makers to reduce decision failures. The analytic network process (ANP),
which is an extension of analytic hierarchy process (AHP), is a powerful
methodology that deals with dependence and feedback (Saaty 1996).
Despite the fact that many conventional MCDM methods are based on the
independence assumption, the ANP technique takes into account the
dependence assumption among individual criteria that is more adapted
with real world application.
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 more complex relationship among the decision
levels and attributes as it does not require a strict hierarchical
structure (Yazgan et al. 2010), and (4) ANP is more adapted with real
world problems.
However, taking into account the aspects of BOCR of an alternative,
including the positive and negative criteria all together, helps
decision makers to fulfill a more comprehensive way in real problems.
The ANP with BOCR has been successfully employed in many different
fields (Table 1).
It is clear that the ANP with BOCR has demonstrated its
capabilities and efficiencies as a practical management and decision
making tool.
Another popular method to solve MCDM problems is the COPRAS
(COmplex PRoportional Assessment) technique which was introduced by
Zavadskas and Kaklauskas (1996). This technique is employed by different
researchers in order to solve many various problems (Table 2), because
this method includes some advantages which are not limited to, as
follows: (1) COPRAS allows simultaneous consideration of the ratio to
the ideal solution and the ideal-worst solution, (2) simple and logical
computations, and (3) results are obtained in shorter time than other
methods such as AHP and ANP.
The MCDM methods are successfully applied to solve certain
problems. But, these techniques are less effective in conveying the
imprecision and fuzziness characteristics (Bashiri et al. 2011).
Zavadskas and Antucheviciene (2007) used first generation fuzzy COPRAS
(COPRAS-F) for multiple criteria evaluation of rural buildings
regeneration alternatives. Zavadskas et al. (2008) used COPRAS method
for selection of the effective dwelling house walls by applying
attributes values determined at intervals (COPRAS-G).
However, a large amount of uncertainty is connected with various
factors of working strategies, and consequently there is a need of fuzzy
theory to handle the existing uncertainty. Fuzzy set theory is a
powerful mathematical tool to solve problems in presence of uncertainty
that is normally found in strategy selection processes.
For this reason, a well designed decision process is needed to help
decision makers to reduce decision failures.
The main objective of the current study is to model the working
strategy decision-making problem as a MCDM problem and provide a
ten-step decision support framework to carefully evaluate working
strategies. For achieving the aim, the fuzzy ANP method is employed to
obtain the relative weights of BOCR criteria but not the entire
evaluation process to reduce the large number of pairwise comparison.
For this reason, fuzzy COPRAS is used to calculate the performance of
alternatives, and to prioritize the working strategies in terms of their
overall performance on evaluation main and sub-criteria.
The rest of this paper is organized as follows. Section 2 describes
fuzzy theory, including fuzzy logic, fuzzy number, and linguistic terms.
Section 3 goes over the key concepts of fuzzy analytic network process
(FANP). Section 4 describes the basics of the fuzzy COPRAS. The proposed
model is presented in Section 5. Section 6 provides a case study of
Fateh Construction Company to demonstrate the potential application of
the proposed model. In order to evaluate the stability of the results a
sensitivity analysis of BOCR factors is discussed in Section 7.
Discussions and conclusions are provided in the last section.
2. Fuzzy theory
Fuzzy theory first was developed by Zadeh (1965) to handle the
inherent uncertainty and imprecision associated with information
concerning different parameters. Fuzzy theory enables decision makers to
tackle the ambiguities involved in the process of the linguistic
assessment of the data (Onut et al. 2009).
A fuzzy set is defined by a membership function, which determines
to each element a grade of membership within the interval [0, 1]. If an
element x fully belongs to a set A, [[mu].sub.A](x) = 1, and if an
element x does not belong to the set under consideration,
[[mu].sub.A](x) = 0 . The higher is the membership value, the greater is
the belongingness of an element x to the set A.
A triangular fuzzy number (TFN) can be denoted as [??] = (l,m,u)
and its membership function [[mu].sub.A](x) can be defined as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (1)
where l, m, and u stand for the lower, middle, and upper value of
the support of [??] , respectively, and I [less than or equal to] m
[less than or equal to] u.
The fuzzy linguistic term is a fuzzy number or a variable whose
values are words or sentences in language terms. These terms can be
divided into miscellaneous linguistic criteria. We deliberately select a
9-point scale for defining the importance weights of the main criteria
(BOCR factors) and evaluation indicators which take part in the second
and third levels of hierarchical model, depicted in Fig. 4. Linguistic
terms for the weights of the BOCR factors and evaluation indicators are
depicted in Table 3. As seen in Table 3, the weights of the BOCR factors
and evaluation indicators are calculated by pairwise comparison matrices
that are formed by the expert team. As well, a 5-point scale for
defining the preference ratings of alternatives is deliberately adopted
as given in Table 4 and Fig. 1.
[FIGURE 1 OMITTED]
3. Fuzzy ANP
Analytic network process (ANP), one of the most comprehensive
frameworks of MCDM methods, is applied to identify the effects of the
evaluation criteria on each other, to determine their importance. The
ANP technique, introduced by Saaty in 1996, is a general form of
analytical hierarchy process (AHP). Saaty proposed the use of AHP to
solve the problem of independence among alternatives or criteria, and
the use of ANP to solve the problem of dependence among alternatives or
criteria (Yuksel, Dagdeviren 2010). AHP decomposes a complex decision
problem into several levels in a structure of hierarchy and then
calculates the weight of the factors with the pairwise comparison. This
model is formed based on the assumptions of unidirectional, hierarchical
relationship among decision levels (Erdogmus et al. 2005).
Many decision problems cannot be structured hierarchically because
they involve the interaction and dependence of higher-level elements in
a hierarchy on lower-level elements, therefore creation of a network of
elements is needed (Begicevic et al. 2010). The ANP method is capable to
take into account both interaction and feedback within clusters of
elements (inner dependence) and between clusters (outer dependence)
(Onut et al. 2011). The relative weights in a network are obtained
similar to the AHP using pairwise comparisons and judgments.
However, the pure ANP technique includes some drawbacks: the ANP
approach is mainly employed in decision making problems with precise and
accurate information; based on the ANP method, the human judgment in
order to obtain relative importance of elements has great influence on
the ANP results; and this method does not handle the inherent
uncertainty associated with the decision. To overcome these problems,
the combination of fuzzy theory with ANP to model the uncertainty,
difficulty, and complexity has been proposed
Since the introduction of FANP, it is effectively employed to solve
various decision-making problems, such as faulty behavior risk
(Dagdeviren et al. 2008); manufacturing (Yuksel, Dagdeviren 2010);
container port selection (Onut et al. 2011); quality function deployment
(Liu, Wang 2010); production strategy evaluation (Lee et al. 2010).
In the pair-wise comparison of elements, experts can use TFN to
express their preferences. Even though the discrete scale of 1-9 has the
advantages of simplicity and easiness for use, it does not take into
account the uncertainty associated with the mapping of one's
perception or judgment to a number (Onut et al. 2009). In this approach,
pair-wise comparison matrices are formed between the BOCR factors with
the help of TFNs. To achieve the aim, a scale of [??] - [??] can be
defined for TFNs instead of the scale of 1-9 as presented in Table 3.
In order to calculate the weights of BOCR factors, we adopted
Chang's extent analysis method (Chang 1996) because the steps of
this approach are relatively easier, less time taking and there are less
computational expense than the other fuzzy AHP (Van Laarhoven, Pedrycz
1983).
The steps of Chang's extent analysis methods are as follows:
Let X = {[x.sub.1],[x.sub.2], ..., [x.sub.n]} be an object set, and U =
{[u.sub.1],[u.sub.2], ...,[u.sub.m]} be a goal set. According to the
method of Chang's extent analysis, each object is taken and extent
analysis for each goal, [g.sub.i], is performed, respectively.
Therefore, m extent analysis values for each object can be obtained,
with the following signs:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
Where all the [M.sup.j.sub.gi] (j = 1, 2, ..., m) are TFNs.
The steps of Chang's extent analysis can be given as in the
following:
Step 1. The value of fuzzy synthetic extent with respect to ith
object is defined as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (2)
To obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],
perform the fuzzy addition operation of m extent analysis values for a
particular matrix such that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (3)
And to obtain [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.],
perform the fuzzy addition operation of [M.sup.j.sub.gi] (j - 1, 2, ...,
m) values such that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (4)
And then compute the inverse of the vector in Eq. (5) such that
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (5)
Step 2. The degree of possibility of [M.sub.2] -
([l.sub.2],[m.sub.2],[u.sub.2]) [greater than or equal to] [M.sub.1] =
([l.sub.1], [m.sub.1], [u.sub.1]) is defined as
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (6)
And can be equivalently expressed as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (7)
where d is the ordinate of highest intersection point D between
[[mu].sub.[M.sub.1]] and [[mu].sub.[M.sub.2]] (see Fig. 2).
To compare [M.sub.1] and [M.sub.2], we need both the values of
V([M.sub.1] [greater than or equal to] [M.sub.2]) and V([M.sub.2] >
[M.sub.1]).
[FIGURE 2 OMITTED]
Step 3. The degree of possibility for a convex fuzzy number to be
greater than k convex fuzzy numbers [M.sub.i]. (i = 1, 2, ... , k) can
be defined by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (8)
Assume that
d'([A.sub.i]) = min V ([S.sub.i] [greater than or equal to]
[S.sub.k]). (9)
For k = 1, 2, ... , n; k [not equal to] i. Then the weight vector
is given by
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (10)
where [A.sub.i] (i = 1, 2, ..., n) are n elements.
Step 4. Via normalization, the normalized weight vectors are
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (11)
where W is a non-fuzzy number.
4. Fuzy COPRAS technique
The COPRAS (COmplex PRoportional ASsessment) method (Zavadskas,
Kaklauskas 1996) assumes direct and proportional dependence of the
significance and utility degree of the investigated versions in a system
of criteria adequately describing the alternatives and of values and
weights of the criteria (Zavadskas et al. 2008; Kaklauskas et al. 2010).
This method is widely applied when a decision-maker has to select the
optimal alternative among a pool of alternatives by considering a set of
evaluation criteria.
In the classical COPRAS method, the weights of the criteria and the
ratings of alternatives are known precisely and crisp values are
employed in the evaluation process. However, under many conditions crisp
data are not capable to model real-life decision problems and it is
often difficult for evaluators to determine the precise ratings of
alternatives and the exact weights of the evaluation criteria. The merit
of using a fuzzy approach is to determine the relative importance of
attributes using fuzzy numbers instead of precise numbers (Sun 2010).
Therefore, the fuzzy COPRAS method is developed to deal with the
deficiency in the traditional COPRAS. Fuzzy COPRAS assigns the weights
of criteria and ratings of alternatives are evaluated by linguistic
terms represented by fuzzy numbers. The procedure of the Fuzzy COPRAS
method includes the following steps:
Step 1. Define the linguistic terms. Linguistic terms used by
decision maker team are presented in Table 4.
Step 2. Construct the fuzzy decision matrix. The preference ratings
of alternatives are expressed with linguistic variables in positive
TFNs.
Step 3. Determine the weights of criteria. In this paper, the
importance weights of main and sub-criteria are considered as linguistic
variables (as shown in Table 3). Due to the existence of dependence and
feedback relation between the BOCR factors, in this study, FANP is
employed to calculate the importance weights of main criteria.
Step 4. Determine the aggregated fuzzy rating [[??].sub.ij] of
alternative [A.sub.i], i = 1, 2, ..., m under criterion [C.sub.j], j =
1, 2, ..., n.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (12)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (13)
where [[??].subijk] is the rating of alternative [A.sub.i] with
respect to criterion [C.sub.j] evaluated by kth expert (here k = 9),
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.].
Step 5. Defuzzify the aggregated fuzzy decision matrix obtained in
previous step and derive their crisp values. This research for
transformation of the fuzzy weights into the crisp weights applies the
center of area method which is a simple and practical method to
calculate the best nonfuzzy performance (BNP) value of the fuzzy weights
of each dimension. The BNP value of the fuzzy number Xj can be found
using Eq. (14):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (14)
Step 6. Normalize the decision matrix ([f.sub.ij]). The
normalization of the decision making is calculated by dividing each
entry by the largest entry in each column to eliminate anomalies with
different measurement units, so that all the criteria are dimensionless.
Step 7. Calculate the weighted normalized decision matrix
([[??].sub.ij]). The fuzzy weighted normalized values are calculated by
multiplying the weight of evaluation indicators ([w.sub.j]) with
normalized decision matrices:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (15)
Step 8. Sums of attributes values which larger values are more
preferable (optimization direction is maximization) calculation for each
alternative (line of the decision-making matrix):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (16)
Step 9. Sums [R.sub.i] of attributes values which smaller values
are more preferable (optimization direction is minimization) calculation
for each alternative (line of the decision-making matrix):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (17)
In formula (17) (m - k) there is number of attributes which must be
minimized.
Step 10. Determine the minimal value of [R.sub.i]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (18)
Step 11. Calculate the relative weight of each alternative
[Q.sub.i]:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (19)
Formula (19) can to be written as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (20)
Step 12. Determine the optimality criterion K:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]. (21)
i
Step 13. Assign the priority of the alternatives. The greater
weight (relative weight of alternative) [Q.sub.i], the higher is the
priority (rank) of the alternatives. In the case of [Q.sub.max], the
satisfaction degree is the highest.
Step 14. Calculate the utility degree of each alternative:
[N.sub.i] = [Q.sub.i]/[Q.sub.max] 100%, (22)
where [Q.sub.i] and [Q.sub.max] are the weight of projects obtained
from Eq. (19). 5. The proposed model
The proposed model is defined in the following steps:
Step 1. Identify the evaluation indicators based on the BOCR
factors.
Step 2. Structure the ANP model hierarchically.
Step 3. Determine the local weights of the BOCR factors and
evaluation indicators by using pairwise comparison matrices (assume that
there is no dependence among the BOCR factors). The fuzzy scale
regarding relative importance to calculate the relative weights is
presented in Table 3. This scale will be utilized in Chang's fuzzy
AHP method.
Step 4. Determine, with fuzzy scale (Table 3), the inner dependence
matrix of each BOCR factor with respect to the other BOCR factors.
This inner dependence matrix is multiplied with the local weights
of the BOCR factors, determined in the previous step, to measure the
interdependent weights of the BOCR factors.
Step 5. Compute the global weights for the evaluation indicators.
The global weights of evaluation criteria are calculated by multiplying
local weight of the evaluation indicators with the interdependent
weights of the factors to which it belongs.
Step 6. Determine the performance ratings of feasible alternatives
by linguistic values (Table 4).
Step 7. Calculate the aggregated fuzzy performance ratings.
Step 8. Calculate the performance of working strategies by fuzzy
COPRAS based on the global weights obtained in Step 5 for the evaluation
indicators and the fuzzy performance ratings determined in previous
step.
Step 9. Rank the working strategies determined by fuzzy COPRAS
methodology.
Step 10. Select the most appropriate strategy according to the
final weights of alternatives.
Schematic diagram of the proposed model for selecting the optimal
working strategy is provided in Fig. 3.
[FIGURE 3 OMITTED]
6. The implementation of the proposed model
The purpose of the empirical application is to illustrate the use
of the proposed method. The experiment was setup upon a real world
decision problem. Fateh is a construction company in Iran that has been
funded in 2005. Fateh offers quality civil construction services in both
urban and remote locations. Fateh Company could improve its brand among
contractors and has a strong reputation for operational excellence. In
order to study different working sectors, a research project entitled
"Selecting the most appropriate working strategy" is defined.
For achieving the aim, the proposed model, which was fulfilled to Fateh
Company, is explained in the following steps.
Step 1. In the first step, a decision committee is established from
nine decision makers with at least 4 year-experience in strategy
management who were involved in decision making process. According to
semi-structured interviews with decision makers, a list of sixteen
strategy process criteria was generated. These sixteen indicators are
classified into four as benefit, opportunity, cost, and risk related
factors. The group names are accepted as the factors and the sub-factors
belonging to these groups are accepted as the evaluation indicators.
The evaluation indicators that are clustered as benefit,
opportunity, cost, and risk related are listed in the following part:
Benefit factor includes four elements;
--Profit (BP);
--Credit (BC);
--Flexibility (BF);
--Sustainability (BS);
--Extensibility (BE).
The alternative priorities resulted from benefit indicators
represent the intensity of positive contribution imparted by each
alternative to the overall decision goal. Therefore, a larger priority
value in these indicators corresponds to more benefit of an alternative.
Opportunity factor includes three elements;
--Financial facilities (OF);
--Previous knowledge (OP);
--Existing equipment (OE).
From opportunity indicators, the weights of alternatives represent
the level of positive impact each alternative has on the overall
decision objective. Therefore, for a particular alternative's
priority, the larger it is, the better.
Cost factor includes three elements;
--Initial capital value (CI);
--The existence of competition (CC);
--The need of the skilled labour force (CS);
--The need for new technology (CT).
Based on cost indicators, the weights of alternatives represent the
intensity of negative impact each alternative has on the overall
decision objective. Therefore, a smaller priority value in these
indicators corresponds to less cost of an alternative.
Risk factor includes three elements;
--Financial risk (RF);
--Risk of time delay (RR);
--Demand risk (RD);
--Operating risk (RO).
According to risk indicators, the intensity of negative impact each
alternative has on the overall decision objective are obtained based on
the weights of alternative. Therefore, for a particular
alternative's priority, the smaller it is, the better.
Step 2. The proposed model established by the BOCR factors,
evaluation indicators (determined in the previous step), and
alternatives are depicted in Fig. 4. FANP model consists of four levels.
In the first level of the model, there is the goal to "select the
most appropriate working strategy". The BOCR factors and the
sub-factors (evaluation indicators) related to them are located in
second and third levels respectively. The arrows in the second level
represent the inner-dependence among the BOCR factors. The BOCR
sub-factors in the third level include: five indicators for the benefit
factor, three indicators for the opportunity factor, four indicators for
the cost factor, and four indicators for the risk factor. Eight
alternative strategies proposed for this study are listed in the last
level of the model. As depicted in Fig. 4, these alternatives are as
follows:
--A1 should be defined as: Constructing a road is a process for
establishing a route or way on land between two places, which generally
has been flatted or improved to allow travel by motor vehicle.
--A2 should be defined as: Building a bridge in order to span
physical obstacles such as valley or road for the goal of providing
passage over the obstacle.
--A3 should be defined as: Construction is the process that builds
the building.
--A4 should be defined as: Damming is a process that impounds water
or underground streams.
--A5 should be defined as: The structures that create a platform
for people to work on in order to drill and extract gas or oil at sea.
--A6 should be defined as: A complex of structures and associated
facilities for generating electric energy from another source of energy,
such as nuclear energy, gas, and hydroelectric dam.
--A7 should be defined as: The petrochemical structures that
generate a large number of chemicals made from petroleum or natural gas
and the petroleum structures that produce a flammable liquid from the
complex mixture of hydrocarbons of various molecular weights and other
liquid organic compounds.
--A8 should be defined as: Tunneling is a process that generate an
artificial underground space in order to provide a capacity for
particular goals such as underground trans-portation, mine development,
and other activities. Step 3. Assuming that there is no dependence among
the BOCR factors, fuzzy pairwise comparison judgement of the BOCR
factors using scale presented in Table 3 is made with respect to the
goal. These fuzzy pairwise comparisons are established by the decision
maker team and the results are depicted in Table 5. For instance,
benefit factor (B) and cost factor (C) are compared by asking "How
important is 'B' when it is compared with 'C'?"
and the answer "EI, EI, IMI, MI, EI, IMI, EI" by nine decision
makers, to this linguistic scale is located in the relevant cell against
the aggregated fuzzy weights (1, 1.57, 4). The aggregated fuzzy weights
of the BOCR factors and evaluation indicators evaluated by nine experts
are calculated through the following relations.
[FIGURE 4 OMITTED]
The aggregated fuzzy pairwise comparison matrix [[??].sub.ij] x i,
j = 1, 2, ..., n. [[??].sub.ijk] is the weight of criterion C in
comparison with criterion C evaluated by k-th expert (here k = 9)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
All the fuzzy pairwise comparison matrices are generated in the
same way and the results are presented in Tables 6-9. The fuzzy pairwise
comparison matrices are evaluated by the Chang's extended analysis
method in order to determine the local weights.
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] (23)
In order to distinguish the matter, as sample the computations of
the local weights of the BOCR factors are presented in the following:
According to the FAHP method, firstly synthesis values must be
calculated. From (Table 6), synthesis values respect to main goal are
calculated like in Eq. (2):
[S.sub.B] = (0.028, 0.047, 0.08)[cross product] (5, 9.31, 16) =
(0.14, 0.439, 1.28),
[S.sub.O] = (0.028, 0.047, 0.08) [cross product] (1.75, 2.48, 3.5)
= (0.049, 0.11, 0.28),
[S.sub.C] = (0.028, 0.047, 0.08)[cross product] (3.25, 6.37, 10) =
(0.09, 0.3, 0.8),
[S.sub.R] = (0.028, 0.047, 0.08) [cross product] (2.45, 3.03, 6) =
(0.069, 0.143, 0.48).
These fuzzy values are compared by using Eq. (7) and these values
are obtained:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = 1,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = 0.89,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = 1,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.] = 0.712.
Then priority weights are calculated by using Eq. (9):
d'(B) = min(1, 1, 1) = 1,
d'(O) = min(0.303, 0.508, 0.89) = 0.303,
d'(C) = min(0.826, 1, 1) = 0.826,
d'(R) = min(0.535, 1, 0.712) = 0.535.
Priority weights form [w'.sub.BOCR] factors = (1, 0.303,
0.826, 0.535) vector. After the normalization of these values priority
weights respect to main goal are obtained as (0.375, 0.113, 0.31, 0.2).
Similar calculations were done for the other fuzzy pairwise comparison
matrices and the results of FAHP analyses were summarized in the last
column of Tables 5-9.
Step 4. In this step, the dependencies among the BOCR factors are
taken into account and interdependent weights of the BOCR factors are
computed. In order to determine the dependence among the BOCR factors,
the impact of each factor on every other factor using fuzzy pairwise
comparisons is evaluated. Based on fuzzy pairwise comparison matrices,
Tables 10-13 present the existing dependencies among the BOCR factors.
These matrices are formed by asking "What is the relative
importance of 'cost factor' when compared with 'risk
factor' on controlling 'benefit factor'?" and
answers were received from nine decision makers as "EI, IMI, MI,
EI, EI, MI, IMI" (1, 1.86, 4). The resulting relative importance
weights are located in the last column of Tables 8-11.
Using the calculated relative importance weights, the dependence
matrix of the BOCR factors is constructed. Interdependent weights of the
BOCR factors are calculated by multiplying the dependence matrix of the
BOCR factors with the local weights of the BOCR factors obtained in
previous step. The interdependent weights of the BOCR factors are
computed in the following part:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]
As shown above, the results are significantly different from when
the interdependent weights and dependencies are not taken into account.
The final results change from 0.375 to 0.304, 0.11 to 0.176, 0.31 to
0.297, and 0.20 to 0.223 for the priority values of factors B, O, C and
R, respectively.
Step 5. In this step, the overall weights of the evaluation
indicators are calculated by multiplying the interdependent weights of
BOCR factors found in previous step with the local weights of evaluation
indicators obtained in Step 3. The overall weights have indicated for
each indicator in Table 14 and Fig. 5.
Based on the overall weights listed in Table 14, the most and the
least important indicators which can affect the working strategy are
"Initial capital value" and "Extensibility",
respectively. As well as, under the benefit sub-factors, the most
important indicator, out of the five indicators, is "Profit",
with a weight of 0.086. This means that the major benefit concern for
the company in selecting the optimal working strategy is to have a high
profit of the activities. Furthermore, under the opportunity
sub-factors, "existing equipment" with a priority of 0.069 is
the most important indicator. This means that a working strategy which
can use existent equipment and facilities is in a high priority for the
company.
[FIGURE 5 OMITTED]
Besides, under the cost sub-factors, "initial capital
value" with a weight of 0.09 is the most significant indicator.
This implies that initial capital is more important than other
evaluation indicators in order to select the most appropriate working
strategy. Finally, under the risk sub-factors, "financial
risk" with a value of 0.073 causes the problem that the company
worries about. This implies that the company is more concerned about any
risk associated with any form of financing.
Step 6. In this step, the fuzzy performance results from various
alternatives under different criteria that are collected from each
expert individually in order to limit the number of pairwise
comparisons. For the evaluation indicators under benefit and opportunity
factors (BP, BC, BF, BS, BE, OF, OP, and OE), the higher the score, the
better the performance of the working strategy is. Whereas, for the
indicators under cost and risk factors (CI, CC, CS, CT, RF, RR, RD, and
RO), the higher the score, the worse the performance of the working
strategy is.
For this reason, experts were asked to form fuzzy decision matrix
by linguistic variables presented in Table 4. It is constructed by
comparing eight alternatives under sixteen evaluation indicators
separately. For example, the fuzzy decision matrix filled by one of the
decision makers is presented in Table 15.
Step 7. In this step, the aggregated fuzzy performance ratings of
working strategies with respect to each criterion are computed by Eq.
(13) and the results are presented in Table 16.
Step 8. In this step, the aggregated fuzzy performance ratings are
defuzzified by Eq. (14) to derive their crisp values. In order to
normalize the current decision matrix, the performance ratings are
transferred into a number between zero to one by dividing the
performance rating of a working strategy on a criterion by the largest
performance rating among all working strategies on the same criterion.
Then, the weighted normalized decision matrix can be calculated by
multiplying the importance weights of evaluation indicators and the
values in the normalized decision matrix as shown in Table 17. According
to the fuzzy COPRAS technique, the maximizing and minimizing indexes for
each alternative are calculated by using Eqs. (16) and (17), as
presented in Table 18. In the last phase of this step, the relative
weight and the utility degree of each alternative are calculated as
presented in Table 18.
Step 9. In this step, the working strategies are ranked as shown in
Table 18 and Fig. 6. According to N values, the ranking of the
alternatives in descending order are A6, A3, A7, A1, A5, A2, A8, and A4.
Step 10. In the last step, according to the final weights of
alternatives, the optimum working strategy is selected. As seen in Table
18, power plant structures (A6) is first in the list of priorities,
while damming (A4) is the fourth.
[FIGURE 6 OMITTED]
7. Sensitivity analysis
Sensitivity analysis is a powerful tool for evaluating the proposed
model in order to calculate the stability of the results by changing the
priorities of the BOCR factors and reflect the strength of the
constructed model. In this paper, the priorities for BOCR factors are
changed one at a time to perform sensitivity analysis, and the changing
range is from 0 to 1. Figs. 7, 8, 9, and 10 depict the sensitivity
analysis graph when the priority of benefits, opportunities, costs and
risks changes, respectively.
For example, the original priority of benefit (B) is 0.304, and a
trial and error method is employed to calculate how the priorities of
alternatives are correlated with changes in B values. As shown in Fig.
7, while the weight of the benefits increases; the share of A7
increases, whereas the share of A6 decreases. The analysis of the
benefit factor shows that A4, A7, A2, and A5 have positive features,
whereas A8, A1 and A6 have negative features. As weight of the benefit
increases, the benefit related with the profit positively affects the
share of A4, A7, A2, and A5. It can be also seen that the results are
very sensitive to the changes in the weight of the benefit, and the rank
of the alternatives changes from "[MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII.]" (for % benefit weight) to
"[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII.]" (for
100% benefit weight).
[FIGURE 7 OMITTED]
[FIGURE 8 OMITTED]
[FIGURE 9 OMITTED]
[FIGURE 10 OMITTED]
Moreover, when O increases to 1, the optimum working strategy
changes from A6 to A1 (as depicted in Fig. 8). In other words, the best
alternative becomes A1 when O increases to 1. When C increases to 1, the
optimum working strategy changes from A3 to A6 (as seen in Fig. 9). As
presented in Fig. 10, the optimum working strategy changes from A6 to
A3, while R increases from 0 to 1.
8. Conclusion
The working strategy selection problem is an important issue and
has significant impacts to the continuity of a company. Decision makers
to simultaneously pursue increased incomes and decreased costs should
select the best working strategy among a pool of feasible working
strategies. To achieve the aim, different types of alternatives are
evaluated with the consideration of the benefit, opportunity, cost and
risk (BOCR) factors. This leads to inter-relationship among factors and
a large set of vague and imprecise data. For this reason, developing an
efficient evaluation technique in order to improve decision quality is
necessary.
In this study, an integrated framework to evaluate working
strategies is proposed, which uses linguistic terms to take into
consideration the subjective judgments of experts and then it adopts
FANP and fuzzy COPRAS to evaluate the decision making problem. The
priorities of BOCR factors are obtained by FANP based on pairwise
comparison matrix so that the inter-relationship among factors and the
linguistic uncertainty of evaluators can be incorporated in the
computation. In order to determine the priorities of the alternatives,
fuzzy COPRAS is employed. Fuzzy COPRAS eliminates many procedures to be
performed only in FANP methodology and enables decision maker to reach a
conclusion in a shorter time. Then the proposed model is tested by a
real case study of working strategy selection in an Iranian construction
company. Through the implementation of the model, the authorities and
decision makers can understand the merits of different working
strategies and the reasons behind why a working strategy should be
selected. A sensitivity analysis is also carried out to measure the
stability of the results. The results of sensitivity analysis show that
the preferences of alternatives vary from the original when the values
of benefit, opportunity, cost or risk are changed. Although the model
was proposed for the use in working strategy selection problem, it can
also be used in other multi-criteria decision making problems in
strategic management.
doi: 10.3846/20294913.2012.667270
Received 04 July 2011; accepted 15 November 2011
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Mohammad Majid Fouladgar (1), Abdolreza Yazdani-Chamzini (2),
Edmundas Kazimieras Zavadskas (3), S. Hamzeh Haji Moini (4)
(1,2,4) Fateh Research Group, Department of Strategic Management,
Milad Building, Mini city, Aghdasieh, Tehran, Iran (3) Faculty of Civil
Engineering, Vilnius Gediminas Technical University, Sauletekio al. 11,
LT-10223 Vilnius, Lithuania E-mails:
[email protected]; (2)
[email protected]; (3)
[email protected] (corresponding
author); (4)
[email protected]
Mohammad Majid FOULADGAR. Master of Science in the Department of
Strategic Management, Manager of Fateh Reaserch Group, Tehran-Iran.
Author of 10 research papers. In 2007 he graduated from the Science and
Engineering Faculty at Tarbiat Modares University, Tehran-Iran. His
interests include decision support system, water resource, and
forecasting.
Abdolreza YAZDANI-CHAMZINI. Master of Science in the Department of
Strategic Management, research assistant of Fateh Reaserch Group,
Tehran-Iran. Author of more than 20 research papers. In 2011 he
graduated from the Science and Engineering Faculty at Tarbiat Modares
University, Tehran-Iran. His research interests include decision making,
forecasting, modeling, and optimization.
Edmundas Kazimieras ZAVADSKAS. Prof., Head of the Department of
Construction Technology and Management at Vilnius Gediminas Technical
University, Vilnius, Lithuania. He has a PhD in Building Structures
(1973) and Dr Sc. (1987) in Building Technology and Management. He is a
member of the Lithuanian and several foreign Academies of Sciences. He
is Doctore Honoris Causa at Poznan, Saint-Petersburg, and Kiev
universities as well as a member of international organisations; he has
been a member of steering and programme committees at many international
conferences. E. K. Zavadskas is a member of editorial boards of several
research journals. He is the author and co-author of more than 400
papers and a number of monographs in Lithuanian, English, German and
Russian. Research interests are: building technology and management,
decision-making theory, automation in design and decision support
systems.
S. Hamzeh HAJI MOINI. Master of Science of Project Management,
research assistant of Fateh Reaserch Group, Tehran-Iran. He is the
author of 5 research papers. His interests include decision support
system, portfolio selection, and artificial intelligence.
Table 1. Recent application of ANP with BOCR
Reference Considered problem
Begicevic et al. 2010 Prioritization of projects
Chen et al. 2010 Strategic selection of management systems
Yazgan et al. 2010 Balanced scorecard
Lee et al. 2010 Model for production strategy
Lee et al. 2011 Model for power industry
Bottero et al. 2011 Wastewater treatment systems
Bobylev 2011 Environmental impact of construction
technologies
Table 2. Recent application of COPRAS
Reference Method Considered problem
Kaklauskas et al. 2010 COPRAS Complex analysis of
intelligent built
environment
Tupenaite et al. 2010 COPRAS Assessment of alternatives
for renovation
Zolfani Hashemkhani et al. 2011 COPRAS-G Forest roads locating
Antucheviciene et al. 2011 COPRAS-F Comparative analysis
fuzzy VIKOR, fuzzy TOPSIS
and COPRAS-F methods
Chatterjee et al. 2011 COPRAS Materials selection
Chatterjee and Chakraborty 2011 COPRAS-G Materials selection
Kildiene et al. 2011 COPRAS Analysis of construction
sector in the time of
crisis
Maniya and Bhatt 2011 COPRAS Selection of flexible
manufacturing systems
Medineckiene and Bjork 2011 COPRAS Preferences regarding
renovation measures
Yazdani et al. 2011 COPRAS-F Risk analysis of critical
infrastructures
Table 3. Linguistic terms for the importance weights of the criteria
Linguistic term Fuzzy Triangular Triangular fuzzy
number fuzzy scale reciprocal scale
Equal importance (EI) 1 (1, 1, 1) (1, 1, 1)
Intermediate (IMI) 2 (1, 2, 3) (1/3, 1/2, 1)
Moderate importance (MI) 3 (2, 3, 4) (1/4, 1/3, 1/2)
Intermediate (ISI) 4 (3, 4, 5) (1/5, 1/4, 1/3)
Strong importance (SI) 5 (4, 5, 6) (1/6, 1/5, 1/4)
Intermediate (IVSI) 6 (5, 6, 7) (1/7, 1/6, 1/5)
Very strong importance (VSI) 7 (6, 7, 8) (1/8, 1/7, 1/6)
Intermediate (IEXI) 8 (7, 8, 9) (1/9, 1/8, 1/7)
Extreme importance (EXI) 9 (8, 9, 10) (1/10, 1/9, 1/8)
Table 4. Linguistic terms for the preference rating of alternatives
Linguistic term Corresponding triangular fuzzy number
Very poor (VP) (0, 1, 3)
Poor (P) (1, 3, 5)
Fair (F) (3, 5, 7)
Good (G) (5, 7, 9)
Very good (VG) (7, 9, 10)
Table 5. Local weights of BOCR factors
BOCR
factors B O C
B (1, 1, 1) (2, 4.32, 6) (1, 1.57, 4)
O (1/6, 0.23, 0.5) (1, 1, 1) (1/4, 0.39, 1)
C (1/4, 0.64, 1) (1, 2.56, 4) (1, 1, 1)
R (1/5, 0.41, 1) (1, 1.16, 3) (1/4, 0.46, 1)
BOCR
factors R Local weight
B (1, 2.42, 5) 0.375
O (1/3, 0.86, 1) 0.115
C (1, 2.17, 4) 0.31
R (1, 1, 1) 0.2
Table 6. Local weights of benefit sub-factors
Benefit
subfactors BP BC BF
BP (1, 1, 1) (1, 1.72, 5) (2, 3.12, 5)
BC (1/5, 0.58, 1) (1, 1, 1) (1/3, 1.79, 4)
BF (1/5, 0.32, 1/2) (1/4, 0.59, 3) (1, 1, 1)
BS (1/4, 0.46, 1) (1/3, 0.74, 3) (1/3, 1.04, 3)
BE (1/6, 0.31, 1/3) (1/4, 0.47, 1) (1/4, 0.72, 1)
Benefit
subfactors BS BE Local weights
BP (1, 2.16, 4) (3, 3.21, 6) 0.283
BC (1/3, 1.34, 3) (1, 2.12, 4) 0.227
BF (1/3, 0.96, 3) (1, 1.39, 4) 0.194
BS (1, 1, 1) (1, 2.17, 5) 0.213
BE (1/5, 0.46, 1) (1, 1, 1) 0.081
Table 7. Local weights of opportunity sub-factors
Oppor-
tunity
sub- Local
factors OF OP OE weights
OF (1, 1, 1) (1/3, 0.87, 3) (1/5, 0.32, 1) 0.282
OP (1/6, 0.23, 0.5) (1, 1, 1) (1/4, 0.67, 3) 0.323
OE (1/4, 0.59, 1) (1, 2.56, 4) (1, 1, 1) 0.395
Table 8. Local weights of cost sub-factors
Cost
sub-factors CI CC CS
CI (1, 1, 1) (2, 3.42, 6) (1, 1.89, 4)
CC (1/6, 0.23, 0.5) (1, 1, 1) (1/3, 0.96, 3)
CS (1/4, 0.59, 1) (1, 2.56, 4) (1, 1, 1)
CT (1/5, 0.41, 1) (1, 1.16, 3) (1/4, 0.46, 1)
Cost
sub-factors CT Local weight
CI (1/3, 1.23, 3) 0.304
CC (1/5, 0.43, 1) 0.188
CS (1/4, 0.64, 3) 0.226
CT (1, 1, 1) 0.28
Table 9. Local weights of risk sub-factors
Risk
sub-factors RF RR RD
RF (1, 1, 1) (1, 1.87, 4) (2, 3.12, 5)
RR (1/6, 0.23, 0.5) (1, 1, 1) (1, 1.61, 4)
RD (1/4, 0.59, 1) (1, 2.56, 4) (1, 1, 1)
RO (1/5, 0.41, 1) (1, 1.16, 3) (1/4, 0.46, 1)
Risk
sub-factors RO Local weight
RF (1, 2.34, 4) 0.329
RR (1/3, 1.32, 3) 0.252
RD (1/4, 0.86, 3) 0.181
RO (1, 1, 1) 0.236
Table 10. The inner dependence matrix of the factors with
respect to "Benefit factor"
Relative
Benefit importance
factor O C R weights
O (1, 1, 1) (0.25, 0.38, 1) (0.33, 0.58, 1) 0.204
C (1, 2.63, 4) (1, 1, 1) (1, 1.86, 4) 0.461
R (1, 1.72, 3) (0.25, 0.52, 1) (1, 1, 1) 0.335
Table 11. The inner dependence matrix of the factors with
respect to "Opportunity factor"
Relative
Oppor- impor-
tunity tance
factor B C R weights
B (1, 1, 1) (0.33, 1.21, 3) (1, 1.34, 3) 0.365
C (0.33, 0.82, 3) (1, 1, 1) (0.33, 1.17, 4) 0.330
R (0.33, 0.74, 1) (0.25, 0.85, 3) (1, 1, 1) 0.305
Table 12. The inner dependence matrix of the factors with respect
to "Cost factor"
Relative
impor-
Cost tance
factor B O R weights
B (1, 1, 1) (1, 1.46, 4) (1, 2.17, 4) 0.430
O (0.25, 0.68, 1) (1, 1, 1) (0.33, 1.23, 3) 0.295
R (0.25, 0.46, 1) (0.33, 0.81, 3) (1, 1, 1) 0.275
Table 13. The inner dependence matrix of the factors with respect
to "Risk factor"
Relative
impor
Risk tance-
factor B O C weights
B (1, 1, 1) (0.25, 0.67, 3) (0.25, 0.46, 1) 0.288
O (0.33, 1.49, 4) (1, 1, 1) (0.33, 0.89, 3) 0.344
C (1, 2.17, 4) (0.33, 1.12, 3) (1, 1, 1) 0.368
Table 14. Overall weight of the evaluation indicators
Weight
of the Local Global
BOCR factors factors Evaluation indicators weights weights
Benefit(B) 0.304 Profit (BP) 0.283 0.086
Credit (BC) 0.227 0.069
Flexibility (BF) 0.194 0.059
Sustainability (BS) 0.213 0.065
Extensibility (BE) 0.081 0.025
Opportunity 0.176 Financial facilities (OF) 0.282 0.050
(O) Previous knowledge (OP) 0.323 0.057
Existing equipment (OE) 0.395 0.069
Cost (C) 0.297 Initial capital value (CI) 0.304 0.090
The existence of
competition (CC) 0.188 0.056
The need of the skilled
labour force (CS) 0.226 0.067
The need for new
technology (CT) 0.28 0.083
Risk (R) 0.223 Financial risk (RF) 0.329 0.073
Risk of time delay (RR) 0.252 0.056
Demand risk (RD) 0.181 0.040
Operating risk (RO) 0.236 0.053
Table 15. A sample of fuzzy evaluation matrix evaluated by one
of the experts
A1 A2 A3 A4 A5 A6 A7 A8
BP VG G VG F VG G VG G
BC F G P VG VG VG VG G
BF P VG G VG G P VG VP
BS F VG VG VG G F VG G
BE G G VG VG VG F G P
OF VG P VG VG F G F F
OP P G P VP P P P G
OE VG F P VP VP P VP G
CI G G P F P VP P G
CC G G VG VP VP VP VP P
CS P G F VG G VG VG G
CT P F VG G VG VG VG G
RF F F VP G F P VP VG
RR VG G P VG G F G F
RD P P VP G VG VG VG F
RO VG G P G P P P G
Table 16. The aggregated fuzzy evaluation matrix
A1 A2 A3 A4
BP (5, 8.32, 10) (3, 6.61, 10) (3, 6.82, 10) (1, 4.36, 7)
BC (1, 5.21, 9) (5, 7.34, 10) (0, 2.78, 7) (5, 8.16, 10)
BF (1, 4.23, 7) (3, 7.12, 10) (3, 6.81, 10) (5, 7.23, 10)
BS (1, 5.16, 7) (3, 7.41, 10) (5, 8.09, 10) (3, 7.31, 10)
BE (5, 7.89, 10) (3, 6.92, 10) (3, 6.96, 10) (5, 7.87, 10)
OF (5, 7.34, 10) (1, 3.43, 7) (5, 7.21, 10) (5, 8.12, 10)
OP (0, 3.21, 7) (3, 5.34, 9) (0, 3.23, 7) (0, 2.12, 5)
OE (5, 8.42, 10) (1, 4.78, 9) (0, 2.34, 5) (0, 1.67, 5)
CI (3, 7.23, 10) (5, 7.46, 10) (1, 4.57, 7) (1, 4.87, 9)
CC (3, 5.23, 9) (3, 6.42, 10) (5, 7.56, 10) (0, 2.36, 5)
CS (1, 4.46, 7) (3, 6.54, 9) (1, 3.21, 7) (5, 7.46, 10)
CT (0, 3.21, 7) (1, 4.67, 7) (5, 8.24, 10) (3, 6.72, 10)
RF (1, 4.32, 7) (3, 5.54, 9) (0, 1.63, 5) (3, 5.67, 9)
A1 A2 A3 A4
RR (3, 6.57, 10) (3, 5.27, 9) (0, 2.56, 7) (5, 7.76, 10)
RD (1, 4.23, 9) (0, 1.67, 5) (0, 2.16, 5) (3, 6.44, 9)
RO (5, 7.89, 10) (3, 5.96, 9) (0, 3.34, 9) (3, 5.57, 9)
A5 A6 A7 A8
BP (5, 7.72, 10) (3, 7.12, 10) (5, 7.92, 10) (3, 6.54, 10)
BC (3, 7.23, 10) (5, 8.23, 10) (3, 7.89, 10) (3, 6.72, 10)
BF (3, 6.85, 10) (1, 4.46, 7) (3, 6.65, 10) (0, 2.21, 5)
BS (3, 6.52, 10) (3, 5.68, 9) (3, 8.12, 10) (3, 6.77, 9)
BE (5, 8.34, 10) (1, 3.83, 7) (3, 7.21, 10) (0, 2.64, 5)
OF (1, 4.34, 7) (3, 7.26, 10) (1, 5.32, 9) (1, 4.67, 7)
OP (0, 3.16, 7) (1, 4.34, 7) (0, 3.46, 7) (3, 7.34, 10)
OE (0, 2.16, 7) (1, 4.46, 9) (0, 1.87, 5) (3, 6.67, 10)
CI (1, 4.67, 7) (0, 2.31, 5) (0, 3.16, 7) (3, 6.43, 10)
CC (0, 2.14, 7) (0, 1.67, 5) (0, 1.89, 5) (0, 3.23, 7)
CS (3, 6.78, 9) (3, 7.34, 10) (5, 7.78, 10) (3, 5.47, 9)
CT (5, 8.24, 10) (5, 7.54, 10) (3, 7.67, 10) (3, 6.31, 9)
RF (1, 4.56, 9) (0, 1.89, 5) (0, 2.12, 7) (5, 7.62, 10)
A5 A6 A7 A8
RR (3 ,6.12, 10) (3, 5.43, 9) (3, 7.42, 10) (1, 4.57, 9)
RD (3, 6.87, 10) (5, 7.57, 10) (5, 8.21, 10) (1, 4.23, 7)
RO (0,1.84, 5) (0, 2.12, 5) (1, 3.67, 7) (3, 6.17, 9)
Table 17. The weighted normalized decision matrix of eight
working strategies
A1 A2 A3 A4 A5 A6 A7 A8
BP 0.086 0.072 0.073 0.046 0.084 0.074 0.085 0.072
BC 0.045 0.066 0.029 0.069 0.060 0.069 0.062 0.059
BF 0.032 0.053 0.053 0.059 0.053 0.033 0.052 0.019
BS 0.037 0.057 0.065 0.057 0.055 0.050 0.059 0.053
BE 0.025 0.021 0.021 0.024 0.025 0.013 0.022 0.008
OF 0.048 0.025 0.048 0.050 0.027 0.044 0.033 0.027
OP 0.029 0.049 0.029 0.020 0.028 0.035 0.029 0.057
OE 0.069 0.044 0.022 0.020 0.027 0.043 0.020 0.058
CI 0.081 0.090 0.050 0.060 0.051 0.029 0.041 0.078
CC 0.043 0.048 0.056 0.018 0.023 0.017 0.017 0.025
CS 0.037 0.055 0.033 0.066 0.055 0.060 0.067 0.051
CT 0.036 0.045 0.083 0.070 0.083 0.081 0.074 0.065
RF 0.040 0.057 0.021 0.057 0.047 0.022 0.029 0.073
RR 0.048 0.042 0.024 0.056 0.047 0.043 0.050 0.036
RD 0.025 0.011 0.012 0.032 0.034 0.039 0.040 0.021
RO 0.053 0.042 0.029 0.041 0.016 0.016 0.027 0.042
Table 18. Fuzzy COPRAS results
A1 A2 A3 A4 A5
[P.sub.i] 0.371 0.388 0.339 0.345 0.359
[R.sub.i] 0.362 0.390 0.308 0.400 0.356
[Q.sub.i] 0.721 0.712 0.750 0.661 0.715
N 93.263 92.190 97.116 85.599 92.484
Rank 4 6 2 8 5
A6 A7 A8
[P.sub.i] 0.360 0.363 0.353
[R.sub.i] 0.307 0.345 0.392
[Q.sub.i] 0.773 0.729 0.676
N 100.000 94.380 87.515
Rank 1 3 7
