Full Chapter Application of Multi Criteria Decision Analysis in Environmental and Civil Engineering 1St Edition Dilber Uzun Ozsahin Editor PDF
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Professional Practice in Earth Sciences
Application
of Multi-Criteria
Decision Analysis in
Environmental and
Civil Engineering
Professional Practice in Earth Sciences
Series Editor
James W. LaMoreaux, Tuscaloosa, AL, USA
Books in Springer’s Professional Practice in Earth Sciences Series present
state-of-the-art guidelines to be applied in multiple disciplines of the earth system
sciences. The series portfolio contains practical training guidebooks and supporting
material for academic courses, laboratory manuals, work procedures and protocols
for environmental sciences and engineering. Items published in the series are
directed at researchers, students, and anyone interested in the practical application
of science. Books in the series cover the applied components of selected fields in
the earth sciences and enable practitioners to better plan, optimize and interpret their
results. The series is subdivided into the different fields of applied earth system
sciences: Laboratory Manuals and work procedures, Environmental methods and
protocols and training guidebooks.
Editors
Application of Multi-Criteria
Decision Analysis
in Environmental and Civil
Engineering
123
Editors
Dilber Uzun Ozsahin Hüseyin Gökçekuş
DESAM Institute Faculty of Civil and Environmental
Near East University Engineering
Nicosia, Turkish Republic of Northern Near East University
Cyprus, Turkey Nicosia, Turkish Republic of Northern
Cyprus, Turkey
Department of Biomedical Engineering
Near East University
James LaMoreaux
Nicosia, Turkish Republic of Northern
P. E. LaMoreaux & Associates, Inc.
Cyprus, Turkey
Tuscaloosa, AL, USA
Medical Diagnostic Imaging Department
College of Health Science
University of Sharjah
Sharjah, United Arab Emirates
Berna Uzun
DESAM Institute
Near East University
Nicosia, Turkish Republic of Northern
Cyprus, Turkey
Department of Mathematics
Near East University
Nicosia, Turkish Republic of Northern
Cyprus, Turkey
This Springer imprint is published by the registered company Springer Nature Switzerland AG
The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Dilber Uzun Ozsahin, Berna Uzun, Aizhan Syidanova,
and Mubarak Taiwo Mustapha
2 Theoretical Aspects of Multi-criteria Decision-Making (MCDM)
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
Berna Uzun, Dilber Uzun Ozsahin, and Basil Duwa
3 Analytical Hierarchy Process (AHP) . . . . . . . . . . . . . . . . . . . . . . . . 17
Dilber Uzun Ozsahin, Mennatullah Ahmed, and Berna Uzun
4 The Technique For Order of Preference by Similarity to Ideal
Solution (TOPSIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Berna Uzun, Mustapha Taiwo, Aizhan Syidanova,
and Dilber Uzun Ozsahin
5 ELimination Et Choix Traduisant La REalité (ELECTRE) . . . . . . 31
Berna Uzun, Rwiyereka Angelique Bwiza, and Dilber Uzun Ozsahin
6 Preference Ranking Organization Method for Enrichment
Evaluation (Promethee) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Berna Uzun, Abdullah Almasri, and Dilber Uzun Ozsahin
7 Vlse Criterion Optimization and Compromise Solution
in Serbian (VIKOR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Berna Uzun and Dilber Uzun Ozsahin
8 Fuzzy Logic and Fuzzy Based Multi Criteria Decision
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Berna Uzun, Dilber Uzun Ozsahin, and Basil Duwa
9 Predict Future Climate Change Using Artificial Neural
Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Hamit Altıparmak, Ramiz Salama, Hüseyin Gökçekuş,
and Dilber Uzun Ozsahin
v
vi Contents
Abstract The application of Multi criteria decision making (MCDM) has sprung
many facet of life. Its application in the field of civil engineering and environmental
studies owe to fact that decision-makers in these fields are always in dilemma when
confronted with challenges involving multiple criteria. In civil engineering, decision-
making is critical to the success of any project. Any wrong decision can be detrimental
not only to people’s life but to the cost and quality of time spent on a project.
Civil engineers are usually confronted with alternatives whenever a project is to be
executed. This alternatives include the type, length and strength of a material to
be used or its longevity. Similar alternatives are peculiar to environmental studies.
Climate change has become the most debatable topic since the peak of industrial
revolution. Greenhouse gasses (carbon-dioxide (CO2), water vapor and methane) has
been emitted in an uncontrollable manner resulting in the damage of the protective
ozone layer. This has led to a far reaching consequences such as drought, heat waves,
shrinking of the glacier ice, bush burning, deforestation etc. To provide a solution to
these, several environmental friendly alternative needs to be consider.
how close it satisfies an objective or multiple objectives. In the MODM approach, the
number of potential decision alternatives may be large. Solving a MODM problem
involves selection.
The MODM approach differs from the MCDM approach in that no different
solutions are provided. MODM demonstrates the mathematical basis for developing
other conclusions. Any candidacy, once concrete, is evaluated by how close it meets
the goal or a huge number of goals. In the MODM scenario, the number of probable
other conclusions has the potential to be tremendous. Conclusion MODM difficulties
imply choice.
It is widely recognized that the bulk of the conclusions adopted in the real world
are accepted in an environment in which goals and limits due to their difficulties
are not literally popular, and thus the problem does not have the ability to be liter-
ally defined or literally presented in exact form. Zadeh (1965) proposed using the
concept of fuzzy sets as a modelling tool for difficult systems that have every chance
of being controlled by people, but which are difficult to literally qualify to deal with
high-quality, inaccurate information or even poorly structured conclusion problems
(Bellman and Zadeh 1970).
Fuzzy logic is a section of arithmetic that allows programs on a computer to
simulate the real world, the same world people live in. This is a simple method to
reason with uncertain, diverse and inaccurate data or knowledge. In Boolean logic,
any statement is considered true or false; that is, it contains the true meaning of 1 or 0.
Numerous Booleans impose strict membership requests. Vague large numbers have
more flexible membership requests that allow selective membership in the kit. Every-
thing depends on the degree, and clear reasoning is considered as a limiting case of
indicative thinking. Therefore, Boolean logic is considered a subset of fuzzy logic.
People take part in the analysis of conclusions because the adoption of conclusions
must take into account the subjectivity of a person, and not only apply impartial
probabilistic measures. This prepares the adoption of fuzzy conclusions important.
(Kahraman 2008).
The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)
is a technique that seeks to find the closest possible solution to the positive ideal solu-
tion (PIS) in a multi-criteria decision environment. It has many benefits. It’s easy to
use and organized. It has been used in supply chain management, logistics, construc-
tion, engineering and manufacturing systems, business and marketing successfully
(Balioti et al. 2018).
From the Serbian language, VIsekriterijumska optimizcija i KOmpromisno
Resenje (VIKOR) is a way of finding a compromise ranking created by Serafim
Oprikovic. VIKOR is a method that determines the superior value in comparing two
alternatives for a final set of other actions that must be ranked and selected between the
criteria, and resolves a discrete multicriteria problem with disparate and conflicting
aspects. VIKOR pays more attention to demanding and choosing one of the best from
the set of variables and determines compromise difficulties with conflicting aspects
that can help decision makers to show the final verdict. A compromise conclusion
is the final conclusion among the alternatives, closer to impeccable (Lee and Yang
2017).
4 D. Uzun Ozsahin et al.
The VIKOR and TOPSIS methods are based on distance calculation, but the
compromise conclusion in VIKOR is guided by mutual concessions, while in TOPSIS
the best conclusion is guided by the minimum distance from PIS and the farthest
distance from NIS (negative ideal solution). PIS is considered to be a type that
consists of the best ratings between all considered criteria or attributes. On the other
hand, NIS is considered a candidate that contain the worst ratings between all the
criteria considered (Lee and Yang 2017).
The Analytical Hierarchy Process (AHP) was developed by Saati in 1980. AHP is
an additive weighting method. It has been reviewed and used in many fields, and its
implementation is maintained by several commercially available, user-friendly soft-
ware packages. It is generally difficult for people who accept conclusions to literally
qualify weights of total importance for a set of characteristics at the same time. As
the number of characters’ increases, the best results are obtained when the problem
is transformed into one of a series of matched analogs. AHP formalizes a change
in the difficulty of weighting characteristics into a more manageable problem of
making a series of pairwise comparison between competing characters. AHP summa-
rizes the results of matched analogs in the “matrix of paired comparisons”. For
any pair of attributes, the person accepting the conclusion reveals the outcome
of”How much more important is one species (example) than another.” Any pairwise
comparison urgently asks the person to accept the conclusion to answer the ques-
tion: “How much characteristic A can be more important, than characteristic B, of a
comparatively common goal?” (Kahraman 2008).
ELimination Et Choice Translating Reality (ELECTRE) is another MCDM
technique. The fundamental concept of the ELECTRE method is how to over-
come with a leading relationship, using paired comparisons between candidates for
any aspect individually. Differences in the two or many choices, significant as Aiĺ Aj,
indicate that the 2 candidates i and j do not mathematically prevail over each other,
the person accepting the conclusion perceives the risk of considering Ai as better than
Aj. A candidacy is considered to be dominant if another candidacy overtakes it, at
least in 1 aspect, and is equated in the remaining aspects. The ELECTRE method of
application is a pairwise comparison of choice based on the degree to which the eval-
uation of alternatives and the authority of preference recognizes or contradict pair
matching with the presence of a predominance between candidates. The decision-
maker has the opportunity to say, in fact, that he/she has a strong, weak or indifferent
predilection, or even has the ability to be unable to express his preference between
the 2 compared candidates (Kahraman 2008).
In comparison to other MCDM methods, PROMETHEE is an efficient technique
that provides more preference functions to decision makers for creating the priority
to alternatives based on each criteria. The advantages of PROMETHEE include
that it is a user-friendly method that can be perfectly applied to real-life problem
structures. Both PROMETHEE I and II as whole enable the ranking of the alternatives
respectively, while still providing simplicity (Ozsahin et al. 2019).
The PROMETHEE II method arranges objects from the best (more precisely, from
the most preferred) to the worst (to the least preferred). To do this, the differences,
Phi = Phi – Phi −, are calculated for each object and then ordered in descending
1 Introduction 5
order. In other words, the ranks of the objects are constructed following the rule:
where largest value of F is set to a rank equal to 1. As a result, each object receives
a rank. The most preferred objects have higher Phi value . In other words, the ranks
can be considered as numbers showing ranking of the objects from best to worst
(Ozsahin et al. 2019).
References
making approaches in solving and analyzing the problem that tilts towards solving
environmental engineering problems, understanding its strengths and weaknesses
involved.
Numerous dialogue was met that led to an organized meeting in 1975 by Zionts
and in 1977 by Buffalo in Jouy-en-Josas, with other relating researchers such as
Fandel Gunter, Tumas Gal, Stan Zionts, Andzej Wierzbicki and Jaap Spronk. These
individuals attended a meeting in Konigswinter, Germany related in 1979 that led to
founding of Special Interest Group (SIG) on MCDM. This gave Zionts a portfolio
of becoming the group leader. These individuals considered some reputable confer-
ence, recorded in France, New York and Jouy-en-Josas with interesting packages
(founding) attached to them, respectively.
In 1980, J. Morse organized a MCDM conference recorded in Dalaware as the
fourth conference recorded and the P. Hansen organized the fifth conference in Mons
Belgium in 1982. These meetings were held in different locations around the globe
every two years. Yacov Haimes organized the sixth meeting in 1984 in Cleveland
Ohio while Y. Sawaragi and H. nakayama organized the seventh conference in 1986
in Japan. A. G Lockett and G. Islei organized the eighth conference in 1988 in
Manchester, United Kingdom.
The ninth International conference was organized in 1990 by Ambrose
Goicoechea in Fairfax, Virginia. The tenth conference was organized by Gwo-
Hshiung and P.L. Yu in 1992 in Taiwa, Taipei province which was hugely assisted
by the Taiwanese government; these recorded high profiling individuals such as the
Russian Billionaire Boris Berezovsky in attendance. The eleventh conference was
in Coimbra (Portugal) in 1994 organized by J. Climaco, while in 1995 the twelfth
10 B. Uzun et al.
conference was organized by G. Fandel and T. Gal in Hagen, Germany. The thir-
teenth conference was organized in Cape Town (South Africa) in 1997 by T. Stewart
while the fourteenth conference, organized by Y.Y Haimes in 1998 in Charlottesvile
(U.S.A).
The fifteenth conference was organized in Ankara, Turkey in 2000 by M. Kksalan.
This was subsequently followed by the sixteenth conference in 2002, organized
by M. Luptacik and R. Vetchera in Semmering (Austria) which was followed by
the seventeenth conference organized by W. Wedley in 2004 in British Columbia,
Canada. The eighteenth conference was organized in Chania (Greece) in 2006 by
C. Zopounidis and followed by the Nineteenth conference organized by M. Ehrgott
in 2008 in Auckland (New Zealand). The twentieth conference was organized by Y.
Shi and S. Wang in June 2009 in Chengdu (China).
These conferences were active and are well organized. This moves simultaneously
to the 25th conference that was organized in 2019 in Istanbul, Turkey, which will
be followed, subsequently by the June 2021 conference scheduled to take place in
Portsmouth, UK.
This study presents an elaborate knowledge on the MCDM, this part also, explains
every term introduced in this book of decision analysis involved.
Multiple (Multi):
As the name implies, multiple, is perceived to be diverse in its look. This in other
words means is when things are numerous in terms, many or tremendously big.
Criteria:
Etiologically, criteria can be affiliated to criterion in its plural form. This term is
perceived to be a form of character or feature possess by an object. This may extend
to give a perfect description of anything.
Decision:
Derived from a latin word, means “to cut off”. In other words, it is an act of decision
that is essential in “cutting off” of anything. Choices are made by individuals or
groups about almost everything. It is a mind resolution to accept or reject after
tremendous analysis to consider.
Analysis:
This is process of breaking any difficult topic or matter into its smaller forms for
a simple and clear understanding. In other words, it can be perceived as a detailed
knowledge to examine elements or structure of anything.
2 Theoretical Aspects of Multi-criteria Decision-Making … 11
MCDM has essential steps to consider. The analytical decisions highly considered
include the following;
STEP 1 Defining The Problem:
This is one of the most important steps to consider when making a decision. Without
identifying the problem, the whole system becomes vague. Furthermore, in any case,
the essential importance to note is to understand a problem before finding the solution.
In many cases people tend to take decisions without understanding them. This could
relatively affect the whole decision without solution.
STEP 2 Determination of the Goal:
This process is done after problem is identified with a defined objective to propose
the decision making. The goal of any decision making is guided by the end result.
In other words, if there is no clear goal for the MCDM, then the result may be
affected. For instance, when an individual intends to purchase an object, the person
may consider an affordable yet qualitative product, which is regarded here as the
objective.
STEP 3 Specify Criteria:
Another important thing to consider is selection of the right criteria in MCDA. This
is considered as an attribute that guides an individual in getting the right objective.
The criteria selected determine the success of our objectives. However, it is important
to consider meaningful criteria when setting an objective. This will enable a better
comparison among the options at hand. Criteria make the objective to have meaning.
It can be expressed when we compare two individuals. For instance, a person buys a
mobile phone and another person buys fruits. These individuals clearly have the same
objective even when they bought different items. Their objectives were to buy cheap
and qualitative objects. Also, their criteria here are obviously different because they
have two different subjects bought. For the individuals that bought fruit, the criteria
attached to the purchase of fruit might be quality and durability while the other
individual that purchased mobile phone might be quality and its capacity such as
camera quality or its version.
STEP 4 Determining the Avaliable Alternatives:
Lists of options are important to design after the criteria are extracted. In other
words, getting the right criteria does not complete our determined objective of getting
something done, it also enables progressive work. Drawing a list of options will
enable our criteria to make more sense for a proper analysis. Another perspective is
when we have items that share the same function and quantity but have different cost
and quality. This can be seen when applying universities. Sometimes, individuals
2 Theoretical Aspects of Multi-criteria Decision-Making … 13
This step introduces us to the use of data collected as mentioned to calculate and
select the best score to consider. This step enables us to obtain result by selecting
and picking the product of score for each criterion, getting the weight and then sum
the scores together. We obtain the final score when we add all the scores together
choosing the option with the best scores.
STEP 7 Reporting the Results:
This process tends to document every detailed desirable results obtained from the
previous options. This process assists in preserving all this as a document for future
use.
MCDA gives us various processes that are advantageous when compared to other
decision-making tools that are not affiliated to any specific criteria, these include the
following:
• It is not vague
• It can be adopted for different scenario simply
• It is rational
• It can be applied in various area
• MCDA assist in making decision
• Data combination could ease the decision maker work
Many theories can be applied to this study which can also be summarized showing
their advantages.
“Data Envelopment Analysis” (DEA) has the advantage of analyzing numerous
input and output with considering and measuring the efficiency togerher (Charnes
et al. 1978). In other words, DEA is applicable to many fields such as, economics,
medicine, software engineering, road safety, utilities, computer technology, agricul-
ture and solving many business problems. DEA is considerably favorable in resolving
problems giving a precise output.
14 B. Uzun et al.
One important, simple and easy method to be considered is the TOPSIS method
(Yahya et al. 2020). This is applicable to fields such as technology, transport and
economics (Behzadian et al. 2012). However, it can be difficult to weight the
importance levels of the criteria.
Another important method is the ELECTRE method. This method is useful
because of its ability to accept anything vague into account (Konidari and Mavradis
2007) and applicable to many fields such as transport and water management. It also
has disadvantage of its ability to process its end products, which may not be able to
be read in simply. This is a difficult process to explain in simple terms.
The PROMETHEE technique is one method that is perceived to be an easy tech-
nique that won’t need proportionate criteria in assumption (Ozsahin et al. 2018). It is
also applicable to many disciplines such as environment, energy, water management,
agriculture, education, business, finance and healthcare (Behzadian et al. 2010).
A similar to the PROMETHEE method, Analytic Hierarchy Process (AHP) is
also a technique based on pairwise comparison without demanding the exact data.
Its ranking structure can also be adjusted to measure different problems involved.
This method is also applicable to many fields such as public policy, political strategy,
and planning and resource management (Lai 1995). Thus, it has its disadvantages
attached such as the interdependence that exists between the options and criteria.
The “Simple Additive Weighting” (SAW) is another method that has the capacity
to adapt amid criteria, its perception in making decisions. This method spreads across
different fields of study such as in business, finance and water management (Podvezko
2011). However, the method needs significant work to prepare considerate data before
it is executed.
The VIKOR method is an MCDA technique that resolves decision-making prob-
lems that seem to contradict other problems. In this method, the person making
the decision tends to seek the best solution that is ideal to defined criteria while
considering the minimum regret (Yu 1973). The method is applicable to engineering.
The Fuzzy Logic Or Fuzzy Set Theory method involves using vague inputs or
insufficient data (Zadeh 1965). It extends its application to different fields such as in
engineering, economics, social, environmental and business problems involved. One
of its disadvantages is that it cannot be developed easily. It needs the experts opinion.
Its hybrid application with the other MCDA techniques gives the best solution of the
alternatives while the vague data arise.
References
Charnes A, Cooper WW, Rhodes E (1978) Measuring the efficiency of decision making units. EJOR
2:429–444
Konidari P, Mavrakis D (2007) A multi-criteria evaluation method for climate change mitigation
policy instruments. Energy Policy 35(12):6235–6257
Lai S (1995) Preference-based interpretation of AHP. Int J Manage Sci 23(4):453–462
Ozsahin I, Uzun B, Isa NA, Mok GSP, Uzun Ozsahin D (2018) Comparative analysis of the common
scintillation crystals used in nuclear medicine imaging devices. In: 2018 IEEE nuclear science
symposium and medical imaging conference proceedings (NSS/MIC), Sydney, Australia, 2018,
pp 1–4. http://doi.org/10.1109/NSSMIC.2018.8824485
Podvezko V (2011) The comparative analysis of MCDA methods SAW and COPRAS. Inzinerine-
Ekonomika-Eng Econ 22(2):134–146
Yahya M, Gökçekuş H, Ozsahin D, Uzun B (2020) Evaluation of wastewater treatment technologies
using TOPSIS. Desalin Water Treat 177:416–422. https://doi.org/10.5004/dwt.2020.25172
Yu PL (1973) A class of solutions for group decision problems. Manage Sci 19(8):936–946
Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353
Zionts S (1979) MCDM—if not a roman numeral, then what?. Interfaces 9(4):94–101. https://www.
mcdmsociety.org
Chapter 3
Analytical Hierarchy Process (AHP)
Abstract This study provides a comprehensive explanation about one of the impor-
tant multi-criteria decision-making technique entitled Analytical Hierarchy Process
(AHP). This chapter will include a summary of the steps required to carry out the
mathematical computation of AHP for problems with both consistency and inconsis-
tency in the decision-maker’s preferences. Hierarchy design, prioritization, criteria
weights, and consistency are all extensively taken into consideration. Further elabo-
rations regarding the different applications of the AHP process will also be discussed,
including various fields such as business-related decision making and decision theory
in the field of medicine. The limitations imposed by the analytical hierarchy process
are also discussed.
3.1 Introduction
is the psychological origin of the scale used to make said comparisons, which leads
to the third pillar which is the inconsistency also denoted as the sensitivity to changes
in judgements. Prioritization is then developed giving rise to an eigenvector that can
be integrated in the AHP general feedback structure, hence reducing the mathemat-
ical method to a one-dimensional normalized ratio scale allowing a unit-less scale
measurement. This methodology can be then marked on the basis of whether or not
the ranking is preserved or reversal is allowed. Finally, implementing mathematical
methodologies into group decision making to generate individual opinions or judge-
ments is crucial to enable the fabrication of a fundamental group decision that would
be compatible with individual predispositions.
There are several steps involved in AHP; when given a complex problem, the first
step is to construct the hierarchy framework, also known as a feedback network. This
hierarchy will have three levels: level one being the goals, level two being the different
criteria and finally, level three being the different alternative options as shown in
Fig. 3.1. The decision-making process is then initiated by systematically comparing
elements two at a time, and giving numerical weight values using scale ratios to each
element based on either actual data or subjective opinion. This is where inconsistency
can be possible, thus leading to the need to calculate the consistency index, which is a
numerical value representing variance or inconsistency. The weights are then used to
make a pairwise comparison matrix which is then used to calculate criteria weights.
The mathematical computations involved in the AHP are categorized as eigenvector
calculations where the Eigen value corresponds to each criteria weight. Depending
on the context of the problem being solved, the same could then be applied to sub-
criteria if they are present. In this way, we can compare criteria with differing scales,
i.e. price and size.
While the analytical hierarchy process is widely applicable to various types of
problems that vary in terms of their degrees of complexity, this method is most effi-
ciently applied in more complicated problems that have a large number of objectives
or criteria that may include sub-divisions within them (sub-criteria). As such, for
more complex problems, it is harder to compare all the objectives to one another and
it can be significantly error prone if not approached in a systematic and consistent
manner. To resolve this problem, the AHP can be applied to complicated issues such
as the prediction of the future of higher education, design choices for a national
transport system and even recruitment options in the workplace. In addition to this,
AHP provides the decision-maker with quantified measurements of compatibility
that can then be utilized to analyse the problem manually (Lee et al. 2007).
20 D. Uzun Ozsahin et al.
In this chapter, we will dissect the mathematical computation of AHP with two
simplified examples to help clarify the methodology. The Eigenvalue method is used
is used for decision makers that have consistency in their preferences. Consistency
is a pivotal concept in AHP as it determines the method to be used. In the case of an
inconsistent decision maker, the Eigenvalue method is inapplicable and so the quan-
tification is made through a matrix solution (2). The identification of inconsistency
as opposed to consistency in decision making will also be extensively discussed.
For example, how can we tell if the decision maker is consistent with their pref-
erences? This will be discussed thoroughly and elaborated with worked examples
giving relevance to the distributive and ideal modes of AHP (Saaty 2001).
As previously mentioned, the first step in AHP is setting clear objectives and goals.
The different criteria are considered along with their sub-criteria and are combined
with the alternatives to form the hierarchy tree network. Then, the different qualities
of each alternative, the criteria, are assessed in a pairwise comparison with respect
to the set objectives to derive their priority as a numerical value using a ratio. The
ratio scale or scale of relative importance developed by Saaty (1987) ranges from
1–9, where 1 denotes equal importance and 9 denotes extreme importance, as illus-
trated in Table 3.1 (Taherdoost 2020). This numerical value is denoted as the criteria
weights. These weights are then put into matrix form and mathematical steps are
carried out to evaluate the alternative weights and consistency ratios. Therefore, we
initially have an input as actual measurements of subjective opinions and our end
result will be the ratio scales, which will be in Eigenvector form (denoted as ω),
as well as the consistency index, which will be in Eigenvalue form (denoted as λ).
The mathematical methodology used here is based on the Eigenvalue problem. The
Eigenvector of alternative weights as well as the consistency index is then utilized
to rank the alternatives, thus clarifying the optimal alternative.
When faced with a choice between x number of choices, one can apply the AHP
method to select the optimal choice. To do this, the decision maker must first design
the hierarchy model. This requires an assessment of the problem at hand by cate-
gorizing the alternatives together, the criteria and finally, setting a goal. They are
then put into a hierarchy network similar to that shown in Fig. 3.1. Secondly, the
decision-maker will use pairwise comparisons to compare each choice with the others
using the ratio scale of relative importance illustrated in Table 3.1. These comparison
values will be used to construct the pairwise comparison matrix A.
A = ai j
• Reciprocal matrix; meaning adjacent inputs will be the reciprocal values of each
other.
1
ai j = for i, j = 1, . . . , n
a ji
In AHP, inconsistency is expected and accounted for. This is because the numerical
values are derived from the decision maker’s preference or individual opinions. In
real life, these values can be inconsistent and therefore these inconsistencies must
be accounted for. To summarize, below is a step-by-step simplified overview of
22 D. Uzun Ozsahin et al.
the methodology followed by several simple examples that will be used to further
reinforce a more developed understanding (Saaty 2008).
1. The decision maker must define the problem and determine the kind of data they
will make the judgments on.
2. The hierarchy is structured and designed, designating the top level as the defined
goal, the second level as the broader interpretation of the determined objectives,
intermediate levels as the sub-criteria to be assessed and finally, the lowest level
will be composed of the different alternative options.
3. Using the ratio scale of relative importance developed by Saaty 1987 (Table 1.1), a
pairwise comparison matrix is constructed where all the elements are comparative
judgements made by the decision maker.
4. The pairwise matrix is normalized, and the criteria weights are derived as the
average of each row in the matrix.
5. Using the derived criteria weights, we can find the Eigen vector (ω) by calculating
the weight sum value for each criterion.
6. The Eigen value (λ) is then found such that Aω = λω
7. Finally, the consistency index is calculated to legitimize the reliability of the
decision maker’s judgments.
The concept of consistency is one of the essential step of the analytical hierarchy
process. In principle, the consistency ratio is calculated as the reliability of the prefer-
ential judgments in comparison to a large number of randomly generated judgments.
Realistically, inconsistency is inevitable as it is non-avoidable, primarily because
the foundation of decision making is based on the personal preference of the deci-
sion maker and it is inevitable that inconsistency will occur in the preference of the
decision maker. In other words, the input of the AHP system is based on personal
preference and therefore highly prone to human error (Dyer and Forman 1991). The
question at hand is the degree of the consistency and whether or not it satisfies the
predetermined standard values (Mu and Pereyra-Rojas 2017).
To quantify the level of consistency in the problem at hand, the consistency ratio
is derived as the ratio of the consistency index to the random index. The consistency
index represents the consistency of the pairwise matrix of the given problem. On the
other hand, the random index matrix is a representation of the average consistency
ratio of 500 randomly generated pairwise matrices. These values are predetermined
and constant; they are singularly dependent on the dimensions (n) of the problem at
hand. The calculated values are illustrated in Table 3.2. Based on the previous work
of Saaty regarding the complexities of the concept of consistency in the analytical
hierarchy process, the consistency ratio is defined as CR where CR = CI/RI (Saaty
2012). He also eluded that the standard CR value is 0.1, meaning that if the consis-
tency ratio is calculated to be equivalent to or less than the standard 0.1 value, then the
problem is acceptably denoted as consistent and the analysis process is legitimized.
3 Analytical Hierarchy Process (AHP) 23
Otherwise, if the consistency ratio is found to be greater than the standard value of 0.1,
then the problem is insufficiently consistent and requires re-evaluation. In the case
where the problem is denoted as inconsistent, the decision-makers must re-assess the
preferential reasoning and identify the source of the variance or inconsistencies to
then rectify and refine them so that consistency holds true for the problem at hand.
Notice that as the number of criteria increases or as the matrix dimension gets
larger, a subsequent incremental effect is imposed onto the corresponding index
value as well. This indicates that as the problem becomes more complex, meaning
it encompasses a greater number of criteria and sub-criteria (dimensions), then the
possibility of inconsistencies in judgments also increases. Relating this ideology to
logic helps enhance the fundamental understanding of the concept. In this sense, if
we increase the instances where the decision-maker has to provide an input based on
personal preference, i.e. criteria, then a higher chance of variations will be induced.
The work done by Saaty proved that for the consistency problem, the pairwise
matrix is reciprocal and positive and holds a maximum Eigen value equivalent to the
dimensions of the comparison matrix (n). In other words:
λmax = n
λmax − n
C.I =
n−1
where n is the dimension of the reciprocal positive comparison matrix and λ max
represents the maximum Eigen value, which in the ideal case (no inconsistencies)
would hold the identical value n (dimension of the matrix). The closer the maximum
Eigen value is to the dimension of the matrix, the more the consistency index
decreases, and the consistency ratio decreases accordingly.
24 D. Uzun Ozsahin et al.
References
{372}
First.
A broad-minded and sympathetic representative of America,
fully authorized to treat, and a lover of peace.
Second.
A strict discipline amongst the American forces.
Third,
The principal aim and object of the Tagal insurrection must be
secured.
F. H. Sawyer,
The Inhabitants of the Philippines,
page 113-114 (New York: Charles Scribner's Sons).
{374}
Admiral Dewey,
Letter, August 29, 1898,
Replying to inquiry of War Department.
General Merritt,
statement before United States Peace Commission at Paris,
October 4, 1898.
General F. V. Greene,
Memorandum concerning the Philippine Islands,
made August 27, 1898.
Major J. F. Bell
[of Engineers, on "secret service"]
Letter to General Merritt, Manila, August 29, 1898.
{375}
John Foreman,
Testimony before United States Peace Commission at Paris.
"The excuse that they [the Filipinos] are not ripe for
independence is not founded on facts. The Filipinos number
more educated people than the kingdom of Servia and the
principalities of Bulgaria and Montenegro. They have fewer
illiterates than the states of the Balkan peninsula, Russia,
many provinces of Spain and Portugal, and the Latin republics
of America. There are provinces in which few people can be
found who do not at least read. They pay more attention to
education than Spain or the Balkan states do. There is no lack
of trained men fit to govern their own country, and indeed in
every branch, because under the Spanish rule the official
business was entirely transacted by the native subalterns. The
whole history of the Katipunan revolt and of the war against
Spain and America serves to place in the best light the
capability of the Filipinos for self-government."
F. Blumentritt,
The Philippine Islands,
page 61.
PHILIPPINE ISLANDS: A. D. 1898-1899 (December-January).
Instructions by the President of the United States to
General Otis, Military Governor and Commander in
the Philippines.
Their proclamation to the people of the Islands as
modified by General Otis.
The effect.
{376}
WILLIAM McKINLEY."