An integrated model for prioritizing strategies of the Iranian mining sector/Irano kasybos sektoriaus strategiju prioriteto nustatymo integruotas modelis.
Fouladgar, Mohammad Majid ; Yazdani-Chamzini, Abdolreza ; Zavadskas, Edmundas Kazimieras 等
1. Introduction
Organizations today deal with unprecedented challenges and
opportunities in carrying out their vital mission. Managers always look
for comprehensive picture of present situation of the organization and a
clear understanding of its future. For this reason, they need background
information of SWOT situation in order to investigate the challenges and
prospects of adopting their organization. SWOT analysis is an effective
framework that helps to address the effectiveness of a project planning
and implementation (Taleai et al. 2009; Podvezko 2009; Podvezko et al.
2010; Diskiene et al. 2008). It is used in different sectors such as
transportation industry (Kandakoglu et al. 2009; Kheirkhah et al. 2009,
Ghazinoory, Kheirkhah 2008; Maskeliunaite et al. 2009), technology
development (Ghazinoory et al. 2009, 2011), device design (Wu et al.
2009), food microbiology (Ferrer et al. 2009), Hazard Analysis Critical
Control Point (Sarter et al. 2010), Environmental Impact Assessment
(Paliwal 2006; Medineckiene et al. 2010), tourism management (Kajanus et
al. 2004). This paper employed the SWOT analysis to identify the
feasible strategies.
The evaluation of strategies performance has a critical importance
to managers and decision makers. Many methods and techniques can be
employed in order to evaluate the strategies. Balanced Scorecard (BSC)
can be a good solution because it is a performance measurement framework
that provides an integrated look at the business performance of a
company by a set of both financial and non-financial measures (Lee et
al. 2008). This technique has attracted considerable interest in recent
years that it is due to its unique merits. Success stories of companies
that have implemented BSC seem to confirm its high benefits (Speckbacher
et al. 2003). It is a proper tool for evaluating of operational
strategies in mining sector. This paper employed this technique to
determine the evaluation criteria.
However, conventional BSC does not consolidate theses evaluations,
and an incorporation of BSC and multi criteria decision making methods,
such as analytical hierarchy process (AHP) and Technique for Order
Preference by Similarity to Ideal Solution (TOPSIS), is an improvement.
In constructing a model, the main aim maximizes its usefulness that
closely connected with the relationship among three key characteristics
of every systems model: complexity, credibility, and uncertainly (Klir,
Yuan 1995). Modeling the uncertainty is very valuable so that it cause
to reduce complexity and increase credibility of the resulting model.
Fuzzy logic is able to model the uncertainty. Fuzzy multi criteria
decision making approach such as Fuzzy Technique for Order Preference by
Similarity to Ideal Solution (FTOPSIS) is a useful tool because of
different advantages, including logical concepts, simple and fast
computations, and tolerating the uncertainty.
According to, Iran is one of the most important mineral producers
in the world, ranked among 15 major mineral rich countries, holding some
68 types of minerals, 37 billion tons of proven reserves and more than
57 billion tons of potential reservoirs. These include coal, iron ore,
copper, lead, zinc, chromium, barite, salt, gypsum, molybdenum,
strontium, silica, uranium, and gold. The mines at Sar Cheshmeh in
Kerman Province contain the world's second largest reserve of
copper ore (5% of the world's total). According to Iran's
fifth development plan, Iranian mining strategies should be determined
and prioritized in order to generate value-added in the mining sector,
adding the target will be achieved by preventing imports and modernizing
technologies. We used an organized methodology for ranking the
strategies of Iranian mining sector because of more precise, accurate,
and sure results.
For achieving the aim, the SWOT analysis determines the feasible
strategies. Then, the BSC technique defines main and sub-criteria.
Finally, FTOPSIS is used to prioritize the strategies of Iranian mining
sector to obtain the final ranking order. The importance weights of BSC
evaluation indicators are calculated via FAHP.
The remainder of this paper is organized as follows. Fuzzy set
theory is explained in the next section. Then in section 3, fuzzy AHP
method is introduced. In section 4, fuzzy TOPSIS method is explained and
the steps of the method are summarized. SWOT analysis and its
application for strategies development is presented in section 5. In
section 6, Balanced Scorecard is discussed. Case study is explained in
section 7. In section 8, a numerical example is given to illustrate the
proposed method and the results that are gained with these methods are
presented. And finally section concludes the paper.
2. Fuzzy set theory
Fuzzy set theory was introduced by Zadeh (1965) in order to deal
with vagueness of human thought. A fuzzy set is a category of objects
with a continuum of grades of membership. The latter is recognized by a
membership function. Membership function is a grade of membership
ranging between zero and one. A fuzzy set is a generalization of a crisp
set. Crisp sets only take full membership (number 1) or non-membership
(number 0) at all, whereas fuzzy sets take partial membership (Ertugrul,
Karakasoglu 2008). Fuzzy sets and fuzzy logic are powerful mathematical
tools in order to model uncertain in decision-making.
Uncertainty is resulted from two areas: (1) uncertainty in
subjective judgments (2) uncertainty due to lack of data or incomplete
information. The former is due to experts may not be 100% sure when
making subjective judgments. The later is caused by sometimes
information of some attributes may not be fully available or even not
available at all.
Fuzzy sets are appropriate in the absence of vague and imprecise
information. These sets are able to describe complex phenomena when
traditional mathematical methods cannot analyze them. As well as, these
sets can find a good approximate solution (Bojadziev, Bojadziev 1998).
There are miscellaneous types of fuzzy membership functions that
triangular fuzzy number (TFN) is one of them (see Fig. 1).
A TFN is shown as [??] = ([a.sub.1], [a.sub.2], [a.sub.3]), where
[a.sub.1]<[a.sub.2]<[a.sub.3] and [a.sub.1], [a.sub.2], [a.sub.3]
are crisp numbers. The membership function of a number such as [??] is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (1)
Let [??] = ([a.sub.1],[a.sub.2],[a.sub.3]), [??] =
([b.sub.1],[b.sub.2],[b.sub.3]) be two fuzzy numbers, so their
mathematical relations expressed as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (2)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (3)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]; (4)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5)
[FIGURE 1 OMITTED]
The distance between two TFNs [??] = ([a.sub.1], [a.sub.2],
[a.sub.3]), [??] = ([b.sub.1], [b.sub.2], [b.sub.3]) can be defined by
the Euclidean distance (Chen 2000):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (6)
3. Fuzzy analytical hierarchy process (FAHP)
Analytical hierarchy process (AHP) was introduced by Saaty (,980)
that is a mathematical technique for multi-criteria decision making.
This technique is based on pair-wise comparison matrix. The AHP method
is based on three principles (Dagdeviren et al. 2009): first, structure
of the model; second, comparative judgment of the alternatives and the
criteria; third, synthesis of the priorities.
AHP method is combined with fuzzy methodology by miscellaneous
methodologies (Buckley 1985; Cheng ,997; Chang 1996).
In this study the extent FAHP is utilized, which was originally
introduced by Chang (1996). 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, gi, is
performed, respectively. Therefore, m extent analysis values for each
object can be obtained, with the following signs: [M.sup.1.sub.gi],
[M.sup.2.sub.gi], [M.sup.m.sub.gi], i = 1, 2, ..., n. 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:
[S.sub.i] = [m.summation over (j=1)][M.sup.j.sub.gi] [coss product]
[[[n.summation over (i=1)][m.summation over (j=1)]
][M.sup.j.sub.gi]].sup.-1]. (7)
To obtain [[summation].sup.m.sub.j=1][M.sup.j.sub.gi], perform the
fuzzy addition operation of m extent analysis values for a particular
matrix such that
[m.summation over (j=1)][M.sup.j.sub.gi] = ([m.summation over
(j=1)][l.sub.i], [m.summation over (j=1)] [m.sub.i], [m.summation over
(j=1)][u.sub.i]). (8)
And to obtain [[[[summation].sup.n.sub.i=1][[summation].sup.m.sub.j=1] [M.sup.j.sub.gi]].sup.-1], perform the fuzzy addition operation of
[M.sup.j.sub.gi] (j = 1, 2, ..., m) values such that
[n.summation over (i=1)][m.summation over (j=1)][M.sup.j.sub.gi] =
([n.summation over (i=1)][l.sub.i], [n.summation over (i=1)] [m.sub.i],
[n.summation over (i=1)][u.sub.i]). (9)
And then compute the inverse of the vector in Eq. (10) such that
[[[n.summation over (n=1)][m.summation over
(j=1)][M.sup.j.sub.gi]].sup.-1] =
(1/[[summation].sup.n.sub.i=1][u.sub.i],
1/[[summation].sup.n.sub.i=1][m.sub.i],
1/[[summation].sup.n.sub.i=1][l.sub.i]). (10)
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]. (11)
And can be equivalently expressed as follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (12)
Where d is the ordinate of highest intersection point D between
[[mu].sub.M1] and [[mu].sub.M2] (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]
[greater than or equal to] [M.sub.1]).
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]. (13)
Assume that
d'([A.sub.i]) = min V ([S.sub.i] [greater than or equal to]
[S.sub.k]). (14)
For k = 1, 2, ..., n; k [not equal to] i. Then the weight vector is
given by
W' = (d'([A.sub.1]), d'([A.sub.2]), ...,
d'([A.sub.n])).sup.T], (15)
where [A.sub.i](i = 1, 2, ..., n) are n elements.
[FIGURE 2 OMITTED]
Step 4: Via normalization, the normalized weight vectors are
W = [(d([A.sub.1]), d([A.sub.2]), ..., d([A.sub.n])).sup.T], (16)
where W is a non-fuzzy number.
4. Fuzzy TOPSIS (FTOPSIS)
TOPSIS approach was developed by Hwang and Yoon (1981). This
approach is used when the user prefers a simpler weighting approach.
TOPSIS technique is based on the concepts that the chosen alternative
should have the shortest distance from the ideal solution, and the
farthest from the negative ideal solution. The usual TOPSIS approach has
been applied for ranking construction and development alternative
solutions since 1986 (Zavadskas 1986; Kalibatas et al. 2011; Tupenaite
et al. 2010; Zavadskas et al. 1994, 2010; Jakimavicius, Burinskiene
2009; Liaudanskiene et al. 2009; Kucas 2010). Evaluation of ranking
accuracy of TOPSIS was performed by Zavadskas et al. (2006). Modified
method applying Mahalanobis distance was proposed by Antucheviciene et
al. (2010). Fuzzy TOPSIS technique was developed as FTOPSIS to solve
ranking and evaluating problems, because fuzzy allows the
decision-makers to handle the incomplete information, non-obtainable
information into decision model (Kulak et al. 2005). FTOPSIS and its
extensions are applied to various applications (see Table 1).
The Fuzzy MCDM can be concisely expressed in matrix format as Eqs.
(17) and (18).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (18)
where [[??].sub.ij], i = 1, 2, ..., m; j = 1, 2, ..., n and
[[??].sub.j], j = 1, 2, ..., n are linguistic triangular Fuzzy numbers,
[[??].sub.ij] = ([a.sub.ij], [b.xsub.ij], [c.sub.ij]) and [[??].sub.j] =
([a.sub.j1], [b.sub.j2], [c.sub.j3]). Note that [[??].sub.ij] is the
performance rating of the ith alternative, Ai, with respect to the jth
criterion, Cj and [[??].sub.j] represents the weight of the jth
criterion, Cj. The normalized Fuzzy decision matrix denoted by [??] is
shown as Eq. (19):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (19)
The weighted Fuzzy normalized decision matrix is shown in Eq. (20):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (20)
The advantage of using a Fuzzy approach is to allocate the relative
importance of the criteria using Fuzzy numbers instead of crisp numbers.
FTOPSIS is particularly suitable for solving the group decision maker
problem under Fuzzy environment. FTOPSIS procedure is defined as follows
(Hwang,Yoon 1992; Yang, Hung 2007):
Step 1: Choose the linguistic ratings ([[??].sub.ij], i = 1,2,. ..,
m, j = 1,2, ..., n) for alternatives with respect to criteria and the
appropriate linguistic variables ([[??].sub.ij], j = 1,2, ..., n) for
the weight of the criteria. The fuzzy linguistic rating ([[??].sub.ij])
preserves the property that the ranges of normalized triangular fuzzy
numbers belong to [0, 1].
Step 2: Construct the weighted normalized fuzzy decision matrix.
The weighted normalized value is calculated by Eq. (20).
Step 3: Identify positive ideal ([A.sup.*]) and negative ideal
([A.sup.-]) solutions. The fuzzy positive ideal solution and the fuzzy
negative-ideal solution are shown in Eqs. (21), (22).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], (21)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (22)
Step 4: Calculate separation measures. The distance of each
alternative from [A.sup.*] and [A.sup.-] can be currently calculated
using Eqs. (23), (24).
[d.sup.+.sub.i] = [n.summation over
(j=1)]d([[??].sub.ij],[[??].sup.+.sub.j]), i = 1,2, ..., m, (23)
[d.sup.-.sub.i] = [n.summation over
(j=1)]d([[??].sub.ij],[[??].sup.-.sub.j]), i = 1,2, ..., m. (24)
Step 5: Calculate the similarities to ideal solution. This step
solves the similarities to an ideal solution by Eq. (25).
[CC.sup.*.sub.i] = [d.sup.-.sub.i]/[d.sup.-.sub.i] +
[d.sup.*.sub.i]. (25)
Step 6: Rank preference order. Choose an alternative with maximum
[CC.sup.*.sub.i] or rank alternatives according to [CC.sup.*.sub.i] in
descending order.
5. SWOT analysis and its application for strategies development
The SWOT analysis has its origins in the 1960s (Kandakoglu et al.
2009). It is an environmental analysis tool that integrates the internal
strengths/weaknesses and external opportunities/ threats.
This method is implemented in order to identify the key internal
and external factors that are important to the objectives that the
organization wishes to achieve (Houben et al. 1999). The internal and
external factors are known as strategic factors and are categorized via
the SWOT analysis. Based on this analysis, strategies are developed
which may build on the strengths, eliminate the weaknesses, exploit the
opportunities, or counter the threats (Kandakoglu et al. 2009).
SWOT maximizes strengths and opportunities, and minimizes threats
and weaknesses (Amin et al. 2010), and transform the identified
weaknesses into strengths, and to take advantage of opportunities along
with minimizing both internal weaknesses and external threats. It can
provide a good basis for successful strategy formulation (Chang, Huang
2006).
According to the high ability of the SWOT analysis, miscellaneous
researches applied this method to strategies development.
Nikolaou, Evangelinos (2010) employed SWOT analysis for
environmental management practices in Greek Mining and Mineral Industry,
their stated policy recommendations both for the government and industry
which, if adopted, could facilitate improved environmental performance.
Arslan, Er (2008) developed strategic plans of action for safer tanker
operation. Chang, Huang (2006) used SWOT analysis to assess the
competing strength of each port in East Asia and then suggest an
adoptable competing strategy for each.
Stewart et al. (2002) employed SWOT analysis in order to present a
strategic implementation framework for IT/IS projects in construction.
Terrados et al. (2007) developed regional energy planning through SWOT
analysis and strategic planning tools, they proved that SWOT analysis is
an effective tool and has constituted a suitable baseline to diagnose
current problems and to sketch future action lines.
Quezada et al. (2009) used a modified SWOT analysis in order to
identify strategic objectives in strategy maps. Zaerpour et al. (2008)
proposed a novel hybrid approach consisting of SWOT analysis and
analytic hierarchy process. Misra, Murthy (2011) developed a SWOT
analysis of Jatropa with specific reference to Indian conditions and
found that Jatropa indeed is a plant which can make the Indian dream of
self-sufficiency in energy-a reality. Chang et al. (2002) applied SWOT
analysis in order to forecast the development trends in Taiwan's
machinery industry. They made SWOT analysis through an integrated
professional team using the Delphi method.
Wang, Hong (2011) proposed a novel approach to strategy
formulation, which utilizes the theory of competitive advantage of
nations (a revised diamond model), SWOT analysis and strategy matching
using the TOWS matrix and competitive benchmarking. Leskinen et al.
(2006) utilized SWOT analyses to form the basis for further operations
that were applied in the strategy process of the forest research
station.
Halla (2007) employed SWOT analysis for planning strategic urban
development using the case of Dar es Salaam City in Tanzania. Dyson
(2004) applied SWOT analysis and strategic development at the University
of Warwick. Taleai et al. (2009) proposed a combined method based on the
SWOT and analytic hierarchy process (AHP) to investigate the challenges
and prospects of adopting geographic information systems (GIS) in
developing countries. Lu (2010) provides an augmented SWOT analysis
approach for strategists to conduct strategic planning in the
construction industry.
6. Balanced Scorecard
Balanced Scorecard (BSC) is created by Kaplan and Norton (1992). It
is looking for the different goals in its implementation. It tries to
build a framework for strategic planning through four different areas;
the four areas are Customer Perspective (CP), Learning and Growth
Perspective (LGP), Financial Perspective (FP) and Internal Business
Process Perspective (IBPP) (Kaplan and Norton 1992). It creates an
insight for both managers and employers to better understanding the
company's objectives. Figure 3 shows the relationship among various
factors of BSC.
The BSC is a systemic approach, which helps integrating physical
and intangible assets into a comprehensive model and builds a meaningful
relationship among different criteria. Whereas ordinary accounting
techniques can measure the physical assets of the companies and it means
less than one--fourth of the value of the corporate sector are
accountable (Niven 2008).
[FIGURE 3 OMITTED]
The concepts of BSC are widely applied to performance measurement.
Lee et al. (2008) used the BSC approach for evaluating performance of IT
department in the manufacturing industry, they define the hierarchy with
four major perspectives of the BSC and then the FAHP approach was
proposed in order to tolerate vagueness and ambiguity of information.
Bremser, Chung (2005) proposed framework based on balanced scorecard
methodology and existing taxonomies of e-business models. Chytas et al.
(2011) developed a methodology based on fuzzy cognitive maps in order to
generate a dynamic network of interconnected key performance indicators.
Wu et al. (2009) proposed a Fuzzy Multiple Criteria Decision Making
approach based on BSC for banking performance evaluation, they the three
MCDM analytical tools of SAW, TOPSIS, and VIKOR were adopted to rank the
banking performance. Yuan, Chiu (2009) developed a three-level feature
weights design to enhance inference performance of case-based reasoning.
Bobillo et al. (2009) proposed a semantic fuzzy expert system which
implements a generic framework for the BSC. Wachtel et al. (1999)
applied the burn center to test whether the BSC methodology was
appropriate for the core business plan of a healthcare strategic
business unit.
7. Case study
Mining is one of the central activities so that other activities
such as manufacturing, construction, and transportation, are directly
and/or indirectly related to raw mineral production. Mining plays a
leading social-economic role in Iran. At its various stages--from
exploration to production and selling--it generates a significant number
of jobs and income for the country. Due to the rising demand for raw
minerals by the industrial countries and most rapidly growing economies,
mining is becoming increasingly important.
Iran is a country located in the Middle East with a non-federated
governmental system. Iran is divided into thirty provinces. Iran has one
of the world's largest zinc reserves and second-largest reserves of
copper. It also has significant reserves of iron, uranium, lead,
chromate, manganese, coal and gold.
8. The implementation of proposed model
The proposed model of this paper uses an integrated model that
provides a framework for ranking the mining strategies of Iran. In order
to implement the model, we first discuss the SWOT, then the BSC is
analyzed; finally the strategies are prioritized the FTOPSIS method. In
this framework, the weights of evaluation criteria are calculated via
FAHP. Schematic diagram of the proposed model for ranking the strategies
is provided in Fig. 4.
The data for the SWOT analysis are based on the aggregate mining
strategy reports of the ministry of industries and mines. The term
'strengths' contains advantages and benefits from the adoption
of strategic management practices. In order to explore the strengths,
some typical questions were designed such as what are the benefits of
such practices, what strategic management practices can do well.
Similarly, weaknesses would encompass agents and parameters that are
difficulties in the efforts of companies to accept any strategic
management practices. Some important questions could be what are not
done appropriately, what should be better or be avoided. Moreover,
opportunities may include external benefits for companies from the
acceptance of strategic management practices. Some relevant questions
are; what benefits may take place for companies future, what competitive
advantages will companies gain and what changes may occur in consumer
demands. Finally, threats may encompass future problems and difficulties
from the prevention of implementing any strategic management practices.
[FIGURE 4 OMITTED]
The basic parameters of the SWOT analysis are fall into two
categories: external and internal. The external category contains
strengths and opportunities and the internal category encompasses
weaknesses and threats.
We prepared a list of strengths, weaknesses, opportunities, and
threats, and then had an interview with the experts in mining strategies
of Iran to modify the list. The results of the SWOT analysis based on
expert knowledge are presented in Table 2.
As shown in Table 2, six strategies are concluded from the SWOT
analysis. These strategies should be ranked due to financial and time
constrains. We applied BSC criteria in order to prioritize the
strategies. Consequently, the weight of criteria, the BSC criteria, is
gained by FAHP and also, the alternatives, strategies obtained from
SWOT, are carried out by FTOPSIS.
Achieving the aim, we first prepared a list of evaluation
indicators base on the four perspectives of the BSC, and then with
having an interview with the mining experts, the list were modified. Two
questionnaires were designed in order to obtain the weights of criteria
and alternatives. One of them is based on the four perspectives of the
BSC and the selected performance indicators using the AHP questionnaire
format, to obtain the relative importance of the four perspectives and
the relative importance of the key performance indicators under each
perspective. The other is provided by using the FTOPSIS questionnaire in
order to gain the appropriate weights for the alternatives with respect
to criteria. The questionnaires were distributed to senior managers from
mining sector.
The Proposed model is continued as follows:
Step 1: Create the hierarchical model for the BSC
The first step changes the complex and multi criteria problems into
a hierarchical structure. According to the case study, the first level
comprises the goal from the different criteria, the second level
includes the main criteria, the third level involves the sub-criteria,
and finally the forth level contains the alternatives. In the Table 3
the hierarchical structure is represented.
Step 2: Accomplish the pair-wise comparison of criteria
After building the hierarchical structure, we designed an AHP
questionnaire format and arrange the pair-wise comparisons matrix.
Firstly each decision maker individually carry out pair-wise comparison
by using Saaty's 1-9 scale (Saaty 1980) as shown in Table 4. The
consistency of the decision maker's judgments during the evaluation
phase is calculated by consistency ratio (CR) that cloud be defined as
follows (Aguaron et al. 2003):
CR = [[lambda].sub.max] - n/n - 1, (26)
where [[lambda].sub.max] is the principal eigenvalue and n is the
rank of judgment matrix. The closer the inconsistency ratio to zero, the
greater the consistency (Torfi et al. 2010). The resulting CR values for
our case study are smaller than the critical value of 0.1, this show
that there is no evidence of inconsistency.
The importance weights of the criteria determined by twelve
decision-makers that are obtained through Eq. (27) are shown in Table 5.
[[??].sub.ij] = ([l.sub.ij], [m.sub.ij], [u.sub.ij]), [l.sub.ij] =
min{[x.sup.k.sub.ij]}, [m.sub.ij] = 1/k [k.sub.k=1] [x.sup.k.sub.ij],
[u.sub.ij] = max{[x.sup.k.sub.ij]}, (27)
where [[??].sub.ij] is the fuzzy importance weights of each
criterion that are determined by all experts, [x.sub.ij] is the crisp
weight of each criterion, k is the number of expert (here, k is equal to
12).
The responses collected from questionnaires are input to the FAHP
system, and the results are analyzed by the FAHP.
According to the FAHP method, firstly synthesis values must be
calculated. From (Table 5), synthesis values respect to main goal are
calculated like in Eq. (8):
[S.sub.F] = (1/36.5,1/18.57,1/10.52) [cross product] (2.16,5.06,10)
= (0.059,0.272,0.95);
[S.sub.I] = (1/36.5,1/18.57,1/10.52) [cross product] (2.08,3.82,7)
= (0.057,0.206,0.665);
[S.sub.F1] = (1/35.5,1/20.32,1/10.6) [cross product] (4.5,7.85,11)
= (0.127,0.386,1.037);
[S.sub.F2] = (1/35.5,1/20.32,1/10.6) [cross product] (2.16,6.56,11)
= (0.061,0.323,1.037);
[S.sub.F4] = (1/35.5,1/20.32,1/10.6) [cross product] (1.91,2.51,6)
= (0.054,0.124,0.565);
[S.sub.C1] = (1/18.5,1/10.97,1/7.7) [cross product] (4,6.09,10) =
(0.216,0.555,1.29);
[S.sub.C2] = (1/18.5,1/10.97,1/7.7) [cross product] (1.45,2.1,2.5)
= (0.078,0.191,0.324);
[S.sub.C3] = (1/18.5,1/10.97,1/7.7) [cross product] (2.25,2.78,6) =
(0.122,0.253,0.779);
[S.sub.I1] = (1/40,1/18.87,1/9.22) [cross product] (2.16,5.21,11) =
(0.054,0.276,1.193);
[S.sub.I2] = (1/40,1/18.87,1/9.22) [cross product] (2.75,6.34,14) =
(0.069,0.336,1.518);
[S.sub.I3] = (1/40,1/18.87,1/9.22) [cross product] (1.78,2.43,5) =
(0.045,0.129,0.54);
[S.sub.I4] = (1/40,1/18.87,1/9.22) [cross product] (2.53,4.89,10) =
(0.063,0.259,1.08);
[S.sub.L1] = (1/21,1/l3.6l,1/8.l7) [cross product] (1.64,2.38,4.5)
= (0.078,0.175,0.55);
[S.sub.L2] = (1/21,1/l3.6l,1/8.l7) [cross product] (5,9.08,13) =
(0.238,0.667,1.59);
[S.sub.L3] = (1/21,1/l3.6l,1/8.l7) [cross product] (1.53,2.15,3.5)
= (0.073,0.158,0.428).
These fuzzy values are compared by using Eq. (12) and these values
are obtained:
V([S.sub.F] > [S.sub.C]) = 0.881, V([S.sub.F] > [S.sub.I]) =
1, V([S.sub.F] > [S.sub.L]) = 1,
V([S.sub.C] > [S.sub.F]) = 1, V([S.sub.C] > [S.sub.I]) = 1,
V([S.sub.C] > [S.sub.L]) = 1,
V([S.sub.I] > [S.sub.F]) = 0.901, V([S.sub.I] > [S.sub.C]) =
0.752, V([S.sub.I] > [S.sub.L]) = 1,
V([S.sub.L] > [S.sub.F]) = 0.806, V([S.sub.L] > [S.sub.C]) =
0.668, V([S.sub.L] > [S.sub.I]) = 0.892,
V([S.sub.F1] > [S.sub.F2]) = 1, V([S.sub.F1] > [S.sub.F3]) =
1, V([S.sub.F1] > [S.sub.F4]) = 1,
V([S.sub.F2] > [S.sub.F1]) = 0.934, V([S.sub.F2] >
[S.sub.F3]) = 1, V([S.sub.F2] > [S.sub.F4]) = 1,
V([S.sub.F3] > [S.sub.F1]) = 0.726, V([S.sub.F3] >
[S.sub.F2]) = 0.806, V([S.sub.F3] > [S.sub.F4]) = 1,
V([S.sub.F4] > [S.sub.F1]) = 0.625, V([S.sub.F4] >
[S.sub.F2]) = 0.717, V([S.sub.F4] > [S.sub.F3]) = 0.921,
V([S.sub.C1] > [S.sub.C2]) = 1, V([S.sub.C1] > [S.sub.C3]) =
1,
V([S.sub.C2] > [S.sub.C1]) = 0.229, V([S.sub.C2] >
[S.sub.C3]) = 0.766,
V([S.sub.C3] > [S.sub.C1]) = 0.65, V([S.sub.C3] > [S.sub.C1])
= 1,
V([S.sub.I2] > [S.sub.I2]) = 0.949, V([S.sub.I1] >
[S.sub.I3]) = 1, V([S.sub.I1] > [S.sub.I4]) = 1,
V([S.sub.I2] > [S.sub.I1]) = 1, V([S.sub.I2] > [S.sub.I3]) =
1, V([S.sub.I2] > [S.sub.I4]) = 1,
V([S.sub.I3] > [S.sub.I1]) = 0.768, V([S.sub.I3] >
[S.sub.I2]) = 0.695, V([S.sub.I3] > [S.sub.I4]) = 1,
V([S.sub.I4] > [S.sub.I1]) = 0.984, V([S.sub.I4] >
[S.sub.I2]) = 0.93, V([S.sub.I4] > [S.sub.I3]) = 1,
V([S.sub.L1] > [S.sub.L2]) = 0.388, V([S.sub.L1] >
[S.sub.L3]) = 1,
V([S.sub.L2] > [S.sub.L1]) = 1, V([S.sub.L2] > [S.sub.L3]) =
1,
V([S.sub.L3] > [S.sub.L1]) = 0.95, V([S.sub.L3] > [S.sub.L2])
= 0.27.
Then priority weights are calculated by using Eq. (13):
d'(F) = min(0.881,1,1) = 0.881.
d'(C) = min(1,1,1) = 1.
d'(j) = min(0.901,0.752,1) = 0.752.
d'(1) = min(0.806,0.668,0.892) = 0.668.
d'(F1) = min(1,1,1) = 1.
d'(F2) = min(0.934,1,1) = 0.934.
d'(F3) = min(0.726,0.806,1) = 0.726.
d'(F4) = min(0.625,0.717,0.921) = 0.625.
d'(C1) = min(1,1) = 1.
d'(C2) = min(0.229,0.766) = 0.229.
d'(C3) = min(0.65,1) = 0.65.
d'(L1) = min(0.949,1,1) = 0.949.
d'(I2) = min(1,1,1) = 1.
d'(I3) = min(0.768,0.695,1) = 0.695.
d'(I4) = min(0.984,0.93,1) = 0.93.
d'(L1) = min(0.388,1) = 0.388.
d'(L2) = min(1,1) = 1.
d'(L3) = min(0.95,0.27) = 0.27.
Priority weights for each criterion are presented in Table 6, The
FAHP analysis of the criteria is summarized in Fig, 5.
[FIGURE 5 OMITTED]
Step 3: Determining the final priority
At this step of the proposed model, the team members were asked to
establish the decision matrix by comparing alternatives under each of
the criteria separately. Linguistic values were used for evaluation of
strategies in this step. The membership functions of these linguistic
values, and the triangular fuzzy numbers related with these variables
are shown in Fig. 6 and Table 7 respectively. The fuzzy performance
ratings of the alternatives with regard to each criterion were
determined by twelve decision makers that are obtained by Eq. (28).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (28)
Fuzzy evaluation matrix for the alternatives with regard to each
criterion is determined. After the fuzzy evaluation matrix was
determined, the next stage is to obtain a fuzzy normalized decision
matrix as presented in Table 8. The fuzzy performance ratings are
normalized into the range of [0,1] through Eqs. (29) and (30) (Yang,
Hung 2007):
[r.sub.ij] = [x.sub.ij] - min{[x.sub.ij]}/[max{[x.sub.ij]} -
min{[x.sub.ij]}] The larger, the better type, (29)
[r.sub.ij] = min {[x.sub.ij]} - [x.sub.ij]/[max{[x.sub.ij]} -
min{[x.sub.ij]}] The smaller, the better type, (30)
[FIGURE 6 OMITTED]
Using the criteria weights calculated by FAHP in the former step,
the fuzzy weighted decision matrix is established with Eq. (20). The
resulting fuzzy weighted decision matrix is presented in Table 9.
Since the all criteria are benefit type, we can define the fuzzy
positive-ideal solution and the fuzzy negative-ideal as
[[??].sup.*.sub.j] = (1, 1, 1) and [[??].sup.-.sub.j] = (0, 0, 0)
respectively. So, the distance of each alternative from [D.sup.*] and
[D.sup.-] can be currently calculated using Eq. (23) and Eq. (24).
Finally, FTOPSIS solves the similarities to an ideal solution by Eq.
(25). In order to distinguish the matter, an example is presented as
follows:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
As a result,
[CC.sub.1] = [D.sup-.sub.1]/[D.sup.*.sub.1] + [D.sup.-.sub.1] =
0.701/13.33 + 0.701 = 0.0499.
[FIGURE 7 OMITTED]
Similar calculations were done for the other alternatives and the
results of FTOPSIS analyses were summarized in Table 10. According to
CCj values, the ranking of the alternatives in descending order are A1,
A5, A6, A4, A3 and A2. The rank of alternatives is depicted in Fig. 7.
Proposed model results indicate that A1 is the best alternative with CC
value of 0.0499.
9. Conclusions
In this study, we developed an integrated model of the SWOT
analysis as well as the BSC model to construct a framework, and gained
the weights of criteria and alternatives based on FAHP and FTOPSIS
respectively. Six strategies were generated by the SWOT analysis of the
Iranian mining sector. Then, the BSC criteria were applied to prioritize
the strategies. Fuzzy MCDM has recognized wide applications in the
solution of real world decision making problems. FAHP and FTOPSIS are
the preferred techniques for obtaining the criteria weights and
performance ratings when information is vague and inaccurate. The
results show that A1 (0.0499) has the highest weighting. As this result,
decision makers are advised to improve the ability of exploitation and
production. Finally, we recommend that the authorities of mining
industries can use this model to evaluate their activities for
development or investment purposes.
doi: 10.3846/20294913.2011.603173
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Zavadskas, E. K.; Zakarevicius, A.; Antucheviciene, J. 2006.
Evaluation of ranking accuracy in multicriteria decisions, Informatica
17(4): 601-618.
Mohammad Majid Fouladgar (1), Abdolreza Yazdani-Chamzini (2),
Edmundas Kazimieras Zavadskas (3)
(1,2) Fateh Research Group, Department of Strategic Management,
Kimia No. 7, Rates, Aghdasieh, Tehran, Iran
(3) Vilnius Gediminas Technical University, Faculty of Civil
Engineering, Sauletekio al. 11, LT-10223 Vilnius, Lithuania
E-mails: (1) manager@fatehidea.com; (2) a.yazdani@fatehidea.com;
(3) Edmundas.Zavadskas@vgtu.lt (corresponding author)
Received 19 January 2011; accepted 21 June 2011
Mohammad Majid FOULADGAR. Master of Science in the Dept 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 Dept 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.
Table 1. The various applications of FTOPSIS
Proposed by Year Used tools Application
Chen 2000 FTOPSIS Fuzzy environment
Antucheviciene 2005 FTOPSIS Evaluations of
alternatives
Wang, Elhag 2006 FTOPSIS Risk assessment,
selecting a system
analysis engineer
Zavadskas, 2006 FTOPSIS Sustainable
Antucheviciene revitalization
Kuo et al. 2007 FTOPSIS, Fuzzy SAW Location selection
Dagdeviren et al. 2009 FTOPSIS, AHP Weapon selection
Continued Table 1
Ebrahimnejad et al. 2009 FTOPSIS, Fuzzy Risk ranking
LINMAP
Sreeda, Sattanathan 2009 FTOPSIS, FAHP To buy an
apartment
Wang, Lee 2009 FTOPSIS, Shannons Software selection
Entropy
Ebrahimnejad et al. 2010 FTOPSIS, fuzzy Risk assessment
LINMAP
Per?in, Kahraman 2010 FTOPSIS, AHP Six Sigma project
selection
Torfi et al. 2010 AHP, FAHP, TOPSIS, Various areas
FTOPSIS, DEA
Kelemenis et al. 2011 FTOPSIS Personnel selection
Rostamzadeh, Sofian 2011 FTOPSIS, FAHP, DSS Production systems
performance
Singh, Benyoucef 2011 FTOPSIS, entropy E-sourcing
Table 2. SWOT analysis and strategic recommendations
SWOT analysis Mining strategies
Internal Strengths:
S1. High potential of ore A1. Improving the ability
deposits, of exploitation and
S2. Large mining production: this strategy
resources, is obtained according to
S3. Miscellaneous S1, S2, O1, O2, O3.
minerals. A2. Investment in
exploration sector: this
Weakness: strategy is resulted by
W1. The lack of a O3, O4, W1, W2.
completed mining database,
W2. Long period from A3. Investing in the earth
exploration to sciences (information,
manufacturing, technology, and labor
W3. Low efficiency in force): this strategy is
mining activities. extracted from W1, W3, T1,
T3.
External Opportunities:
O1. Cheap Labor force, A4. Making persuasive
O2. Access to energy policies to attract mining
resource, investors and promotion of
O3. The geopolitical R&D: this strategy is
situation of Iran, obtained through S1, S2,
O4. Increasing demand for S3, T1, T2, T4.
raw materials.
A5. The privatization of
Threats: mines and mineral
T1. Exporting raw industries: this strategy
material, is resulted by O4, O3, W2,
T2. Non-membership of Iran W3.
in WTO,
T3. High risk involved, A6. Revising the mining
T4. The fluctuations of law and cadastral system:
raw mineral prices. this strategy is extracted
by T1, T2, T3, S2.
Table 3. The hierarchical structure
Alternatives
Goal Perspectives Evaluation indicators extracted from
the SWOT
analysis
Selection Financial (F) F1. Enhancing the A1
of the added value. A2
best F2. Increasing the A3
strategy investments. A4
for mining F3. Decreasing the A5
sector of costs. A6
Iran F4. Risks reduction.
Customer (C) C1. Improvement of
the level of
services.
C2. Customer
satisfaction.
C3. Management of
supply chain.
Internal I1. Increasing the
business (I) level of production.
I2. The efficiency
improvement.
I3. Raising the gross
domestic production
(GDP).
I4. Marketing.
Learning and L1. Innovation and
growth (L) creativeness.
L2. Employing the
high technology.
L3. Improving the
labor force
efficiency.
Table 4. Pair-wise comparison scale (Saaty 1980)
Numerical
Option value(s)
Equal 1
Marginally strong 3
Strong 5
Very strong 7
Extremely strong 9
Intermediate values to reflect fuzzy inputs 2, 4, 6, 8
Reflecting dominance of second alternative compared reciprocals
with the first
Table 5. Importance weight of criteria and sub-criteria
BSC
criteria F
F (1,1,1)
C (0.5, 1.04,3)
I (0.33,0.75,2)
L (0.25,0.59,3)
Sub-
criteria F1 F2
F F1 (1,1,1) (0.5,1.86,3)
F2 (0.33,0.54,2) (1,1,1)
F3 (0.33,0.36,0.5) (0.2,0.35,3)
F4 (0.25,0.45,1) (0.33,0.47,2)
C C1
C2
C3
I I1
I2
I3
I4
L L1
L2
L3
BSC
criteria F
F (1,1,1)
C (0.5, 1.04,3)
I
L
Sub-
criteria F3 F4
F F1 (2,2.77,3) (1,2.22,4)
F2 (0.33,2.89,5) (0.5,2.13,3)
F3 (1,1,1) (0.5,1.69,3)
F4 (0.33,0.59,2) (1,1,1)
C C1
C2
C3
I I1
I2
I3
I4
L L1
L2
L3
BSC
criteria C
F (0.33,0.96,2)
C (1,1,1)
I (0.25,0.43,1)
L (0.2,0.36,0.5)
Sub-
criteria C1 C2 C3
F F1
F2
F3
F4
C C1 (1,1,1) (2,2.77,5) (1,2.32,4)
C2 (0.2,0.36,0.5) (1,1,1) (0.25,0.74,1)
C3 (0.25,0.43,1) (1,1.35,4) (1,1,1)
I I1
I2
I3
I4
L L1
L2
L3
BSC
criteria I
F (0.5,1.34,3)
C (1,2.33,4)
I (1,1,1)
L (0.33,0.61,2)
Sub-
criteria I1 I2
F F1
F2
F3
F4
C C1
C2
C3
I I1 (1,1,1) (0.33,1.26,4)
I2 (0.25,0.79,3) (1,1,1)
I3 (0.33,0.61,2) (0.25,0.45,1)
I4 (0.33,0.76,3) (0.2,0.43,1)
L L1
L2
L3
BSC
criteria I
F (0.5,1.34,3)
C (1,2.33,4)
I (1,1,1)
L (0.33,0.61,2)
Sub-
criteria I3 I4
F F1
F2
F3
F4
C C1
C2
C3
I I1 (0.5,1.64,3) (0.33,1.31,3)
I2 (1,2.21,4) (0.5,2.34,5)
I3 (1,1,1) (0.2,0.37,1)
I4 (1,2.7,5) (1,1,1)
L L1
L2
L3
BSC
criteria L
F (0.33,1.76,4)
C (2,2.76,5)
I (0.5,1.64,3)
L (1,1,1)
Sub-
criteria L1 L2 L3
F F1
F2
F3
F4
C C1
C2
C3
I I1
I2
I3
I4
L L1 (1,1,1) (0.14,0.21,0.5) (0.5,1.17.3)
L2 (2,4.76,7) (1,1,1) (2,3.32,5)
L3 (0.33,0.85,2) (0.2,0.3,0.5) (1,1,1)
Table 6. Priority weights for each criterion
Criteria Weights under Normalized Normalized
the same weights under weights among
perspective the same all indicators
perspective
F 0,881 0,267 --
C 1 0,303 --
I 0,752 0,228 --
L 0,668 0,202 --
F1 1 0,304 0,081
F2 0,934 0,284 0,076
F3 0,726 0,221 0,059
F4 0,625 0,190 0,051
C1 1 0,532 0,161
C2 0,229 0,122 0,037
C3 0,65 0,346 0,105
I1 0,949 0,266 0,060
I2 1 0,280 0,064
I3 0,695 0,194 0,044
I4 0,93 0,260 0,059
L1 0,388 0,234 0,047
L2 1 0,603 0,122
L3 0,27 0,163 0,033
Table 7. Linguistic values and fuzzy numbers
Linguistic values Fuzzy numbers
Very low (VL) (0, 0, 0.2)
Low (L) (0, 0.2, 0.4)
Medium (M) (0.2, 0.4, 0.6)
High (H) (0.4, 0.6, 0.8)
Very high (VH) (0.6, 0.8, 1)
Excellent (E) (0.8, 1, 1)
Table 8. Fuzzy normalized decision matrix
A1 A2 A3
F1 (0.45,0.73,1) (0.0,0.27,0.55) (0.0,0.27,0.55)
F2 (0.22,0.56,0.89) (0.22,0.56,0.89) (0.11,0.44,0.78)
F3 (0.4,0.7,1) (0.3,0.6,0.8) (0.2,0.5,0.8)
F4 (0.42,0.67,1) (0.0,0.25,0.5) (0.08,0.33,0.58)
c1 (0.42,0.67,0.92) (0.0,0.25,0.5) (0.25,0.5,0.75)
c2 (0.45,0.73,1) (0.0,0.18,0.45) (0.18,0.36,0.64)
c3 (0.3,0.5,0.8) (0.0,0.3,0.6) (0.0,0.2,0.5)
I1 (0.5,0.75,1) (0.25,0.5,0.75) (0.08,0.25,0.5)
I2 (0.42,0.67,0.92) (0.0,0.17,0.42) (0.08,0.25,0.5)
I3 (0.5,0.75,1) (0.0,0.08,0.25) (0.08,0.33,0.58)
I4 (0.33,0.67,1) (0.0,0.11,0.33) (0.0,0.22,0.56)
L1 (0.5,0.7,1) (0.0,0.1,0.3) (0.0,0.2,0.5)
L2 (0.36,0.64,0.91) (0.0,0.18,0.45) (0.09,0.27,0.55)
L3 (0.5,0.75,1) (0.0,0.08,0.25) (0.0,0.25,0.5)
A4 A5 A6
F1 (0.09,0.36,0.64) (0.18,0.45,0.73) (0.0,0.27,0.55)
F2 (0.0,0.33,0.67) (0.33,0.67,1) (0.22,0.56,0.89)
F3 (0.0,0.3,0.6) (0.1,0.4,0.7) (0.2,0.5,0.8)
F4 (0.08,0.25,0.5) (0.33,0.58,0.83) (0.08,0.33,0.58)
c1 (0.08,0.25,0.5) (0.17,0.42,0.67) (0.5,0.75,1)
c2 (0.09,0.27,0.55) (0.45,0.73,1) (0.27,0.55,0.82)
c3 (0.2,0.5,0.8) (0.4,0.7,1) (0,0.3,0.6)
I1 (0.33,0.58,0.83) (0.08,0.33,0.58) (0,0.25,0.5)
I2 (0.08,0.33,0.58) (0.5,0.75,1) (0.17,0.42,0.67)
I3 (0.17,0.42,0.67) (0.08,0.42,0.67) (0.17,0.42,0.67)
I4 (0.0,0.22,0.56) (0.11,0.44,0.78) (0.11,0.44,0.78)
L1 (0.2,0.4,0.7) (0.3,0.6,0.9) (0.1,0.4,0.7)
L2 (0.18,0.45,0.73) (0.45,0.73,1) (0.0,0.36,0.64)
L3 (0.08,0.25,0.5) (0.33,0.58,0.83) (0.08,0.42,0.67)
Weight
F1 0.081
F2 0.076
F3 0.059
F4 0.051
c1 0.161
c2 0.037
c3 0.105
I1 0.060
I2 0.064
I3 0.044
I4 0.059
L1 0.047
L2 0.122
L3 0.033
Table 9. Fuzzy weighted decision matrix
A1 A2 A3
F1 (0.04,0.06,0.08) (0.0,0.02,0.04) (0.0,0.02,0.04)
F2 (0.02,0.04,0.07) (0.02,0.04,0.07) (0.01,0.03,0.06)
F3 (0.02,0.04,0.06) (0.02,0.04,0.05) (0.01,0.03,0.05)
F4 (0.02,0.03,0.05) (0.0,0.01,0.03) (0.0,0.02,0.03)
C1 (0.07,0.11,0.15) (0.0,0.04,0.08) (0.04,0.08,0.12)
C2 (0.02,0.03,0.04) (0.0,0.01,0.02) (0.01,0.01,0.02)
C3 (0.03,0.05,0.08) (0.0,0.03,0.06) (0.0,0.02,0.05)
I1 (0.03,0.05,0.06) (0.02,0.03,0.05) (0.01,0.02,0.03)
I2 (0.03,0.04,0.06) (0.0,0.01,0.03) (0.01,0.02,0.03)
I3 (0.02,0.03,0.04) (0.0,0.0,0.01) (0.0,0.01,0.03)
I4 (0.02,0.04,0.06) (0.0,0.01,0.02) (0.0,0.01,0.03)
L1 (0.02,0.03,0.5) (0.0,0.0,0.01) (0.0,0.01,0.02)
L2 (0.04,0.08,0.11) (0.0,0.02,0.06) (0.01,0.03,0.07)
L3 (0.02,0.02,0.03) (0.0,0.0,0.01) (0.0,0.01,0.02)
A4 A5 A6
F1 (0.01,0.03,0.05) (0.01,0.04,0.06) (0.0,0.02,0.04)
F2 (0.0,0.03,0.05) (0.0,0.03,0.05) (0.02,0.04,0.07)
F3 (0.0,0.02,0.04) (0.01,0.02,0.04) (0.01,0.03,0.05)
F4 (0.0,0.01,0.03) (0.02,0.03,0.04) (0.0,0.02,0.03)
C1 (0.01,0.04,0.08) (0.03,0.07,0.11) (0.08,0.12,0.16)
C2 (0.0,0.01,0.02) (0.02,0.03,0.04) (0.01,0.02,0.03)
C3 (0.02,0.05,0.08) (0.04,0.07,0.11) (0.0,0.03,0.06)
I1 (0.02,0.04,0.05) (0.01,0.02,0.04) (0.0,0.02,0.03)
I2 (0.01,0.02,0.04) (0.03,0.05,0.06) (0.01,0.03,0.04)
I3 (0.01,0.02,0.03) (0.0,0.02,0.03) (0.01,0.02,0.03)
I4 (0.0,0.01,0.03) (0.01,0.03,0.05) (0.01,0.03,0.05)
L1 (0.01,0.02,0.03) (0.01,0.03,0.04) (0.0,0.02,0.03)
L2 (0.02,0.06,0.09) (0.06,0.09,0.12) (0.0,0.04,0.08)
L3 (0.0,0.01,0.02) (0.01,0.02,0.03) (0.0,0.01,0.02)
Table 10. FTOPSIS results
Alternatives [D.sup.+ [D.sup.- [CC.sub.j] Rank
.sub.j] .sub.j]
A1 13.33 0.701 0.0499 1
A2 13.71 0.346 0.0246 6
A3 13.65 0.403 0.0286 5
A4 13.63 0.428 0.0305 4
A5 13.44 0.603 0.0429 2
A6 13.56 0.504 0.0358 3
