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Iranian Journal of Fuzzy Systems
Volume 17, Number 6, (2020), pp. 57-74
A combination risk-based approach to post-earthquake temporary
accommodation site selection: A case study in Iran
M. Dabiri1, M. Oghabi2, H. Sarvari3, M. S. Sabeti4and H. R. Kashefi5
1Department of Civil Engineering, Sanandaj Branch, Islamic Azad University, Sanandaj, Iran
2Department of Civil Engineering, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran
3Department of Civil Engineering, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran
4Department of Civil Engineering, Sanandaj Branch, Islamic Azad University, Kurdistan, Iran
5Department of Mathematics Education, Farhangian University, Tehran, Iran
jalilialvand123@gmail.com, m.oghabi@iauksh.ac.ir, h.sarvari@khuisf.ac.ir, mssabeti@iausdj.ac.ir, hkashefi@cfu.ac.ir
Abstract
One of the most important problems after natural disasters in every country is the preparation of temporary accom-
modations for victims. The developers of preventive plans are also faced with numerous uncertainties in this crisis
management topic. Furthermore, uncertainty is not defined in classical mathematical sets. Therefore, the use of in-
tuitionistic fuzzy sets, which include considerations for uncertainty, can be useful in prospective planning in order to
counteract possible risks. The main aim of this study is to propose a combined method using risk management and
Intuitionistic Fuzzy Analytic Hierarchy Process (IF-AHP) for locating and prioritizing the post-earthquake temporary
accommodation sites. To this end, the city of Sanandaj in Iran was selected as the case study of this method. First,
brainstorming sessions with 9 crisis management experts from various organizations of Kurdistan province were used
to determine 6 decision-making criteria. These criteria were based on identified risks in temporary accommodation
process after an earthquake in the region, and criteria extracted from previous studies regarding temporary accommo-
dation locations. The possible alternatives for temporary accommodation sites in this study were 13 different urban
public spaces. The pairwise comparison of criteria based on the aim and pairwise comparison of alternative temporary
accommodation options based on each criterion was carried out by experts and using intuitionistic fuzzy sets. Finally,
the IF-AHP process was used to determine the priority of each alternative.
Keywords: Temporary accommodation, risk management, intuitionistic fuzzy sets, AHP, Iran.
1 Introduction
In recent decades, the effects of disasters have raised rapidly around the world, and have affected all sectors, in both
rich and poor countries. Millions of people are affected annually by disasters, and losses were recorded at 371 billion
in 2012. This average has increased in recent years according to the United Nations International Strategy for Disaster
Reduction (UNISDR). These Natural disasters consist of floods, earthquakes, etc. [3]. The number of natural disasters
has increased sharply and has caused a great deal of damage to buildings. Many homes have been damaged and are
unusable, which threatens a large number of homeless people. Housing reconstruction programs play a determinative
role in disaster recovery, and providing temporary accommodation is an important step in these programs. This allows
the victims to have a private and safe place to return to their normal lives during the reconstruction of permanent
accommodations [13]. Temporary accommodation has always remained a major issue for the injured families after any
natural or man-made disaster [16]. Managing disaster risks can be improved by investing in methods for dealing with
changeable fundamental determinants [27]. Pervious experiences have shown that post-earthquake temporary accom-
modation process is one of the topics which always preoccupies managers in the field of crisis management. In this
Corresponding Author: H. Sarvari
Received: September 2019; Revised: May 2020; Accepted: June 2020.
58 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
regard, decision-making based on proven scientific theories and equations can improve the certainty and credibility of
the decisions. Therefore, the main goal of this study is to provide a combined method using risk management and
Intuitionistic Fuzzy Analytic Hierarchy Process (IF-AHP) for predicting suitable post-earthquake temporary accommo-
dation sites. The model proposed in this study attempts to combine current theories in the field of crisis management
and risk management, decision-making management and intuitionistic fuzzy sets in order to fill the gap in the literature
and previous studies. The use of these theories in the proposed combined model is due to several reasons; including:
(i) Providing temporary accomendations after earthquakes is one of the important processes in crisis management and
is always accompanied with a great deal of uncertainty. Therefore, in order to remove or reduce the risks of tempo-
rary accommodation process, it is necessary to use a preventive risk management plan. Identifying and evaluation of
risks and their effects in various temporary accomendation programs is one of the stages of crisis management after
earthquake disasters since most of these risks can be reduced to a controlled level through use of suitable strategies
[1], (ii) Due to the existence of numerous criteria for selection of proper location for temporary accomendation sites,
use of multivariable decision-making methods is necessary. During the process of multi-variable decision-making, pair-
wise comparison of options based on decision-making criteria and determination of relative priorities of these variables
requires the use of experts opinions. In this regard, use of methods such as Delphi approach or brainstorming can be
useful, (iii) The use intuitionistic fuzzy sets seem necessary in multi-criteria decision making in which, in addition to
the degree of membership and non-membership, the degree of uncertainty is another factor also considered. This is
due to the fact that a factor called hesitation or uncertainty is not defined in classical sets and even fuzzy sets. The
intuitionistic fuzzy set has shown certain advantages over fuzzy sets in managing of ambiguity and uncertainty [40].
Interval Valued Intuitionistic Fuzzy Set theory (IVIFS) is an effective and simple tool for creation of MultiAttribute
Group DecisionMaking (MAGDM) models. Furthermore, this method is useful for dealing with uncertainty in the
complex decision-making support systems [22]. In the current study, a combined model was applied for identification
and prioritization of post-earthquake temporary accomendation sites in the Sanandaj-Iran. The participants in the
Delphi panel included crisis management experts employed in 18 organizations of Kurdistan province. Some of the
identified risks in this stage included: Lack of desire among people for living in determined temporary accommodation
sites outside of the city limits; challenges related to hot and cold weather; challenge of waste disposal, snow and rain
challenge; trash disposal challenge; blocking of roads due to snow and rain and subsequent disruption in services dur-
ing winter; the outbreak of infectious diseases; challenges of wind and storm; unsittable positioning of the temporary
accommodation site and lack of attention to required criteria (including access to services, distance from fault lines and
flood paths, access to gas lines, etc.); and challenges related to provision of drinking water and health products. In the
current study, the risks were identified through comprehensive literature reviews and conducting a brainstorming session
with crisis management experts of Kurdistan province. As a result, Six criteria were selected as decision criteria for
post-earthquake temporary accommodation site selection. These criteria were then used to prioritize various locations
in the Sanandaj city using IF-AHP approach.
2 Literature review and research background
2.1 Literature review on temporary accommodation after the disaster
Temporary accommodation plays a key role in the disaster process. The creation and use of temporary sites at the
location of a disaster are used to accommodate victims during an emergency situation, and reconstruction and renovation
after disaster occurrence, until permanent accommodation is provided [18]. Temporary accommodation is a vital but
controversial part of disaster recovery. Disaster-stricken families who have lost their homes need a private and safe
place to do their daily activities as soon as possible after the disaster [23]. Typically, three types of accommodations
are required after a destructive earthquake in a crowded region: (i) Emergency accommodations that often include
tent, (ii) Temporary accommodations which are usually used for 1 to 2 years, (iii) Permanent accommodations or
permanent living spaces[15]. It is generally accepted that provision of emergency and temporary accommodations
after an earthquake uses a vast amount of resources in a short time[37]. The temporary accommodation problem,
medium-term accommodations and finally permanent accommodations of victims after earthquakes is one of the largest
challenges during disaster recovery and reconstruction [25]. According to disaster relief act of Japan, the maximum
allowed duration for use of temporary accommodations is 2 years. However, some victims use these accommodations
for more than 7 years, especially after the large earthquake of 2012 on Eastern Japan [37]. Design of temporary
accommodation sites should consider various factors to ensure than these accommodations can meet the needs of the
victims. Architecture and design must be part of the solution and not part of the problem and the process must start
years before the disaster, by using sufficient time and a multidisciplinary team including technical and humanities experts
(various engineers), production companies, etc. and not during the disaster itself [9]. In the study of post-disaster
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 59
temporary accommodation, Principles of Presentation, Design and Construction are used for design, construction,
and preparation of temporary accommodations with suitable characteristics including Quick availability, Using of local
resources and considering local standards in terms of location and service facilities, design of Temporary accommodations
for long-term housing needs, the ability to easily remove the site and maintain the environment after the duration of
temporary accommodations, preventive planning before the event, and aadopting a developed strategy for recovery and
reconstruction. Research findings on the decline in physical performance of residents of temporary accommodation after
the Great East Japan earthquake have shown that a poor living environment in temporary accommodations may have a
negative impact on the physical performance of individuals, especially the elderly [20]. In the article ”Towards Effective
Crisis Management in Egypt,” five suggestions were proposed as key steps for setting better disaster management routes
in Egypt [17] including Risk management; Damage management; Event control; Resource management; and Reducing
the impact of the crisis. A survey research on the selection of post-disaster temporary accommodation was carried out by
Anand et al. in 2015. This study examined various models for selecting post-disaster temporary rehabilitations. Each
of these methods provides selection criteria and minimum standards for handling the needs of the victims. The result
of this study shows that availability of basic services such as health centers, transportation, and livelihoods are major
concerns when site is chosen for temporary accommodations [4]. In a research entitled ”Temporary accommodation
site in earthquake crisis using AHP and Geographic Information System”, the criteria for temporary accommodation
are divided into three categories of the physical, social and environmental criteria, and have been used in the process
of finding temporary accommodation sites, using AHP and GIS, according to the weight and importance of the criteria
mentioned [12]. Another article titled ”The role of temporary accommodation buildings for post-disaster housing
reconstruction” investigated the cultural and environmental challenges of the temporary accommodation settlements,
and mentioned that the key to reducing the vulnerability of the victims is the prediction of temporary accommodation
before the occurrence of the crisis. To this end, using existing places with permanent infrastructure near the initial
location of victims has been suggested [14]. Site selection criteria for temporary accommodations after the earthquake
was carried out using Delphi Panel by Soltani et al. in 2015 to provide a list of appropriate criteria for deciding on the
choice of a temporary accommodation site. To determine the criteria, three methods were used including examining
previous studies, conducting interviews with the experts and performing a Delphi Panel. Finally, the main criteria to
select a temporary accommodation site were categorized in four sections consisting of land suitability, social and cultural
considerations, availability to services and disaster risk reduction [38]. The previous studies on crisis management and
temporary accommodation, and how they are carried out, are presented in Table 2.
2.2 Research background
2.2.1 Crisis management
Crisis management is a set of pre-designed processes which are implemented and applied to prevent or reduce the
effects, during pre-occurrence, occurrence and post-occurrence of disasters [26]. Crisis management consists of three
stages of Pre-crisis step (prevention and preparation), crisis step (reaction) and post-crisis step (learning and revision)
[10]. Crisis Management is a multidisciplinary subject that includes many sciences including social sciences, foreign
sciences, medicine, engineering, and many other disciplines which are used for investigation of major unpredictable
events [7].
2.2.2 Risk management
Risk management in a project consists of the risk management planning processes, identification, analysis, response
planning, and risk control in a project. Increasing the likelihood and impact of positive events and reducing the
likelihood and impact of negative events is one of the objectives of the risk management in a project [35].
The process of risk management in projects is a logical chain of methods, planned and implemented by decision
makers, which control the results to maintain project implementation under certain conditions (Time, cost, and quality
parameters) [32].
Risk management is about identification of risks that are imminent. Identifying and designing measures for reducing
risk consists of identifying possible risks, determining the occurrence probability of each risk, and estimating the extent
of risk effects in communities. One of the risk management processes is Implementation of these measures and reducing
the threats [17].
60 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
Table 1: Studies conducted related to the topic of research
No Author/s Issue Method
1 [38] provide a list of appropriate criteria for
deciding on the choice of a temporary
accommodation site
(i) Extracting 27 criteria to select accomendation site
provided by reviewing issued articles, (ii) Identifica-
tion of 12 other criteria during the interview process
with experts, (iii) Approval of 21 criteria during the
Delphi process, (iv) Categorizing criteria for selecting
temporary accommodation in four sections: Land suit-
ability, Social and cultural considerations, availability
to services and reduce disaster risk
2 [17] Post-disaster temporary accommoda-
tion site: Principles of presentation,
design and constructing, the review
of a set of guidelines for designing
and construction a successful and high
quality, and at the same time, sensitiv-
ity to controversial issues in addition to
saving the costs and time
(i) Analyzing and reviewing the briefs, (ii) Matching
the executed cases with briefs, (iii) Providing the nec-
essary suggestions for designing and constructing of a
temporary accommodation site
3 [24] Temporary accommodation site locat-
ing after earthquake: one case for
Turkey
(i) Reviewing some cases of past actions in tempo-
rary accommodation, (ii) determinating of the locat-
ing metrics, (iii) Compilation of a linear program for
optimal location, (iv) Testing the compiled program
4 [31] Urban vulnerability assessment using
AHP in 19 Qazvin areas
(i) Determination of three main criteria and 20 sub-
criteria, (ii) Using questionnaire, (iii) Using AHP
method for prioritization of urban vulnerability fac-
tors
5 [5] Proposing a model for the post-
disaster design in temporary accom-
modation based on the needs of the
victims with the post-implementation
evaluation approach (Case study: Seis-
mic villages in Harris, East Azarbai-
jan)
(i) Different methods of documentary and library, (ii)
Field studies through interviews and questionnaires
6 [12] Presenting a Method Using AHP and
Geographic Information System (Case
Study: Damavand Area)
(i) Using Geographic Information System (GIS) , (ii)
Using ARCMAP software, (iii) Propagating maps with
three factors: faults, earthquakes and soil resistance,
(iv) Using the AHP model, (v) Data was collected by
library methods and field studies.
7 [19] Providing a multi-criteria decision-
making method for locating post-
disaster temporary accommodation in
urban areas
(i) Documentary studies, (ii) Logical studies, (iii)
Knowledge of Experts Participating in the Seminar,
(iv) SWOT approach, (v) AHP model, (vi) Design and
application (medal app)
8 [18] Exploring ways to better manage nat-
ural disasters in Egypt
(i) Identifying the various types of natural disasters
that Egypt is vulnerable to them, (ii) A general pic-
ture of the crisis management problems in Egypt, (iii)
Providing a set of briefs, a solution to the crisis man-
agement problem in Egypt, (iv) investigating a set of
considerations to ensure the correct implementation of
the briefs.
9 [20] Investigating the Length of Physical
Operation of Residents in Temporary
accommodation sites, after earthquake
in Great East Japan
(i) Implementation of physical performance tests on
residents in site and temporary accommodation con-
trol group by physiotherapists, (ii) Comparing the re-
sults of the tests performed on these two groups
10 [29] Searching the best practices for post-
disaster sustainable temporary accom-
modation that have features such as:
being cheap, fast built, maintaining en-
vironmental and social issues, paying
attention to the weather conditions of
the place and paying attention to all
needs of the victims.
(i) Documentary study of natural disasters occurring
in the world and the extraction of the statistics of
the refugees and casualties caused by the incident, (ii)
Extracting the various social and economic damages
of each of these events, (iii) Investigating the type of
structure used in previous natural disasters, and the
advantages and disadvantages each one, (iv) Investi-
gating the challenges that have occurred accommoda-
tion process in the past
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 61
Table 2: Relative risk ranking of the earthquake in the Kurdistan Provincial Demographic Centers according to Iran’s 2800
Code
No. Demographic Center Relative earthquake risk
Low Medium High Very High
1 Baneh *
2 Bijar *
3 Dehglan *
4 Divandareh *
5 Saghez *
6 Sav aabad *
7 Sanandaj *
8 Gharaveh *
9 Kamyaran *
10 Marivan *
2.2.3 Multi-criteria decision making
Description of criteria and gathering of descriptive information are two important uses of MCGDM for prioritizing
various considered options [30]. Multi-Criteria Decision Making (MCDM) is a process which allows decision-making
using numerous and sometimes contradicting criteria. MCDM topics can be divided into two main categories: (i)
Multi-Attribute Decision Making (MADM): This method is focused on selecting the best option among the predeter-
mined options, (ii) Multi-Objective Decision Making (MODM): This method includes design of alternative options for
optimization of multiple decision-making objectives.
2.2.4 Area of the study
The city studied in this study was Sanandaj, the capital of Kurdistan province in Iran (Figure 1). Kurdistan province
is located in the northwestern part of Iran. Iran is located in the alpine-Himalayan seismic belt and is one of the most
active tectonic areas in the world. Historically, this country often suffers from large and destructive earthquakes, and
has experienced several major earthquakes in the last few decades. More than 70 percent of Iran’s major cities are
located near seismic faults. In some cases, active faults cross the cities [21]. Regulations for the Design of Buildings
against earthquakes [8] divide Iran into four parts in terms of seismic risk which include relatively low, moderate, high,
and very high-risk areas (Table 1). According to this standard, Sanandaj is located in high risk area of earthquakes.
Figure 1: Location of Kurdistan Province and Sanandaj City in Iran.
3 Research methodology
This research is a descriptive-applied study, which used documentary methods, interview and holding a storm meeting
for data collection. In the documentary study, previous studies on the process of post-earthquake temporary accommo-
dation in Iran and the world have been investigated. Furthermore, in this section, geographic conditions, topographic
62 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
conditions, population amount, places and the existing infrastructure of Sanandaj were studied. In this study, the
combination of risk management and intuitionistic Fuzzy Analytic Hierarchy Process (IF-AHP) has been used to locate
the post-earthquake temporary accommodation site. This paper is part of a research carried out by the authors which
identified the risks involved in the temporary accommodation process in its previous sections, and has prioritized 94
identified risks in its results including Lack of desire among people for living in determined temporary accommodation
sites outside of the city limits; challenges related to hot and cold weather; challenge of waste disposal, snow and rain
challenge; trash disposal challenge; blocking of roads due to snow and rain and subsequent disruption in services during
winter; the outbreak of infectious diseases; challenges of wind and storm; unsittable positioning of the temporary accom-
modation site and lack of attention to required criteria (including access to services, distance from fault lines and flood
paths, access to gas lines, etc.); and challenges related to provision of drinking water and health products. These risks
were combined in a brainstorming session with crisis management experts of Kurdistan province until 6 criteria were
selected including the existence of infrastructure, proper availability, distance from fault lines and flood paths and other
natural hazards, appropriate land gradient, proximity to service centers, and capacity for receiving victims, in order to
locate and prioritize the existing locations in Sanandaj for temporary accommodation sites. In this research, the Fuzzy
Delphi method was also used to identify the risks of temporary accommodation, and the questionnaire was completed
by specialists and experts in the field of crisis management in Kurdistan, which consists of 18 departments and organi-
zations. The challenge of people’s disclination to reside in established sites of temporary out-of-town accommodation
has been introduced as a risk in this process. Furthermore, due to the mountainous conditions of the surrounding
studied area, this study attempts to use the existing urban spatial areas that were previously considered by the crisis
management authorities to accommodate emergency situations. If these predetermined sites met the necessary condi-
tions, they were used for temporary accommodation after a short period of emergency accommodation. To summarize
the comments, in order to select the appropriate criteria for determination of the available alternatives determining the
weight against each option, and also the weight of the Alternatives against the criteria, the brainstorming session was
conducted with 9 specialists and experts in the field of crisis management in Kurdistan province. Figure 2 shows the
schematic illustration of research methodology for this research.
3.1 Analytic Hierarchy Process (AHP)
The Analytic Hierarchy Process (AHP) was first introduced by Saaty [33]. AHP is a measurement theory through
dual comparisons and depends on the judgment of the experts to obtain prioritization scales [34]. Some key steps in
this approach are [39]: (i) Statement of the problem, (ii) Expanding the goals of the problem or considering all the
actors, goals and their consequences, (iii) Identifying effective criteria for decision making, (iv) Creating the hierarchy
structure of the problem consisting of different levels of purpose, criteria, sub-criteria, and alternatives, (v) Comparing
each element at the corresponding level and calibrating them on a numerical scale. This requires n (n-1)/2 comparisons,
where n is the number of elements with case of comparison. The diagonal elements equal 1, or other elements are simply
intertwined with previous values, (iv) Calculating the maximum specific values consisting of compatibility index, CI,
compatibility ratio, CR and normalized values for each criterion/option, and (vii) If the maximum Eigen value, CI and
CR are satisfactory, the decision is made on the basis of normal values. Otherwise, this method will be repeated until
the values are within the desired range.
3.2 Introducing intuitionistic fuzzy sets
In the classical logic of mathematics, the value or correctness of a proposition is defined with 1 as true and zero as false.
Zadeh introduced fuzzy sets for the first time [41]. In fuzzy logic, the accuracy value is a real number which is selected
from the range of [0, 1]. Atanassov added, another real number in the range [0, 1] entitled ”Degree of non-accuracy” to
this definition in the presentation of intuitionistic fuzzy sets [6]. Therefore, two values of ν(p) and µ(p) are attributed
to the proposition p, such that: ν(p) + µ(p)≤1. An intuitionistic Fuzzy set of A in the reference set X is defined as
follows:
A={hx, µA(x), νA(x)i|x∈X}
µA:X−→ [0,1]
νA:X−→ [0,1]
∀x∈X: 0 ≤µA(x) + νA(x)≤1.
The real values of µA(x) and νA(x) are the degree of membership and the degree of non-membership of x to A, which
belongs to the interval [0, 1]. Each set A’, is a special case of intuitionistic fuzzy sets and can be represented as an
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 63
Figure 2: Schematic illustration of research methodology.
intuitionistic fuzzy set A’ [28]. For each intuitionistic fuzzy set, A’ from X, we have:
A0=0{hx, µA0(x),1−µA0(x)i|x∈X},
πA0(x):1−µA0(x)−νA0(x).
πA0(x), is called the intuitionistic index xin A0. In fact, this is the degree of xhesitancy in A0. Clearly, for each x
belonging to X, we have: 0 ≤πA0(x)≤1. In each fuzzy set of A0from Xwe have:
∀x∈X:πA0(x) = 1 −µA0(x)−[1 −µA0(x)] = 0.
The sum of the multiplication of two intuitionistic fuzzy sets is in accordance with formulas 1 and 2 [40], [11].
rtl = (µtl, vtl ), rik = (µik, vik ),
n= 1,2,3,· · · , k = 1,2,3,· · · .
degree of membership = µik,
degree of non-membership = νik,
degree of uncertainly = πik.
rik ⊕rtl = (µik +µtl −µikµtl , vikvtl ),(1)
rik ⊗rtl = (µikµtl , vik +vtl −vikvtl ).(2)
4 Intuitionistic fuzzy analytic Hierarchy
The purpose of this example is to prioritize available places in Sanandaj to determine the best post-earthquake temporary
accommodation site.
64 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
Table 3: Examined alternatives table for locating and prioritizing the temporary accommodation site
No. Site Name Area (hectare) Useful Area (hectare) Moderate slope (percent) Available facilities Capacity (preson)
Water Electricity W.C
1 A1 81 63.2 15 Yes Yes Yes 21067
2 A2 10 10 4 Yes Yes Yes 3333
3 A3 17.6 14.3 12 No No No 4767
4 A4 0.95 0.96 1 Yes Yes Yes 320
5 A5 7.6 6.4 9 Yes Yes Yes 2133
6 A6 8.4 7.2 11 Yes Yes Yes 2400
7 A7 70 57.4 13 No No No 19133
8 A8 18.5 16.3 10 No No No 5433
9 A9 6.5 6 4 Yes Yes No 2000
10 A10 26 25.5 4 No No No 8500
11 A11 3.3 3 4 Yes Yes Yes 1000
12 A12 4.25 3.4 14 Yes Yes Yes 1133
13 A13 3.7 2.7 18 Yes Yes Yes 900
4.1 Recognizing the effective criteria for multi-criteria decision making
In this study, six criteria are considered, including (i) Distance from fault lines, flood paths and other natural hazards,
(ii) Appropriate ground gradient, (iii) Existence of necessary infrastructure, (iv) Availability, (v) Proximity to service
centers, and (vi) Admission Capacity. These 6 criteria were used to rank places in Sanandaj to determine the best site
of temporary accommodation. Specifications of the places examined in this research are as shown in Table 3.
4.2 Formation of decision-making structure
The overall decision-making structure in this example consists of three levels of goals, criteria and alternatives (Fogure
3). Often the set of criteria is presented with C={C1, C2, C3,· · · , Cn}and the set of Alternatives or available methods
for prioritize is presented with A={A1, A2, A3,· · · , An}.
Figure 3: The multicriteria decision-making structure (IF-AHP) of the study .
4.3 Determining the intuitionistic fuzzy linguistic variables to pairwise comparison
Since difference in linguistic variables used by different individuals might lead to different interpretations, in this study,
in order to create a unify procedure in evaluating experts opinions regarding the importance of each criterion compared
to others, intuitionistic fuzzy linguistic variables (µA, νA) are used. Here, µAis the degree of membership and νAis the
degree of non-membership. Table 4 shows the intuitionistic fuzzy linguistic variables used for pairwise comparisons.
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 65
Table 4: Intuitionistic fuzzy linguistic variables for determining the priority in pairwise comparison
Scale Variables
(0.00 , 1.00) Absolutely low importance
(0.05 , 0.90) Very very low importance
(0.10 , 0.80) Very low importance
(0.20 , 0.70) Low importance
(0.30 , 0.60) Slightly low importance
(0.50 , 0.50) Equally importance
(0.60 , 0.30) Slightly high importance
(0.70 0.20) High importance
(0.80 0.10) Very high importance
(0.90 0.05) Very very high importance
(1.00 0.00) Absolutely high importance
Table 5: The pairwise comparison matrix of criteria
Staying far
from faults,
streams and
other natural
hazards
Appropriate
ground gradien
Existence
of necessary
infrastructure
Availability Proximity to
service centers
Admission Ca-
pacity
Staying far from faults,
streams and other nat-
ural hazards
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7) (0.5 , 0.5)
Appropriate ground
gradient
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7)
Existence of necessary
infrastructure
(0.2 , 0.7) (0.7 , 0.2) (0.5 , 0.5) (0.5 , 0.5) (0.5 , 0.5) (0.5 , 0.5)
Availability (0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.5 , 0.5) (0.7 , 0.2) (0.7 , 0.2)
Proximity to service
centers
(0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.2 , 0.7) (0.5 , 0.5) (0.7 , 0.2)
Admission Capacity (0.5 , 0.5) (0.7 , 0.2) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.5 , 0.5)
4.4 Determination of intuitionistic fuzzy linguistic variables for pairwise comparison of
options
Intuitionistic fuzzy linguistic variables used to determine the pairwise comparison of options for each criterion in this
study are presented in Table 4.
4.5 Formation of matrix the importance of criteria paired with each other
Pairwise comparison of criteria based on intuitionistic fuzzy linguistic variables ( µA, νA) carried out in a brainstorming
session with 9 disaster management experts and according to regional conditions and the results are presented in Table
5.
rik = (µik, vik )
n= 1,2,3,· · · , k = 1,2,3,· · ·
Degree of membership =µik
Degree of non-membership = vik
4.6 Formation of preferential - paired relationship alternatives with the criteria
The pairwise priority relation matrices of options based on criteria, determined based on the values presented in Table
4 by experts are presented in Appendixes 1 - 6.
66 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
Table 6: Matrix R (Relationship of the importance of the criteria paired with each other)
Staying far
from faults,
streams and
other natural
hazards
Appropriate
ground gradi-
ent
Existence
of necessary
infrastructure
Availability Proximity to
service centers
Admission Ca-
pacity
Staying far from faults,
streams and other nat-
ural hazards
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7) (0.5 , 0.5)
Appropriate ground
gradient
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7) (0.2 , 0.7)
Existence of necessary
infrastructure
(0.2 , 0.7) (0.7 , 0.2) (0.5 , 0.5) (0.5 , 0.5) (0.5 , 0.5) (0.5 , 0.5)
Availability (0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.5 , 0.5) (0.7 , 0.2) (0.7 , 0.2)
Proximity to service
centers
(0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.2 , 0.7) (0.5 , 0.5) (0.7 , 0.2)
Admission Capacity (0.5 , 0.5) (0.7 , 0.2) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.5 , 0.5)
4.7 Investigating the compatibility of matrix, the importance of criterion paired- intu-
itionistic with each other
4.7.1 Formation of matrix R (Relationship of the importance of the criteria paired with each other)
[40]
. The pairwise comparison of the criteria was calculated based on the results of the brainstorm panel and intuitionistic
fuzzy verbal variables (Table 4). The results have been shown in Table 6.
4.7.2 Forming matrix R
In order to determine the memberships and non-membership degrees in this matrix, the following equations can be
used [40]
µik =
k−i−1
qΠk−1
t=i+1µit µtk
k−i−1
qΠk−1
t=i+1µit µtk +k−i−1
qΠk−1
t=i+1(1 −µit )(1 −µtk)
k > i + 1,(3)
vik =
k−i−1
qΠk−1
t=i+1vit vtk
k−i−1
qΠk−1
t=i+1vit vtk +k−i−1
qΠk−1
t=i+1(1 −vit )(1 −vtk)
k > i + 1.(4)
In order to carry out the pairwise comparison of the criteria, intuitionistic fuzzy linguistic variables were calculated
based on formulas (3) and (4). The results of Matrix Rare presented in Table 7.
4.7.3 Calculating the distance between matrix Rand matrix R [40]
d(R−R) = 1
2(n−1)(n−2)
n
X
i=1
n
X
k=1
|µik −µtl|+|vik −vtl |+|πik −πtl|,(5)
(R−R) = 1
2(6 −1)(6 −2)(0.6463 + 0.6463 + 1.2926) = 0.0646
After calculating this gap, we will have: d(R−R)=0.0646
Since the distance between R
.and Ris less than 0.10, it is possible to move to the next step without revising the
pairwise comparison matrix created in this step [36], [40].
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 67
Table 7: Matrix R
Matrix RStaying far
from faults,
streams and
other natural
hazards
Appropriate
ground gradi-
ent
Existence
of necessary
infrastructure
Availability Proximity to
service centers
Admission Ca-
pacity
Staying far from faults,
streams and other nat-
ural hazards
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.249 , 0.595) (0.276 , 0.538)
Appropriate ground
gradient
(0.5 , 0.5) (0.5 , 0.5) (0.2 , 0.7) (0.2 , 0.7) (0.276 , 0.529) (0.305 , 0.481)
Existence of necessary
infrastructure
(0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.5 , 0.5) (0.7 , 0.2) (0.7 , 0.2)
Availability (0.7 , 0.2) (0.7 , 0.2) (0.5 , 0.5) (0.5 0.5) (0.7 , 0.2) (0.849 , 0.059)
Proximity to service
centers
(0.595 , 0.249) (0.529 , 0.276) (0.2 , 0.7) (0.2 , 0.7) (0.5 0.5) (0.7 , 0.2)
Admission Capacity (0.538 , 0.276) (0.481 , 0.305) (0.2 , 0.7) (0.059 , 0.845) (0.2 , 0.7) (0.5 0.5)
4.8 Calculating weight of criteria and Alternatives in an intuitionistic fuzzy environ-
ment
The following formula can be used to calculate the weight of criteria and Alternatives [40] Therefore, the weight of
criteria were calculated based on formula (6) and the results are presented in Table 8.
Table 8: The weight of criteria with each other
1∗2∗3∗4∗5∗6∗wj
C1C2C3C4C5C6
µAνAµAνAµAνAµAνAµAνAµAνAµAνA
Staying far
from faults,
streams and
other natural
hazards
C10.5 0.5 0.5 0.5 0.2 0.7 0.2 0.7 0.249 0.595 0.276 0.538 0.098 0.849
Appropriate
ground gradi-
ent
C20.5 0.5 0.5 0.5 0.2 0.7 0.2 0.7 0.277 0.529 0.305 0.481 0.101 0.842
Existence
of necessary
infrastructure
C30.7 0.2 0.7 0.2 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.193 0.743
Availability C40.7 0.2 0.7 0.2 0.5 0.5 0.5 0.5 0.7 0.2 0.845 0.059 0.201 0.734
Proximity
to service
centers
C50.595 0.249 0.529 0.276 0.2 0.7 0.2 0.7 0.5 0.5 0.7 0.2 0.139 0.794
Admission
Capacity
C60.538 0.276 0.481 0.305 0.2 0.7 0.059 0.845 0.2 0.7 0.5 0.5 0.101 0.836
1∗: Staying far from faults, streams and other natural hazards.
2∗: Appropriate ground gradient.
3∗: Existence of necessary infrastructure.
4∗: Availability.
5∗: Proximity to service centers.
6∗: Admission Capacity.
ωi= ( Pn
k=1 µik
Pn
i=1 Pn
k=1(1 −vik ),1−Pn
k=1(1 −vik )
Pn
i=1 Pn
k=1 µik
).(6)
For example, in order to calculate the weight for C1 (Distance from fault lines, flood paths and other natural hazards)
we have:
68 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
ω1= ( P6
k=1 µik
P6
i=1 P6
k=1(1 −vik ),1−P6
k=1(1 −vik )
P6
i=1 P6
k=1 µik
)
ω1= ( 1.9254
4.0746 + 4.0182 + 2.2+2.0552 + 3.2763 + 4.022 ,
1−2.4665
3.5335 + 3.4094 + 1.8+1.6588 + 2.6254 + 3.3266 )
ω1= ( 1.9254
19.6463,1−2.4665
16.3537)
ω1= (0.0980,0.8492).
In order to calculate the weight of alternatives according to each criterion, fuzzy numbers presented in Apendixes 1-6
as well as equation (6) are used. For example, in order to calculate the alternatives weights in regards to C1 (Distance
from fault lines, flood paths and other natural hazards), the intuitionistic fuzzy numbers of table 4 and equation (6)
are used. These results are presented in Table 9.
Table 9: The weight of alternatives in regard to criterion (distance from fault lines, flood paths and other natural hazards)
Criterion C1Pn
k=1 µik Pn
k=1(1 −vik )Pn
i=1 Pn
k=1(1 −vik )Pn
i=1 Pn
k=1 µik ωi
Pn
k=1 µik
Pn
i=1 Pn
k=1(1 −vik )1−
Pn
k=1(1 −vik )
Pn
i=1 Pn
k=1 µik
A1 5.3 8.1 88.8 80.2 0.0822 0.8990
A2 5.3 8.1 88.8 80.2 0.0822 0.8990
A3 7.3 8.1 88.8 80.2 0.0822 0.8990
A4 5.5 8.1 88.8 80.2 0.0822 0.8990
A5 5.5 6.6 88.8 80.2 0.0653 0.9177
A6 5.5 5.9 88.8 80.2 0.0597 0.9264
A7 5.5 5.9 88.8 80.2 0.0597 0.9264
A8 5.3 5.9 88.8 80.2 0.0597 0.9264
A9 5.3 8.1 88.8 80.2 0.0822 0.8990
A10 7.3 6 88.8 80.2 0.0619 0.9252
A11 5.5 6 88.8 80.2 0.0619 0.9252
A12 5.5 6 88.8 80.2 0.0619 0.9252
A13 5.5 6 88.8 80.2 0.0619 0.9252
Table 10 shows the results of pairwise comparison calculations for all alternatives for each criterion.
4.9 Final weights of research criteria and alternatives
Equation (7) is used to calculate the final weight of each alternative based on intuitionistic fuzzy set [40]:
wi=⊕6
j=1(wj⊗wij ) (7)
To calculate equation (7) requires the use of equations (1) and (2) [40], [11]. An example of calculations for alternative
1 is shown below:
w1=⊕6
j=1(wj⊗w1j)
= (0.0980,0.8492) ⊗(0.822,0.899) ⊕(0.1009,0.8416) ⊗(0.211,0.9659)
⊕(0.1934,0.7432) ⊗(0.0813,0.9033) ⊕(0.2008,0.7345) ⊗(0.0866,0.8965)
⊕(0.1386,0.7936) ⊗(0.0836,0.8953) ⊕(0.1007,0.8365) ⊗(0.1036,0.871)
= (0.654,0.8896).
Table 11 shows the final weignts of alternatives and criteria.
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 69
Table 10: The weight calculation for each alternative based on criteria
Alternative 1∗2∗3∗4∗5∗6∗
C1C2C3C4C5C6
A1 0.0822 0.899 0.0211 0.9659 0.0813 0.9033 0.0866 0.8965 0.0836 0.8953 0.1036 0.871
A2 0.0822 0.899 0.1036 0.8762 0.0813 0.9033 0.0681 0.9245 0.0836 0.8953 0.0634 0.9208
A3 0.0822 0.899 0.0581 0.9267 0.0601 0.9207 0.0785 0.9135 0.0836 0.8953 0.0691 0.9144
A4 0.0822 0.899 0.0939 0.8907 0.0813 0.9033 0.0681 0.9245 0.0635 0.9193 0.0351 0.9489
A5 0.0653 0.9177 0.0581 0.9267 0.0813 0.9033 0.0681 0.9245 0.0836 0.8953 0.0634 0.9208
A6 0.0597 0.9264 0.0717 0.9154 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144
A7 0.0597 0.9264 0.0581 0.9267 0.0445 0.938 0.0855 0.8989 0.0424 0.9382 0.0991 0.8761
A8 0.0597 0.9264 0.0615 0.9217 0.0445 0.938 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144
A9 0.0822 0.899 0.1002 0.8812 0.0579 0.9219 0.0704 0.9233 0.0836 0.8953 0.0691 0.9144
A10 0.0619 0.9252 0.1002 0.8812 0.0412 0.9418 0.0704 0.9233 0.0424 0.9382 0.0895 0.8838
A11 0.0619 0.9252 0.1002 0.8812 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0521 0.9298
A12 0.0619 0.9252 0.0535 0.9305 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144
A13 0.0619 0.9252 0.0211 0.9659 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0351 0.9489
1∗: Staying far from faults, streams and other natural hazards.
2∗: Appropriate ground gradient.
3∗: Existence of necessary infrastructure.
4∗: Availability.
5∗: Proximity to service centers.
6∗: Admission Capacity.
Table 11: The weight calculation for each alternative based on criteria
1∗2∗3∗4∗5∗6∗wj
C1C2C3C4C5C6
µAνAµAνAµAνAµAνAµAνAµAνAµAνA
0.0980 0.8492 0.1009 0.8416 0.1934 0.7432 0.2008 0.7345 0.1386 0.7936 0.1007 0.8365
A1 0.0822 0.899 0.0211 0.9659 0.0813 0.9033 0.0866 0.8965 0.0836 0.8953 0.1036 0.871 0.0654 0.8896
A2 0.0822 0.899 0.1036 0.8762 0.0813 0.9033 0.0681 0.9245 0.0836 0.8953 0.0634 0.9208 0.0659 0.8909
A3 0.0822 0.899 0.0581 0.9267 0.0601 0.9207 0.0785 0.9135 0.0836 0.8953 0.0691 0.9144 0.0599 0.8988
A4 0.0822 0.899 0.0939 0.8907 0.0813 0.9033 0.0681 0.9245 0.0635 0.9193 0.0351 0.9489 0.0592 0.9016
A5 0.0653 0.9177 0.0581 0.9267 0.0813 0.9033 0.0681 0.9245 0.0836 0.8953 0.0634 0.9208 0.0596 0.9007
A6 0.0597 0.9264 0.0717 0.9154 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144 0.0586 0.9036
A7 0.0597 0.9264 0.0581 0.9267 0.0445 0.938 0.0855 0.8989 0.0424 0.9382 0.0991 0.8761 0.0532 0.9054
A8 0.0597 0.9264 0.0615 0.9217 0.0445 0.938 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144 0.0505 0.9128
A9 0.0822 0.899 0.1002 0.8812 0.0579 0.9219 0.0704 0.9233 0.0836 0.8953 0.0691 0.9144 0.0620 0.8948
A10 0.0619 0.9252 0.1002 0.8812 0.0412 0.9418 0.0704 0.9233 0.0424 0.9382 0.0895 0.8838 0.0531 0.9066
A11 0.0619 0.9252 0.1002 0.8812 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0521 0.9298 0.0600 0.9008
A12 0.0619 0.9252 0.0535 0.9305 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0691 0.9144 0.0570 0.9056
A13 0.0619 0.9252 0.0211 0.9659 0.0813 0.9033 0.0704 0.9233 0.0635 0.9193 0.0351 0.9489 0.0503 0.9160
1∗: Staying far from faults, streams and other natural hazards.
2∗: Appropriate ground gradient.
3∗: Existence of necessary infrastructure.
4∗: Availability.
5∗: Proximity to service centers.
6∗: Admission Capacity.
4.10 Prioritize temporary accommodation site based on intuitionistic fuzzy analytic
Hierarchy process
After the defuzzification of the final weights of alternatives in the process of selecting the intuitionistic fuzzy hierarchical
multi criteria, alternatives or locations are prioritized based on the final defuzzification weights for each location. In
this study, the geometrical average calculated using equation (8) is used for defuzzification of variables [2]:
(8) MG(µ, v) = pµ(1 −v).
70 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
Table 12: Prioritize alternatives for selecting temporary post-earthquake accommodation
Prioritized arrangement Option Defuzzification weights
1 A1 0.0850
2 A2 0.0848
3 A9 0.0808
4 A3 0.0779
5 A11 0.0772
6 A5 0.0769
7 A4 0.0763
8 A6 0.0752
9 A12 0.0733
10 A7 0.0710
11 A10 0.0704
12 A8 0.0663
13 A13 0.0650
For example, the final defuzzified weight of A1 alternative is calculated as follows:
MA1(µ, v) = p0.0654(1 −0.8896) = 0.085.
Table 12 shows the defuzzified weight of all options in the order of their priority.
5 Conclusions
Pairwise comparison of the criteria and alternatives based on each criterion is one of the main stipulations and steps of
the multi-criteria decision-making process. One of the important features of risk-based preventive planning for the post-
earthquake temporary accommodation process is the presence of multiple uncertainties. In fact, due to the nature of the
risk, a number of uncertainties will be added in the decision-making process. Given the fact that uncertainty factor is not
considered in the classical studies, using intuitionistic fuzzy sets can be very useful in multi-criteria planning and decision
making. In expert’s opinions, the result is more accurate in calculations and optimal selection, when taking into account
the three elements of degree of membership, the degree of non-membership, and degree of doubt and uncertainty. In this
study, the combination risk-based approach was applied to post-earthquake temporary accommodation site selection in
Sanandaj-Iran. The proposed model combines risk management and Intuitionistic Fuzzy Analytic Hierarchy Process
(IF-AHP). Some of the practical features of this approach include: (i) Ability to measure the compatibility between the
pairwise comparison of the criteria and therefore the judgment of the experts opinions regarding the importance of each
criterion with the intended goal; (ii) Participation of all organizations and departments involved in preventive decision-
making of crisis management (This is useful not only due to the use of various specializations and disciplines but also
due to improved cooperation between various crisis management elements); and (iii) Planning to respond to risks while
choosing a suitable location for the post-earthquake temporary accommodation (Given that the criteria for selecting a
location are determined by the expert in charge of the temporary accommodation process and based on the risks). The
decision-making included six criteria. These criteria were selected using the brainstorming method and were based on
opinions of crisis management experts of Kurdistan Province organizations. The criteria were determined by combining
the identified risks of the temporary accommodation process after the earthquake in the region and the location criteria.
In this study, 13 alternative locations were assessed for temporary accommodation after the earthquake. According to
the results of the IF-AHP approach, the top five options among the 13 alternatives for the post-earthquake temporary
accommodation site in the Sanandaj-Iran include: (i) The alternative A1 is known to be the most suitable site for the
post-earthquake temporary accommodation; (ii) The alternative A2 was recognized as the second-best alternative; (iii)
The alternative A9 is the third-best suitable place for the temporary accommodation site in Sanandaj; and (iv) The
alternative A3 and A11 were ranked fourth and fifth, respectively. It is worth mentioning that this prioritization is
carried out based on the stated criteria and their weights as calculated through agreement between crisis management
experts of Kurdistan province during this study and might be different for other regions or in studies using different
criteria. This is due to the fact that each region has its specific characteristics including climate, city structure, city
type, medical centers, etc. Therefore, while the authors believe that the presented method to be applicable and highly
recommend its application, it is recommended that the terms and conditions of the study area be carefully considered
when selecting criteria for selecting a temporary accommodation site.
A combination risk-based approach to post-earthquake temporary accommodation site selection . . . 71
Acknowledgement
The authors wish to express their appreciation for several excellent suggestions for improvements in this paper made
by the referees.
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6 Apendix
Table 13: Preferential - paired relationship Alternatives with criterion C1 (staying far from faults, streams and other
natural hazards)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A2 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A3 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A4 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A5 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A7 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A8 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A9 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A10 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A11 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A12 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A13 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Table 14: Preferential - paired relationship Alternatives with criterion C2 (Appropriate ground gradient)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.05 0.9 0.1 0.8 0.05 0.9 0.1 0.8 0.1 0.8 0.1 0.8 0.1 0.8 0.05 0.9 0.05 0.9 0.05 0.9 0.1 0.8 0.5 0.5
A2 0.9 0.05 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.8 0.1 0.8 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1 0.9 0.05
A3 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.8 0.1 0.8 0.1 0.8 0.5 0.5 0.8 0.1
A4 0.05 0.5 0.5 0.5 0.8 0.8 0.5 0.5 0.8 0.1 0.8 0.1 0.8 0.1 0.8 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1 0.9 0.05
A5 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.8 0.1 0.8 0.1 0.8 0.5 0.5 0.8 0.1
A6 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1
A7 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.8 0.1 0.8 0.1 0.8 0.5 0.5 0.8 0.1
A8 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.8 0.1 0.8 0.1 0.8 0.8 0.1 0.8 0.1
A9 0.9 0.05 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1 0.9 0.05
A10 0.9 0.05 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1 0.9 0.05
A11 0.9 0.05 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.1 0.9 0.05
A12 0.8 0.1 0.1 0.8 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.5 0.5 0.1 0.8 0.1 0.8 0.1 0.8 0.1 0.8 0.5 0.5 0.8 0.1
A13 0.5 0.5 0.05 0.9 0.1 0.8 0.05 0.9 0.1 0.8 0.1 0.8 0.1 0.8 0.1 0.8 0.05 0.9 0.05 0.9 0.05 0.9 0.1 0.8 0.5 0.5
Table 15: Preferential - paired relationship Alternatives with criterion C3 (Existence of necessary infrastructure)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A2 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A3 0.5 0.5 0.3 0.6 0.5 0.5 0.3 0.6 0.3 0.6 0.3 0.6 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.3 0.6 0.3 0.6 0.3 0.6
A4 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A6 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A7 0.2 0.7 0.2 0.7 0.3 0.6 0.2 0.7 0.2 0.7 0.2 0.7 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.2 0.7 0.2 0.7 0.2 0.7
A8 0.2 0.7 0.2 0.7 0.3 0.6 0.2 0.7 0.2 0.7 0.2 0.7 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.2 0.7 0.2 0.7 0.2 0.7
A9 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.3 0.6 0.3 0.6 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.3 0.6 0.3 0.6 0.3 0.6
A10 0.2 0.7 0.2 0.7 0.3 0.6 0.2 0.7 0.2 0.7 0.2 0.7 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.2 0.7 0.2 0.7 0.2 0.7
A11 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A12 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
A13 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.7 0.2 0.7 0.2 0.6 0.3 0.7 0.2 0.5 0.5 0.5 0.5 0.5 0.5
74 M. Dabiri, M. Oghabi, H. Sarvari, M. S. Sabeti, H. R. Kashefi
Table 16: Preferential - paired relationship Alternatives with criterion C4 (Availability)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A2 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A3 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A4 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A5 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A6 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A7 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3
A8 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A9 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A10 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A11 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A12 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
A13 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.3 0.6 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
Table 17: Preferential - paired relationship Alternatives with criterion C5 (Proximity to service centers)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.7 0.2 0.6 0.3 0.5 0.5 0.7 0.2 0.6 0.3 0.6 0.3 0.6 0.3
A2 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.7 0.2 0.6 0.3 0.5 0.5 0.7 0.2 0.6 0.3 0.6 0.3 0.6 0.3
A3 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.7 0.2 0.6 0.3 0.5 0.5 0.7 0.2 0.6 0.3 0.6 0.3 0.6 0.3
A4 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
A5 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.7 0.2 0.6 0.3 0.5 0.5 0.7 0.2 0.6 0.3 0.6 0.3 0.6 0.3
A6 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
A7 0.2 0.7 0.2 0.7 0.2 0.7 0.3 0.6 0.2 0.7 0.3 0.6 0.5 0.5 0.3 0.6 0.2 0.7 0.5 0.5 0.3 0.6 0.3 0.6 0.3 0.6
A8 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
A9 0.5 0.5 0.5 0.5 0.5 0.5 0.6 0.3 0.5 0.5 0.6 0.3 0.7 0.2 0.6 0.3 0.5 0.5 0.7 0.2 0.6 0.3 0.6 0.3 0.6 0.3
A10 0.2 0.7 0.2 0.7 0.2 0.7 0.3 0.6 0.2 0.7 0.3 0.6 0.5 0.5 0.3 0.6 0.2 0.7 0.5 0.5 0.3 0.6 0.3 0.6 0.3 0.6
A11 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
A12 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
A13 0.3 0.6 0.3 0.6 0.3 0.6 0.5 0.5 0.3 0.6 0.5 0.5 0.6 0.3 0.5 0.5 0.3 0.6 0.6 0.3 0.5 0.5 0.5 0.5 0.5 0.5
Table 18: Preferential - paired relationship Alternatives with criterion C6 (Admission capacity)
A1A2A3A4A5A6A7A8A9A10 A11 A12 A13
Alternatives µAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνAµAνA
A1 0.5 0.5 0.8 0.1 0.8 0.1 0.9 0.05 0.8 0.1 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.7 0.2 0.05 0.9 0.8 0.1 0.9 0.05
A2 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.2 0.7 0.5 0.5 0.7 0.2
A3 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.7 0.2 0.5 0.5 0.7 0.2
A4 0.05 0.9 0.2 0.7 0.2 0.7 0.5 0.5 0.2 0.7 0.2 0.7 0.05 0.9 0.2 0.7 0.2 0.7 0.1 0.8 0.5 0.5 0.2 0.7 0.5 0.5
A5 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.2 0.7 0.5 0.5 0.7 0.2
A6 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.7 0.2 0.5 0.5 0.7 0.2
A7 0.5 0.5 0.8 0.1 0.8 0.1 0.9 0.05 0.8 0.1 0.8 0.1 0.5 0.5 0.8 0.1 0.8 0.1 0.3 0.6 0.05 0.9 0.8 0.1 0.9 0.05
A8 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.7 0.2 0.5 0.5 0.7 0.2
A9 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.7 0.2 0.5 0.5 0.7 0.2
A10 0.2 0.7 0.6 0.3 0.6 0.3 0.8 0.1 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.6 0.3 0.5 0.5 0.8 0.1 0.6 0.3 0.8 0.1
A11 0.05 0.9 0.7 0.2 0.2 0.7 0.5 0.5 0.7 0.2 0.2 0.7 0.05 0.9 0.7 0.2 0.2 0.7 0.1 0.8 0.5 0.5 0.2 0.7 0.5 0.5
A12 0.1 0.8 0.5 0.5 0.5 0.5 0.7 0.2 0.5 0.5 0.5 0.5 0.1 0.8 0.5 0.5 0.5 0.5 0.3 0.6 0.7 0.2 0.5 0.5 0.7 0.2
A13 0.05 0.9 0.2 0.7 0.2 0.7 0.5 0.5 0.2 0.7 0.2 0.7 0.05 0.9 0.2 0.7 0.2 0.7 0.1 0.8 0.5 0.5 0.2 0.7 0.5 0.5