Assignment 3
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School
University of South Africa *
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Course
3704
Subject
Mathematics
Date
Nov 24, 2024
Type
Pages
3
Uploaded by ChancellorFang8501
DSC3704/102/1
1
2.3
Assignment 03: Semester 1
Unique number: 649834
Due date: 03 May 2023
This assignment covers all the study material for this module, as well as the reading and
studying of articles published in accredited scientific journals.
Questions may involve performing a literature review on a relevant subject and writing a report
about it.
Feedback by the lecturer will be provided on individual assignments. Marks will be allocated
for your creativity, originality, the logical flow of
your arguments and the clarity of your
explanations.
You must write from your own perspective and put things in context. No marks
will be awarded if your work is deemed to be simply copied or plagiarized. Quotes must be
properly referenced.
Type all answers in the form of a report. Clearly state your name (optional), student number,
the module code and assignment number on a title page. Submit your ordered answers in a
single pdf file on myUnisa.
Question 1
In your web browser, go to the official website of the Operations Research Society of South
Africa (ORSSA) at http://www.orssa.org.za. Then link to the site for its journal
ORiON
and
download the article titled
A note on the statistical analysis of point judgment matrices
,
authored by MG Kabera and LM Haines, in Volume 29, No. 1, 2013, that is, pp.75
−
86.
Read the article.
Then answer the following questions.
1.1
What is the main aim of the paper?
1.2
What is a point judgement matrix? How can its elements be expressed in mathematical
notation?
1.3
Name and very briefly describe two examples of a relative preference scale.
1.4
Who first introduced a statistical approach to the analysis of point judgement matrices?
What is this method called?
1.5
Which method other than the LLSM method should be used to verify that the LLSM
weights in Table 1 in the article were indeed calculated correctly? Why?
1.6
Verify that the LLS weights in Table 1 were calculated correctly.
DSC3704/102/1
2
Question 2
Suppose you are considering buying a new car (or any other item that you are interested
in buying now).
2.1
Design SMART scoring functions for at least six characteristics that you consider
important.
2.2
Order these characteristics in a tree structure with at least two levels in the hierarchy.
Assume that weights are divided equally among every branch on the same level of the
hierarchy and calculate a weight for every leaf.
2.3
Determine the SMART scores for three car
models according to their specifications for
each of the characteristics.
Calculate the value functions (weighted SMART scores)
for the two cars.
Explain which car you would buy.
Question 3
Use the analytic hierarchy process (AHP) to solve the following problem.
Kabelo is ready to select his mate for life and has determined that beauty, intelligence, and
personality are the key characteristics that he is looking for in a satisfactory mate.
Let beauty be indicated by the letter B, intelligence by the letter I, and personality by the letter
P. Then his pairwise comparison matrix for these three characteristics, B, I and P, is as follows:
Characteristic
B
I
P
Nthati
Dineo
Lerato
1
3
1
1
5
3
1
3
5
1
3
1
He has been dating three women: Nthati, Dineo, and Lerato
. His views of these women’s
beauty, intelligence and personality are given in the following pairwise comparison matrices.
DSC3704/102/1
3
•
Characteristic B (Beauty):
Woman
A
B
C
Nthati
Dineo
Lerato
1
1
5
2
1
3
1
5
3
1
2
1
•
Characteristic I (Intelligence):
Woman
A
B
C
Nthati
Dineo
Lerato
1
1
6
4
1
2
1
6
1
2
4
1
•
Characteristic P (Personality):
Woman
A
B
C
Nthati
Dineo
Lerato
1
4
1
1
4
9
1
4
1
4
9
1
Questions and required calculations
3.1
Whom should Kabelo choose as his lifetime mate if he uses the analytic hierarchy
process (AHP) to determine his optimal choice? Substantiate your answer by showing
all relevant calculations of weights and total weighted scores obtained by applying the
analytic hierarchy process (AHP).
3.2
Check the pairwise comparison matrices for consistency. (Note that all four pairwise
comparison matrices in this problem must be tested for consistency.)
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