1. ENS 491 – Graduation Project (Design)
(Draft) Proposal
Project Title: What Does “Significantly More” Mean?
Project #104
Group Members:
Dilara ERŞAHİN - 17671
Sarp UZEL - 18184
Emir ÇAKAR - 16732
Berk ÇETİN - 16508
Supervisor: Kemal KILIÇ
Date: 28.10.2016

2. ABSTRACT
The purpose of this project is to determine the quantitative range corresponding to the
individuals’ understanding of being “significantly more” for the comparison of two criteria.
The Analytic Hierarchy Process, developed in 1977 by Thomas Saaty, uses a scale of 1-9 to
assign importance relations among the criteria. However, this scale may sometimes create
inconsistency for the application of the comparison matrix in AHP. The project team’s
concern is to find out the reason of this inconsistency, and develop a coding algorithm for the
formation of the scale for each individual, which will decrease the level of inconsistency. The
first phase of this project involves preparation of or performing one/more survey(s) in order to
understand whether the reason of inconsistency is the scale itself or the individuals’ false
adjudication on assigning the relations. The project team will further analyse the survey
results and decide on the cause that the inconsistency is orginating from. The final phase of
this project consists of developing an algorithm for the scale for each individual by coding.
This will provide an option for the scale selection of AHP method, and increase the level of
reliability of the AHP method.

3. INTRODUCTION
With the rise of the Industrial Revolution, started in 1760’s, and the demand arose
during the World War II for operating military operations in the most effective way, decision
making became extremely crucial. However, the area of operations research was based on
decision making methods with single subject in their focus. For instance, during the World
War II, England tried to maximize the damaged area with using less number of bombs in their
inventories. But in reality, people tried to maximize/minimize more than one objective. This
insufficiency of the current methods was eliminated by the introduction of Thomas Saaty’s
Analytic Hierarchy Process in 1977.
AHP can be described as a method of making decisions when there are multiple criteria to
be considered, and it is a tool for simplifying the procedure of evaluating these criteria (Budak
et al., 2006, p. 2). First, a hierarchical structure is obtained by deciding on the goal of the
current problem and the factor affecting the subjective opinion of the decision maker on this
goal. Then, pair-wise comparisons are performed between the criteria using a scale of 1-9,
which was also developed by Saaty, and forming a comparison matrix (Saaty, 1990, p. 15).
The scale refers to the importance of one criterion over another. Table 1 shows the scale and
explanation of the relations;
1 Equal Importance
3 Moderate Importance
5 Strong Importance
7 Very Strong Importance
9 Extreme Importance
2, 4, 6, 8 Intermediate values
Table 1 : Saaty’s Scale

4. The comparison matrix structure is shown in Table 2;
𝑤1
𝑤1
= 1 ⋯
𝑤1
𝑤 𝑛
⋮ ⋱ ⋮
𝑤 𝑛
𝑤1
⋯
𝑤 𝑛
𝑤 𝑛
= 1
Table 2 : nxn Pair-wise Comparison Matrix
Next, the weights of the criteria are computed from the comparison matrix. The following
step is to calculate the consistency related to the criteria comparisons, by computing the
consistency index and the consistency rate. Saaty’s consistency measurement is based on
eigen vectors, eigen values (λ), and random index (RI) which is already calculated by Saaty:
𝐶𝐼 =
𝜆 𝑚𝑎𝑥 −𝑛
𝑛−1
𝐶𝑅 =
𝐶𝐼
𝑅𝐼
If the resulting CI value is consistent or is inconsistent with at most 10% of the RI value, our
comparison is accepted. The next step is to compute the scores of the main and sub-criteria as
a matrix, as well. The resulting decision is made upon the importance scores of the criteria.
Our project is based on the issue of the inconsistency of the comparison matrix
structured by the decision maker. A wide range of literature states that the decision maker
uses false approach while assigning the values of the comparison matrix. However, it is
highly probable that the problem is due to the scale that does not match with the decision
maker’s opinions. Hence, our project goal is to prove that the inconsistency is not caused by
the individuals’ assigning the scale numbers, but the scale itself. In case of an inconsistency in
the comparison matrix or when a much more complex problem is faced, the AHP method
becomes hard to obtain, resulting in the usage of a heuristic method. When looked up in the
⋮
Criteria 1
Criteria n
Criteria 1 … Criteria n

5. literature, there are several solutions to this problem of inconsistency, using different scales.
“Clearly one scale may be appropriate for one application and may not be appropriate for
another. In this situation, a different scale could and should be chosen for each
application.”(Harker & Vargas, 1987, p. 1390). Each solution has its own benefits for specific
type of problems, but they all encounter difficulties when applied to different types of
problems. With this fact, it is hard to state a specific solution, since each is applicable with
certain types of problems. This issue creates a need for a new analytical coding which can be
used for a variety of problems and by all decision making individuals. Therefore, the main
focus of our team is first to perform a survey which is expected to support our claim that the
scale itself is inconsistent, rather than the individuals, and following the survey, to decrease
the inconsistency ratio by using individualized scales, using analytical code development.
PROPOSED SOLUTION AND METHODS
If this project achieves success, the project team would eliminate the issue of
inconsistency emerging from the comparisons matrix results of the AHP method. The
meaning of “significantly more”, referring to the relations in the scale, will be defined. The
problems of the Saaty’s scale will be pointed out, the claim of its inconsistency will be
proven, and a new scale algorithm which is applicable to most of the problems needing AHP
method and suitable to all decision makers.
The solution proposed, will not cover the realization procedures of the AHP method,
but the theoritical basis of this method and mainly the rating and comparison steps of the
procedure.
In order to obtain accurate results, the team members are required to have analytical
and linear algebra knowledge, along with the AHP method; and the application of the project
requires moderate level of coding and algorithm skills.

6. At the end of this project, the team goal is to achive a solution which is applicable to
all of the AHP problems and decision makers; rather than the already existing solutions that
are specific to certain multi-criteria problem types.
The methods needed for this project can be listed as:
 Analytical
 Experimental (as for the surveys)
 Code development
Throughout the project, the tasks planned to do are:
 Finding appropriate survey contents to be prepared for examining the relation
between the scale and the individuals’ opinions on ranking. Selecting the most
appropriate one, or more.
 Carrying out the survey(s) that has been decided by the project team members
and supervisor. Repeat the survey with the same people if needed. The expected
outcome of the surveys is to prove that there is no inconsistency caused by the
decision makers’ usage of the 1-9 scale.
 Research on the existing algorithms for scale development.
 Developing an algorithm for the scale formation. The developed algorithm is
expected to increase the consistency ratio of the AHP method.
This project fundamentally consists of two main stages: research and coding. For the
research part, the resources needed will be people to be surveyed, the materials that are going
to be used in the surveys (which are not decided yet); and for the coding part softwares will be
needed, such as CPLEX, C++, and possible optimization softwares.

7. REALISTIC CONSTRAINTS
Since this project is based on mostly research, survey, and coding; the constraints are
only regarding to economic, social, and time.
The project does not require a large amount of budget. The only budget needed is for
the survey preparation stage, and if expertise on coding is demanded.
In order to observe the consistency of the results given by the survey participants, it is
crucial for the survey to be repeatable. Therefore, the project team should be able to contact
the participants when needed. The issue of being able to find the participants after a time
period, restricts the number of participants to be selected. Also, the surveys will take place on
campus, and this again restricts the number of participants.
The most important realistic constraint of the project is the time frame. The time
management should be done in a way that the team members will have enough time to
complete the surveys and repeat them if wanted, and to develop a working and a free of error
coding.
COMPLEX PROBLEM
Our problem in hand does not have a straight-forward solution. In fact, the problem
does not have an obvious solution, it requires abstract thinking in terms of preparing a suitable
survey, and a deep analysis for formulating applicable methods. Until reaching to the coding
part, the project is focused on research-based knowledge which provides an analytical
approach.

8. RISKS
One possible risk of this project is that the team members may be insufficient for
developing a complete coding algorithm. In this case, an outside service will be needed. The
project team might get help from Computer Science students of Sabancı University, or from
an expert institution.
Another possible risk, is that the already surveyed participants may not want to
participate in the repetition of the same survey. If the team encounters this kind of a problem,
the only change that will be made is to eliminate the results of that particular participant from
the first survey.
PROJECT SCHEDULE
Figure 1 : Gannt Chart of the Project Tasks

9. REFERENCES
Çimren, E., Çatay, B., & Budak, E. (2006). Development of a machine tool selection system using
AHP. The International Journal of Advanced Manufacturing Technology Int J Adv Manuf
Technol, 35(3-4), 363-376. doi:10.1007/s00170-006-0714-0
Harker, P. T., & Vargas, L. G. (1987). The Theory of Ratio Scale Estimation: Saaty's Analytic
Hierarchy Process. Management Science, 33(11), 1383-1403. doi:10.1287/mnsc.33.11.1383
Saaty, Thomas L. "How to Make a Decision: The Analytic Hierarchy Process."European Journal of
Operational Research 48.1 (1990): 9-26. Web. 1 Oct. 2016.