Comparison of Two Fuzzy Multi Criteria Decision Methods for

Potential Airport Location Selection

Sedat Belbag

, Muhammet Deveci

and

Ahmet Serhat Uludag

Gazi University, Business & Administration, Incitas Street, Ankara, Turkey

Yildiz Technical University, Industrial Engineering, Besiktas, Istanbul

Gazi University, Business & Administration, Incitas Street, Ankara, Turkey

Keywords: Facility Location, Airport Location Selection, Multi Criteria Methods, Fuzzy TOPSIS, Fuzzy ELECTRE I.

Abstract: Facility location selection is a very important multi criteria decision problem for many companies. As other

strategic decisions, any failure in facility location selection has also irreversible consequences that affect the

future of a company. Multi criteria decision methods (MCDM) are widely used in comparison related

problems. These methodologies give more obvious and rational solutions in decision process. This study is

proposed fuzzy TOPSIS and fuzzy ELECTRE I to overcome facility location selection problem. We

combine fuzzy sets theory with two different multi criteria decision methods to eliminate the vagueness of

linguistic factors that stem from the uncertain and imprecise assessment of decision-makers. The proposed

methods have been applied to a facility location selection problem that determines a potential second airport

in Ankara, Turkey.

1 INTRODUCTION

Strategic decisions are usually evaluated as

irreversible decisions that affect the future of a

company. The reason behind this situation is the

risky nature of strategic decisions. Any mistaken

decision may cause terrible consequences that will

threat the existence of the company. Facility location

selection may be the most important decision among

strategic decisions. The aim of facility location is

determining the optimal location for a company.

Facility location selection requires sizable financial

investment and can affect operating costs and

revenues. So, poor location selection causes high

distribution costs, expensive or incapable labor,

inadequate raw materials, financial loss and low

competitive advantage (Reid and Sanders, 2011). On

the one hand, facility location selection aims to keep

variable costs as low as possible in order to reach

customer zones; on the other hand, facility location

selection causes high fixed costs.

Several papers attempt to find the best solution

for facility location problem from past to present.

Many papers aim to find an optimal solution with

mathematical programming methods. Spath (1984)

tried to minimize weighted sum of distances to their

minimum location centre. Aikens (1985), Owen and

Daskin (1998), and Melo et al., (2009) reviewed vast

number of papers in which several mathematical

models were developed in order to find the best

facility location for different requirements.

Nevertheless, mathematical programming models

take into consideration only quantitative factors,

qualitative factors such as linguistic factors are not

always considered. On the other hand, multi criteria

decision methods (MCDM) usually merge both

quantitative and qualitative factors. Thus, decision-

maker (DM) takes into account both type of factors

that affect facility location selection. Mostly, the

values for the qualitative criteria are not accurately

defined for decision-makers. Moreover, value and

importance weight of criteria are usually defined e.g.

“very low”, “low”, “medium”, “high”, “very high".

So, it is very hard to accurately quantify the rating of

each alternative location.

To select best facility location, different multi

criteria decision methods have been suggested in

various papers. Yang and Lee (1997) used analytical

hierarchy process (AHP) to select facility location

from the view of organizations which contemplate

locations of a new facility or a relocation of existing

facilities. Market, transportation, labor and

community were determined as main factors, and

then every factor is divided into three sub-factors.

Badri (1999) tried to combine AHP and goal

122

Belbag S., Deveci M. and Uludag A..

Comparison of Two Fuzzy Multi Criteria Decision Methods for Potential Airport Location Selection.

DOI: 10.5220/0004279702700276

In Proceedings of the 2nd International Conference on Operations Research and Enterprise Systems (ICORES-2013), pages 270-276

ISBN: 978-989-8565-40-2

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

programming in order to minimize the overall

deviations in the objective function. Proposed model

aims to solve facility location-allocation problem for

Biochemical Company. Yang et al., (2008)

developed AHP-ANP approach for evaluating

location characteristics in order to help managers to

realize the advantages and disadvantages of potential

location. To establish a location selection model, this

study suggested three-step procedure. It consists of

building initial criteria, modifying dimensions and

detailed criteria, and building an evaluation model,

respectively. In study of Erden and Cosgun (2010),

AHP and geographic information systems (GIS)

combination used to find optimal site location

among pre-selected fire stations. GIS has been used

for supporting spatial decision-making. After the

determination of possible locations, decision maker

decides main criteria for AHP procedure. Deluka-

Tibljas et al., (2010) proposed an AHP approach to

solve the problem of selecting a location for the

garage-parking facility in a town.

Except AHP related models, other MCDM have

also been used for facility selection problems.

Gundogdu (2011) suggested an ELECTRE I method

for selecting facility location of industrial plants

when considering environmental priorities. Huang et

al. (2011) formulated potential influence location

ranking theory. Authors offered a nearest location

circle algorithm and a voronoi diagram based

algorithm to process the query. Zhang (2011) used

two stage procedure GIS model in order to select

facility location for biofuel production company.

When the first stage revealed potential locations

related to railroads, roads, and other transportation

channels, the second stage was detected facility

exact location by using a total transportation cost

model. Combining Bayesian Networks and Total

Cost of Ownership (TCO), Dogan (2012) analyzed

facility location problem for an international

manufacturing plant. With suggested model,

decision maker selects the facility that has minimum

total cost when considering multiple criteria.

In real world, the evaluation of decision process

can rarely be given precisely because of the

uncertain structure of linguistic terms. In fact,

defining linguistic terms without losing the meaning

can be extremely challenging issue for researchers.

To eliminate the vagueness of linguistic terms, fuzzy

sets have been integrated with several MCDM.

Liang and Wang’s (1991) study is one of the first

attempts to combine a MCDM and fuzzy sets into a

model. The model helps decision maker to assess

precisely the weighting criteria and the

determination of facility location. Chen (2001)

solved the location selection problem of distribution

center by using a fuzzy approach that express the

ratings of alternatives and the weights of criteria in

triangular fuzzy numbers. After that, all potential

locations were ranked in a fuzzy manner. Kaboli et

al. (2008) and Tabari et al. (2008) were both

combining fuzzy sets and AHP method to select

facility location. Proposed models insert AHP

method into the fuzzy sets. As a result of that,

interval judgments become much more reliable than

fixed value judgments during the process of facility

location selection.

Chu (2002), developed a fuzzy TOPSIS model in

which the ratings and weights of each alternative

location could be aggregated by interval arithmetic

and α-cuts of fuzzy numbers. Moreover, Hu et al.

(2009) applied fuzzy sets into TOPSIS method in

order to select best distribution center for a

manufacturer. Ulukan and Kop (2009) used fuzzy

TOPSIS method in two step procedure. Firstly,

candidate locations were defined by a trapezoidal

membership function. Then, this trapezoidal

numbers embedded into criteria and alternatives in

TOPSIS. Finally, suitable facility location selected

for waste disposal company. Kahraman (2003)

compared four different multi criteria decision

methods (Blin's Fuzzy Method, Fuzzy Synthetic

Evaluation, Yager's Weighted Goals, Fuzzy AHP)

and showed basic differences among them. In this

context, fuzzy AHP applied to motor vehicle

manufacturer for facility location selection. Ertugrul

and Kasapoglu (2008) presented another

compression study between fuzzy AHP and fuzzy

TOPSIS. Each approach was used to select the best

facility location for a textile company. In a recent

study, Ozdagoglu (2011) proposed fuzzy ANP

method to overcome the problem of facility location

selection. First step of fuzzy ANP includes the

determination of fuzzy AHP solution. Next step

focused on integrating fuzzy AHP solution into ANP

approach. Kaya and Cinar (2007) investigated three

different preference models to explain fuzzy

outranking methods with the application of facility

location selection for motors manufacture company.

To select facility location for a high tech company,

Chou et al., (2008) integrated fuzzy set theory, factor

rating system and simple additive weighting into

Fuzzy Simple Additive Weighting System. Momeni

et al., (2011) attempted to extend VIKOR method by

adding fuzzy sets into it. Fuzzy VIKOR solved

facility location problem in eight consecutive steps

when taking into account all criteria and alternatives.

Literature review shows that although several

MCDM have been developed to solve different

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123

facility location problems, there is a huge gap about

potential facility location selection for an airport.

This study aims to fill this gap with suggested fuzzy

TOPSIS and fuzzy ELECTRE I method. The criteria

that belong to airport location selection are

determined by structured interview with several

experts from public and private sectors. After

interviews, not only are criteria determined but also

potential locations for airport are decided by the

views of interviewees. The population of Ankara,

the capital of Turkey, grows in each year because of

immigration from rural regions. Also, these

condense population give rise to growth in air

transportation. Even though, Esenboğa, the only

airport in Ankara, is the main stream of air

transportation, lack of capacity makes air traffic

more crowded as time progressed. We compare the

solutions of two different MCDM in facility location

selection for a second airport in Ankara. In section 2,

we give brief information about fuzzy TOPSIS and

fuzzy ELECTRE I methods. In section 3, we

illustrate findings that are related to the application

of airport location selection. In section 4, we sum up

with our conclusions and future research directions.

2 METHODOLOGY

In this study we select two different MCDM in order

to compare and comment the findings of these

MCDM. Moreover, fuzzy TOPSIS and fuzzy

ELECTRE use different way to make pairwise

comparison between alternatives. Fuzzy TOPSIS

ranks each alternative from the best to the worst by

considering different criteria. On the other hand,

fuzzy ELECTRE I outranks each alternatives by the

aid of concordance and discordance matrices. These

reasons take our attention when the determination

process of MCDM selection among other MCDM.

Below, we give some basic information about fuzzy

TOPSIS and fuzzy ELECTRE I.

3 FUZZY TOPSIS

TOPSIS method was firstly introduced in 1981 by

Hwang and Yoon. In TOPSIS, the chosen alternative

should have the shortest distance from the positive

ideal solution and the farthest distance from negative

ideal solution. Then, alternatives have ranked from

the best to the worst one. Positive ideal solution

maximizes the benefit criteria and minimizes the

cost criteria (Chen, 2000). On the other hand,

negative ideal solution maximizes the cost criteria

and minimizes the benefit criteria. Fuzzy TOPSIS

emerges the adaptation of fuzzy sets into TOPSIS

method in which linguistic variables are represented

by fuzzy numbers and evaluated by the weights of

criteria and the ratings of alternatives. Fuzzy

TOPSIS algorithm consists of several steps and

follows a hierarchical way as shown below;

Step 1: Form "n" number of decision-maker, decide

"k" number of evaluation criteria and "m" number of

alternatives. (n=3, k=34, m=5).

Step 2: Choose the appropriate linguistic variables

for the importance weight of the criteria and the

linguistic ratings for alternatives with respect to

criteria. The linguistic variables used for

determining the criteria weights, the significance

degrees of the alternatives and the related fuzzy

numbers are indicated in Table 1.

Table 1: Linguistic variables and Fuzzy Numbers.

Linguistic variables for the

importance weight of each criterion

Linguistic variables for the

ratings of each alternatives

Linguistic

variables

Fuzzy Numbers Linguistic

variables

Fuzzy

Numbers

Very Low (0, 0, 0.1) Very Poor (0, 0, 1)

Low (0, 0.1, 0.3) Poor (0, 1, 3)

Medium Low (0.1, 0.3, 0.5) Medium Poor (1, 3, 5)

Medium (0.3, 0.5, 0.7) Fair (3, 5, 7)

Medium High (0.5, 0.7, 0.9) Medium Good (5, 7, 9)

High (0.7, 0.9, 1) Good (7, 9, 10)

Very High (0.9, 1, 1) Very Good (9, 10, 10)

(Chen, 2000; 5)

Step 3: Calculate the fuzzy weight of each criteria

and alternatives.

Step 4: Construct the fuzzy decision matrix and the

normalized fuzzy decision matrix, the weighted

normalized fuzzy decision matrix.

Step 5: Construct the normalized fuzzy decision

matrix.

Step 6: Construct the weighted normalized fuzzy

decision matrix.

Step 7: Calculate the distance of each alternative

from fuzzy positive-ideal solution (FPIS, A

) and

fuzzy negative-ideal solution (FNIS, A

respectively.

Step 8: Calculate the closeness coefficient of each

alternative.

Step 9: Rank alternatives according to their

closeness coefficient that are between 0 and 1, then

choose the alternative whose closeness coefficient is

adjacent to 1.

4 FUZZY ELECTRE I

By using binary outranking relations S (means at

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least as good as), ELECTRE I models preferences.

Considering two actions a and b, four situations may

happen; aSb and not bSa (a is the strictly preferred to

b), bSa and not aSb (b is the strictly preferred to a),

aSb and not bSa (a is indifferent to b) or not aSb and

not bSa (a is incomparable to b). ELECTRE I can

build one or several (crisp, fuzzy or embedded)

outranking relations (Figueira et al., 2005). The

fuzzy ELECTRE I method uses concordance and

discordance indexes to analyze the outranking

relations among the alternatives (Rouyendegh and

Erkan, 2012). The fuzzy ELECTRE I method

proposed here can be described in 4 steps;

Step 1: Form "n" number of decision-maker, decide

"k" number of evaluation criteria and "m" number of

alternatives.

Step 2: Choose the appropriate linguistic variables

for the importance weight of the criteria and the

linguistic ratings for alternatives with respect to

criteria.

Step 3: Calculate the fuzzy weight of each criteria

and alternatives.

Step 4: Construct the fuzzy decision matrix and the

normalized fuzzy decision matrix, the weighted

normalized fuzzy decision matrix.

Step 5: The distance between two alternatives p and

r with respect to each criterion (Construct to

concordance and discordance sets)

Step 6: Form concordance and discordance

matrices.

Step 7: Calculate the average of matrices.

Step 8: Determine the superiority among

alternatives by comparing the averages of matrices.

Step 9: Create a global matrix and a decision graph

that indicates the superiority of alternatives, and then

rank the alternatives from best to worst. 

Although linguistic variables and the evaluation

of weighting are same in both MCDM, there are

several differences between fuzzy TOPSIS and

fuzzy ELECTRE I (Hatami-Marbini and Tavana,

2011). The main difference between two

methodologies is the ranking technique. Fuzzy

ELECTRE I method focuses on the selection a

single action among a small set of good actions, on

the contrary fuzzy TOPSIS method purposes the

selection of a complete or partial order of the

actions. In other words; TOPSIS makes the decision

of alternative selection and want the best alternative

should be farther from the negative-ideal solution

and closer to the positive-ideal solution than other

alternatives. However, ELECTRE I outranks

unsuitable alternative with help of concordance and

discordance matrices.

In this study, both fuzzy TOPSIS and fuzzy

ELECTRE I take into account uncertain and

imprecise linguistic assessments provided by

decision makers. We aim to select and compare

alternative airport locations in the city of Ankara

with two fuzzy MCDM. It is desired to select a

suitable location for a second airport in Ankara

among five candidate region. By the result of the

interviews with decision-makers and comprehensive

literature review, nine main criteria (geographical

specifications, climatic conditions, infrastructure

conditions, costs, transportation, the possibility of

extension, legal restrictions and regulations,

potential demand, environmental and social effects)

are determined to analyze with fuzzy TOPSIS and

fuzzy ELECTRE I, comparatively. These main

criteria have divided into 34 sub-criteria in order to

evaluate each alternative more precisely.

5 FINDINGS

Table 2: The Importance Fuzzy Weights of Decision

Criteria.

Decision Criteria (wj)

Crt. l m u Ranking

16 0,9 1 1 1

12 0,83 0,97 1 2

29 0,83 0,97 1 2

1 0,77 0,93 1 3

14 0,77 0,93 1 3

15 0,77 0,9 0,97 4

9 0,7 0,9 1 5

26 0,7 0,9 1 5

30 0,7 0,9 1 5

32 0,7 0,9 1 5

13 0,63 0,8 0,93 6

3 0,63 0,8 0,9 7

5 0,63 0,8 0,9 7

28 0,57 0,77 0,9 8

34 0,57 0,73 0,87 9

27 0,5 0,7 0,87 10

2 0,5 0,7 0,83 11

4 0,43 0,63 0,8 12

8 0,47 0,63 0,77 12

31 0,47 0,6 0,73 13

7 0,4 0,57 0,73 14

10 0,3 0,5 0,7 15

33 0,3 0,5 0,7 15

6 0,27 0,43 0,63 16

11 0,23 0,43 0,63 17

17 0,17 0,37 0,57 18

18 0,17 0,37 0,57 18

19 0,17 0,37 0,57 18

20 0,17 0,37 0,57 18

21 0,13 0,3 0,5 19

22 0,13 0,3 0,5 19

23 0,13 0,3 0,5 19

25 0,13 0,3 0,5 19

24 0,1 0,3 0,5 20

ComparisonofTwoFuzzyMultiCriteriaDecisionMethodsforPotentialAirportLocationSelection

125

This study aims to determine potential facility

location for a second airport within Ankara territory,

the capital city of Turkey, by using fuzzy TOPSIS

and fuzzy ELECTRE I, separately. Alternatives are

determined after the interview with aviation experts

who have worked in public and private sectors. We

made a structural interview with the experts, and

then final decision for potential airport locations has

been concluded. To eliminate the vagueness of

linguistic values, it is decided to use fuzzy triangular

numbers. The importance weights of the nine main

criteria and thirty-four are sub-criteria are described

using the following linguistic terms: very low, low,

medium low, medium, medium high, high and very

high. Table 2 shows the importance fuzzy weights of

decision criteria and the ranking of each criterion.

Note 1: C16: Capacity rate, C12: Connection with

urban or rural areas, C29: Contribution to regional

economy, C1: The topography of landscape, C14:

Transportation to downtown and residential area,

C15: Extension potential, C9: Condition of

transportation network, C26: Expectations related to

future demand, C30: Effects on social life in the

region, C32: Security risk, C13: The density of

traffic, C3: The risk of freeze, fog, hurricane or

flood, C5: Wind speed, C28: The condition of

wastes and effects on environment, C34: Regional

residents attitudes towards second airport, C27: The

impact on ecological balance of region, C2: The

geological and tectonic pattern of landscape, C4:

The average annual pressure, temperature and

moisture, C8: The condition of energy network,

C31: The potential risk for regional residents, C7:

The condition of communication network, C10: The

cost of land, C33: The risk and density of traffic, C6:

The sewer system condition, C11: Construction

costs, C17: Value-added tax exemption, C18: Tariffs

exemption, C19: Tax discounts, C20: The support of

social insurance (employer ration), C21: The

discount of income tax stoppage, C22: The support

of social insurance, C23: Support for interest

payment, C25: The repayment of value-added tax

Note 2: Crt.: Criteria, w

: fuzzy weights, Triangular

Membership Function defined by three main

parameters. l, u and m mean the lower bound, the

upper bound and mean, respectively (Tavakkoli-

Moghaddam, 2008).

The results related to fuzzy TOPSIS method are

presented in Table 3. The distance of each

alternative to Fuzzy Positive Ideal Solution (d*) and

Fuzzy Negative Ideal Solution (d

) and closure

coefficients of the alternatives (CC) are indicated

that A

is the best location for a possible second

airport in Ankara. Alternatives are ranked from the

best to worst A

, A

, and A

respectively for

the selection of potential airport.

Table 3: The Result of Fuzzy TOPSIS Method.

Alternatives d* d

CC Ranking

12,805 15,215 0,543 1

13,516 14,54 0,518 2

16,346 11,399 0,411 4

16,648 11,205 0,402 5

16,206 11,648 0,418 3

Table 4 indicates that the result of fuzzy

ELECTRE I method has as same ranking as the

result of fuzzy TOPSIS method. Considering

concordance and discordance values, alternatives are

ranked from the best to the worst. Likewise, we can

conclude that A

is the best location for second

airport; on the other hand, A

, A

and A

are less

suitable locations than A

. Finally, decision graph of

fuzzy ELECTRE I method is depicted in figure 1.

Table 4: The Result of Fuzzy ELECTRE I Method.

Fuzzy ELECTRE I

Alternatives Ranking

4 1

3 2

1 3

0 4

Figure 1: Decision Graph of fuzzy ELECTRE I.

6 CONCLUSIONS

Facility location selection problem is the one of the

most important decision among strategic decisions

for a company. Generally, a mistaken investment

decision about facility location can cause much more

loss than expectations. Not only does it affect

financial structure of a company but also future

investment opportunities may be affected by this

failure. Therefore, a vast number of methods have

been developed to solve facility location selection

problem. Subjective factors usually give rise to



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uncertainty and vagueness in decision making

process. MCDM can help decision-makers to

overcome the uncertainty and the vagueness of

subjective factors.

In this study, we present fuzzy TOPSIS and

fuzzy ELECTRE I methods to cope with facility

location selection problem for a possible second

airport in Ankara. With the view of experts in

aviation sector and comprehensive literature review,

nine main criteria (geographical specifications,

climatic conditions, infrastructure conditions, costs,

transportation, possibility of extension, legal

restrictions and regulations, potential demand,

environmental and social effects) are determined to

analyze with fuzzy TOPSIS and fuzzy ELECTRE I.

Fuzzy TOPSIS and fuzzy ELECTRE I resemble

each other when converting linguistic values into

performance ratings and evaluating the weight of

criteria. On the other hand, fuzzy ELECTRE I aims

to select a single action among a small set of good

actions, fuzzy TOPSIS purposes the selection of a

complete or partial order of the actions. According

to fuzzy TOPSIS method, location A

was

determined as the top compromising solution. In this

context, it can be proposed that selecting location A

is the best decision for fuzzy TOPSIS method.

According to the ranking order of other alternatives

is A

. Both fuzzy TOPSIS and fuzzy

ELECTRE I methods suggest very similar solution

to facility location problem for second airport in

Ankara. According to fuzzy ELECTRE I method,

alternatives are ranked as A

Even though facility location selection problem

is so crucial investment decision for a company,

there are a few numbers of studies about aviation

sector. Therefore, this study aims to indicate how

fuzzy TOPSIS and fuzzy ELECTRE I can be used

for facility location selection problem in aviation

sector. Indeed, both methods can be applied in other

sectors like textile, electronics, manufacturing, retail,

logistics etc. in future studies. Also, other MCDM

(fuzzy AHP, fuzzy ANP, fuzzy PROMETHEE etc.)

can be used to solve facility location selection

problems.

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