0.450
1
0.236
4.358
4.235
1
For the final ranking of the three Courses, we obtain the
following weights according to detailed spreadsheet
instructions in [25] and [39]:
W
11
=0.651, W
21
=0.120, W
31
=0.240
Fig. 1.
Ranking of the three Courses, according to students’ preferences by
AHP.
D.
Calculation of the Consistency Ratios for Each
Pairwise Comparison Matrix
A matrix is said to be consistent if it holds:
α
ij
*
α
jk
=
α
ik
, for
every i, j and k. We must calculate the Consistency Ratios
for every pairwise comparison matrix and these Ratios [26],
must not exceed appreciably 0.10, otherwise we must revise
some of our judgments.
The Consistency Ratio is given by:
CR=
n
r
n
n
*
)
1
(
)
(
max
where
λ
max
is the maximum eigenvalue given by the
average Consistency Measure for all alternatives [25, 39], n
is the number of alternatives for this problem (n=3) and r
n
is
a random number given by Saaty [26], for n=3, the number
of alternatives r
n
=0.58. The Consistency Ratios calculated in
the same manner for the matrices A, B, C, and D, using
Microsoft Excel [10, 25, 39] are given below:
TABLE
I
C
ONSISTENCY
R
ATIOS FOR THE
P
AIRWISE
C
OMPARISON
M
ATRICES
Pairwise
Comparison
Matrix
Consistency
Ratio
Pairwise
Comparison
Matrix
Consistency
Ratio
A
0.070
C
0.082
B
0.050
D
0.066
Note, that every Consistency Ratio is less than 0.10,
according to the guidelines of Saaty [26]. Hence, the
judgments of the evaluators are fairly consistent.
E.
The Pairwise Comparison Matrices for the Sub-criteria
of Each Criterion
Now, we turn our attention to the pairwise comparisons
of the sub-criteria corresponding to each criterion. We form
the following pairwise matrix E, for the sub-criteria of the
first
criterion:
“Effectiveness
of
teaching
Professor”
described in paragraph (d) of Section (II).
1
1.111
0.428
0.298
0.294
900
.
0
1
0.321
0.278
0.273
333
.
2
3.111
1
0.289
0.333
3.347
3.586
3.455
1
0.275
3.400
3.662
3
3,626
1
RACTIV
FRIENDC
COMMNCA
PEXPER
ACQUAL
RACTIV
FRIENDC
COMMNCA
PEXPER
ACQUAL
E
We next find the following weights, summarized
graphically in the following graph and the Consistency
Ratio for matrix E:
Fig. 2.
Ranking of qualities for Academic Teacher. Consistency Ratio=
0.081.
We can see that the highest weight of “importance” is
assigned to “Academic Qualifications” whereas the lowest
Proceedings of the World Congress on Engineering 2014 Vol II,
WCE 2014, July 2 - 4, 2014, London, U.K.
ISBN: 978-988-19253-5-0
ISSN: 2078-0958 (Print); ISSN: 2078-0966 (Online)
WCE 2014