Article in Journal of Sustainability Science and Management · April 019 citations 11 reads 1,581 authors: Some of the authors of this publication are also working on these related projects

Weights Assignment 
 
In calculating the weights of the criteria, 
the Expert Choice 2000 software (Expert 
Choice, Arlington, Virginia, USA) was used in 
carrying out the pair-wise comparison matrix
in a hierarchical manner. This permits the 
comparison of two factors at a time with respect 
to their level of influence in undermining public 
transport 
utilization, 
provision, 
and 
development in Dammam. 
A matrix was set up as 
based on the 
priority ratings assigned by the experts, where 
“n” was the number of factors. Thus, in this 
study, a
matrix was used, where a
diagonal one was automatically assigned to 
each factor when compared by itself. Each 
factor was evaluated against its peers in relation 
to the goal and objectives of the study. So, this 
process was used throughout the comparisons 
of the rest of the criteria. A numerical work 
took place after assigning all the rankings 
assigned by the experts. 
Consequently, the rankings in each column 
were summed up to give a column total; each
of the column elements (value) was divided 
by its column total to calculate the normalized 
matrix which, when summed up resulted in one 
or 100 %. Hence, in calculating the weight of 
each factor, the rows of the normalized matrix 
were rounded up by summing up all the rows’ 
elements and divided by the number of factors. 
The weights of the factors were calculated
in accordance with the stages defined by 
Malczewski (1999). Therefore, the pair-wise 
comparisons of the factors were considered as 
the input, whereas the normalized values of 
the eigenvector were used as the final output. 

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Journal of Sustainability Science and Management 
Volume 14 Number 2, April 2019 : 157-171 
164 
ISSUES UNDERMINING PUBLIC TRANSPORT UTILIZATION IN 
DAMMAM CITY, SAUDI ARABIA: AN EXPERT-BASED ANALYSIS 
Determining the weights helped in identifying 
the factors that were more responsible in 
undermining public transport utilization. 
The priority weights were further validated 
through the calculation of a CR. The CR indicated 
the robustness of the findings. In checking the 
inconsistency, the initial rankings assigned by 
the experts in Figure 2 were multiplied by the W 
vector that was calculated under the normalized 
matrix W
S 
vector. The W
S 
was determined using 
equation (2). 
In calculating the consistency vector, the Dot 
Product (•) of 
W
S 
was used, as one vector could not
be divided by another vector. That was why the Dot 
Equation (3) came up with the consistency vector, 
which was rounded up to get value. The value
was used in calculating the Consistency Index (CI) 
using equation (4). 
where, 
n = number of criteria (i.e. 6) and = average value
of the consistency vector determined. Lastly, the 
Consistency Ratio was determined by using equation 
(5). 
where, 
RI = random consistency index whose value depends 
on the number (n) of factors being compared; for n = 
Product (•) of 
W
S 
was used as shown in equation (3). 
6, RI = 1.24 as shown in Table 3 below. 
The 
W
S 
was then used for division throughout the 
elements of vector W. 
Table 3: Random consistency index (Source: Saaty, 1980) 
N 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
R 
0 
0 
0.58 
0.0 
1.12 
1.24 
1.32 
1.41 
1.45 
1.49 
The rule of thumb in a CR was that a value 
greater than 0.1 implied an unacceptable level 
of the priority weights calculated. Therefore, 
the pair-wise comparisons of the factors should 
be revised until an acceptable level was 
reached. Similarly, a CR less than or equals 0.1 
implied an acceptable level of the calculated 
priority weights.