Parsimonious Best Worst Method

Received 3 January 2023, accepted 30 January 2023, date of publication 3 February 2023, date of current version 23 February 2023.
Digital Object Identifier 10.1109/ACCESS.2023.3242120
A Novel Parsimonious Best Worst Method for
Evaluating Travel Mode Choice
SARBAST MOSLEM
School of Architecture Planning and Environmental Policy, University College of Dublin, Belfield, Dublin 4, D04 V1W8 Ireland
e-mail: sarbast.moslem@ucd.ie
This work was supported in part by the European Commission through the SENATOR Project, and in part by the Research and Innovation
Actions (RIA) under Project H2020MG-2018-2020 and Project 861540.
ABSTRACT There is an obvious trade-off between the amount of information obtained from user surveys
and low-cost and time-efficient survey. In this study, we propose a Parsimonious Best Worst Method
(P-BWM) to unburden the evaluators from the extensive number of pairwise comparisons required originated
by numerous factors and alternatives required by the Best Worst Method (BWM) in the complex decision
problems. The new Parsimonious BWM model assigns priorities to many elements by contrasting pair
wisely some reference elements, also it combines the straightforwardness of direct evaluations with the
dependability and stability of the BWM approach. The developed Parsimonious BWM technique has been
experimented and validated in a real-world problem of Mersin city in Turkey, to evaluate travel mode
alternatives. Moreover, a comparative analysis has been applied to the correlation of the adopted outcomes
between BWM and P-BWM.
INDEX TERMS Multiple criteria analysis, best worst method, parsimonious preference information,
pairwise comparison matrix, travel mode choice.
I. INTRODUCTION
In general, the scholars are confronted by the riddle in prefer-
ence surveys, where several complicated questions are asked
to get precious data as much as possible, or in other cases, they
construct unsophisticated evaluations to get a large number of
responses through the high response rate.
The Analytic Hierarchy Process (AHP) is the most applied
approach for scaling performances taking into consider-
ation factors and alternatives and their significance [1].
For scrutinizing the main advancement of AHP approach,
see [2], [3], [4], [5], [6], and [7]. However, the evalua-
tors spend enormous time and effort for evaluating even
small decision problems. Despite the many advantages of
AHP, the recently created Best Worst Method (BWM) has
quickly become the second favored choice application to
evaluate the complex decision issues after the Analytic Hier-
archy Process (AHP). Owing to the required efforts from
the decision-makers, the questionnaire of BWM considers a
fewer number of pairwise comparisons (PCs) comparing to
The associate editor coordinating the review of this manuscript and
approving it for publication was Agostino Forestiero .
other complex matrix-based Multi Criteria Decision Making
(MCDM) methodologies. For instance, in AHP, the estima-
tion process requires (n(n-1)/2) comparisons while BWM
requires only (2n-3) comparisons, where n is the number
of the evaluated elements [8]. More comparisons lead to a
long time for estimation process and vigorous effort from
the evaluator side. The other unique characteristic of BWM
is represented by the high reliability degree of the derived
weights, which comes from the consistency of the obtained
results, because the consistency check in BWM is for test-
ing reliability degree for evaluating the comparisons, on the
opposite of other MCDM methodologies, the consistency
check is for testing whether the comparisons are reliable
or not, reduces efficiently the risk of getting a confusing
or uncertain evaluation. The further advantage of BWM is
using merely the integer numbers and which makes it simpler
and more comprehensive for participants than other MCDM
methodologies, for instance, AHP. The BWM has a precise
conspicuous advantage in comparison to any other survey
methodologies [9].
The Parsimonious Best Worst Method (P-BWM) allows
to employ the methodology for estimating complex decision
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VOLUME 11, 2023

S. Moslem: Novel Parsimonious Best Worst Method for Evaluating Travel Mode Choice
problems dealing with a big number of factors and alter-
natives. The model is proposed for reducing the cognitive
effort of the evaluator to supply data. In our paper, the min-
imizing process for PCs numbers is compared with BWM.
The P-BWM model is saving the time and efforts efficiently,
which interns pacify the evaluator during the evaluation pro-
cess. For instance, if we have 10 alternatives it would be
necessary following the rules of the conventional BWM to
ask (2 × 10-3 =17) 17 PCs, while in the P-BWM model
only 3 PCs evaluations are required. If we suppose that
for evaluating each PC, in average, the evaluators would
spend 30 seconds, then they should take (17 × 30 = 510)
8.5 minutes for evaluating 17 PCs by using BWM, however,
they would spend only (3 × 30 = 90) 1.5 minutes for eval-
uating 3 PCs by using P-BWM. Even if we considered the
time of direct evaluation, the proposed model still reduces
evaluation time. For instance, 10 alternatives would consume
about 2 minutes to be rated and the total evaluation time
would be 2 + 1.5 = 3.5 minutes which still shorter than
8.5 minutes. So, the proposed model reduces the time of
pairwise comparisons for evaluators, even if we consider the
time of direct evaluations. In fact, we cannot limit the time for
evaluators, we just spot the light on the actual efforts and time
that the evaluators spend for conducting the evaluation pro-
cess. This small example reflects the tremendous difference
between BWM and the proposed P-BWM model.
As being a new model, there are no previous applications
of it and this leads to several open questions in terms of
the conditions and limitations related to conducting P-BWM.
The proposed model permits to use the logic of the BWM,
nevertheless reducing the number of preference comparisons
asked from the evaluators. The new model consists of four
main steps: (I) direct evaluation of the factors with respect
to the considered alternative, (II) choosing reference evalu-
ations; (III) application of BWM to reference evaluations;
(IV) revision of the direct evaluation on the basis of the
prioritization supplied by BWM on reference evaluations.
This paper proposes a novel Parsimonious Best Worst
Method (P-BWM) model for travel mode choice evaluation
and have been applied in a real case. Compared with the con-
servative BWM model, it is acknowledged that this P-BWM
method can reduce the number of pairwise comparisons. In a
certain extent, this study can save the time and efforts in
decision making process.
To validate the new P-BWM model we conducted the real-
world survey with experts from engineering departments in
Mersin University, whom were asked to estimate the travel
mode in Mersin city. The rest of the work is structured as
follows; In the Methodology section both BWM and P-BWM
are presented. The Results section introduces expert surveys
applied by BWM and P-BWM, which illustrate the merits of
the new model. Finally, conclusions are drawn related to the
application of the created model.
II. METHODOLOGY FOR THE PROPOSED RESEARCH
In this section, the basic Best Worst Method is presented, then
the novel parsimonious extension is illustrated.
A. THE BEST WORST METHOD (BWM)
The Best-Worst Method (BWM) approach has been cre-
ated recently for evaluating complex decisions, when there
are multiple factors or alternatives involved. Because it is
more convenient than other MCDM approaches, it has been
conducted for evaluating a large number of different com-
plex problems since its creation [10], [11], [12], [13], [14].
Additionally, many modified BWMs have been introduced
recently by relevant scholars to improve the performance of
the classical BWM [15], [16], [17], [18], [19], [20]. The
reliability and efficiency of BWM is quite high with respect
to the amount of data needed (see [13] for a general review on
the main improvements of BWM and [12], [21], [22], [23] for
some recent contributions related to BWM). Similarly, to the
AHP approach, BWM uses PCs to compute the weight scores
of factors and alternatives. However, the BWM approach
requires fewer comparisons (2n − 3) compared to the AHP
approach (n(n − 1)/2) [9]. Moreover, BWM approach is
easy to apply and more reliable compared to other method-
ologies [9]. The main steps of BWM approach for deriving
scores are depicted in Figure 1.
To provide an overview on all stages, we define the phases
in the following order:
Step 1: Identifying the problem and the set of alternatives.
In the first step, the decision maker defines n alternatives
(A1, A2, . . . , An) that are used to make the judgment.
Step 2: Defining the best and worst alternative by simple
scoring of the participant experts.
Step 3: Evaluating PCs between the best alternative to other
types by using a scale of 1 to 9, where 1 means ‘‘equal
importance’’ and 9 means ‘‘extremely more important’’. The
result of this step is represented by the following best to others
vector:
VB = (vB1, vB2, . . . , vBn) (1)
where vBj is the preference of alternative B (the most impor-
tant or the best) over the alternative j and vBB = 1.
Step 4: Conducting the PCs between the worst mobility
type and all other types by using a scale of 1 to 9. The result
of this step is represented by the following vector:
Vj = (v1W , v2W , . . . , vnW ) (2)
where vjD is the preference of alternative j (the most important
or the best) over the alternative W and vWW = 1.
Step 5: Calculating the final optimal weights (D∗
1, D∗
2, . . . ,
D∗
n) of the alternatives, and the indicator of the optimal con-
sistency of comparisons ξ∗.
The maximum absolute difference has to be minimized by:
min maxj

DB
Dj
− vBj ,
Dj
DW
− vjW

s.t.
X
j
Dj = 1, Dj ≥ 0, for all j (3)
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TABLE 1. The consistency index values for computing the consistency
ratio.
FIGURE 1. The main steps of the BWM approach.
After that the solution could be obtained by solving the
following linear programing problem:
min ξ∗
s.t.
DB
Dj
− vBj ≤ ξ∗
, for all j
Dj
DW
− vjW ≤ ξ∗
, for all j
X
j
Dj = 1
Dj ≥ 0, for all j (4)
Step 6: The Consistency Check
The following formula computes the Consistency Ratio to
check the tolerable inconsistent of the PCs [16].
Consistency Ratio = ξ∗
Consistency Index (5)
where the Consistency Index (CI) is given in Table 1 [16]
gained by random experiments for different number of
comparisons.
B. THE PARSIMONIOUS BEST WORST METHOD (P-BWM)
Despite the unique advantages of BWM, it still suffers from
handling with high number of elements and to overcome
this bottleneck, the new Parsimonious BWM model has been
invented.
The prevalent steps of the proposed new P-BWM model
for Fm factors and a alternatives can be summarized in the
following:
1) Direct rate evaluation of the factor Fm with respect to
alternative a;
2) Choosing a number of reference factors. Let us remark
the reference alternatives by s, and the number of ref-
erence factors by tm;
3) The participated evaluators are asked to conduct BWM
to the set composed of the reference evaluations (let
us denote γms the direct evaluation of the s reference
element by the evaluators) defined on Step 2 adopting
the normalized evaluations u(γms), for all m = 1, . . . , n
and for all s = 1, . . . , tm;
4) The following items have to be checked and discussed
with the evaluators: the consistency of the PCs has
to calculated by the consistency ratio, the normalized
evaluations u(γms), for all m = 1, . . . , n and for all s =
1, . . . , tm, have to be compared with the corresponding
ratings rm(γms) controlling that the monotonicity is
satisfied, that is verifying that rm (γms1) rm(γms2)
if u (γms1) u(γms2),
5) The rating of the evaluations provided by evaluators
(which are not the reference evaluations) are adopted
by linear interpolation for the normalized evaluations
which have to be computed in the previous step. Let
us donate: u(rm (a)) the normalized evaluation score
of the factor m with respect to alternative a, which is
calculated from the interpolation of the values adopted
by the reference BWM in the 3. and 4. Steps, u(γms) the
normalized BWM score of s+1 reference factor gained
from the PC, γms the direct evaluation of the s reference
factor by the evaluators, γms+1 the direct evaluation of
the s+1 reference element by the evaluators, rm (a) the
direct corresponding rating provided by the evaluator
to the alternative a, For each rm (a) ∈ [γms, γms+1], the
following value has to be computed, which avoids the
rank reversal issue:
u(rm(a)) = u(γms)
+
u (γms+1) − u (γms)
γms+1 − γms
(rm (a) − γms)
(6)
Basically, in P-BWM we have a monotonic increasing
order of the factors, determined by direct evaluation
on a factor level. From this order we select tm ref-
erence factors and conduct the PCs on them. Their
increasing order has to be kept and consistency to be
checked. Afterwards, we substitute their weight values
with the direct ratings and get back to the original
monotonic increasing order. In this order normalizing
any rj elements mean to find its low (γms) and high
(γms+1) neighbor out of the reference factors. Their
monotonic order cannot be changed, which is assured
by formula (6).
III. A CASE STUDY FOR TESTING P-BWM MODEL FOR
TRAVEL MODE ANALYSIS
In order to validate the proposed P-BWM model we applied
a real survey with 7 evaluators from engineering departments
in Mersin University, they were asked to evaluate the travel
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FIGURE 2. The travel types.
TABLE 2. The aggregated scores for travel mode alternatives by using
BWM approach.
mode problem in Mersin city. In this case study, no factors
have been adopted, only the alternatives (the transport modes
themselves) were estimated, since we relied on expert con-
siderations and did not strive to influence their decisions by
any factor selection. In the applied survey six mobility types
were utilized as listed in Figure 2 (Public transport, Car,
Car-pooling, Walk, Bike and Home office).
In the real-world case study, two user surveys were
applied by BWM and P-BWM in a Turkish city, Mersin
in December, 2021, seven answers from the academic stuff
members in engineering departments have been received.,
the survey process has been started with BWM survey (each
person evaluated 9 PCs).
Having selected the commuting alternatives and imple-
mented the BWM logic, the following short questionnaire
was created.
• ‘‘Please select the best and worst mobility type for
commuting!’’
• ‘‘Please evaluate other mobility types with respect to the
best type using a scale of 1 to 9’’
• ‘‘Please evaluate other mobility types with respect to the
worst type using a scale of 1 to 9’’
After computing weights of mobility alternatives for every
evaluator in all group, and calculating the consistency,
we aggregated the weights for each group by utilizing the
geometric mean to get the final weight vectors.
The total number of PCs for the evaluators is 2n-3 =
9, where n = 6. After aggregating 7 score vectors which
were generated from 7 responses, the results are presented
in Table 2.
A. P-BWM MODEL FOR EVALUATING TRAVEL MODE
The experiments, they were done face to face with 7 academic
experts in the engineering field, before filling up the survey,
we explained the target of the survey and main steps of the
application. The meeting was in same day for each expert.
The P-BWM process has a unique difference point from
BWM, which is the direct rating for the alternatives, in this
point we ensure that the evaluator would not be impacted by
the traditional steps of the BWM.
FIGURE 3. The framework of the proposed P-BWM model.
The main five steps of P-BWM model for our case are
illustrated as follows (Figure 3):
Step 1: Constructing the structure: six alternatives were
selected for estimating travel mode, the selection process was
done with decision makers in the related field;
Step 2: Direct rating for the six alternatives: the evaluators
did the estimation process with respect to the goal, then we
aggregated the normalized ratings for all of them;
Step 3: Choosing the reference evaluations: the evaluator
defined 3 reference elements [31], [32].
Step 4: Evaluating the reference evaluations: The PC eval-
uation of the reference elements done by employing BWM.
The evaluator asked to compare the best reference element
with the other and compare the worst reference element with
the others. Then the consistency of the PC was tested to detect
the reliability [8];
Step 5: Prioritizing all evaluations by interpolation: the
scores for all other alternative have been computed by inter-
polation taking in consider the adopted priority values from
the previous step (Formula 6).
The main difference here is that in BWM approach the
evaluator asked to highlight the best and the worst alternatives
and conduct PC for all alternatives with respect to the best
alternative and with the worst alternative, however, in our
P-BWM model, firstly the direct rate is asked to be con-
ducted which provides at the same time the best alternative
and worst alternative, then conduct BWM on the reference
elements. The original idea is minimizing the time and effort
for evaluators.
Before starting the evaluation process, we explained the
process for each evaluator, since the surveys have been done
face to face with each evaluator alone and we guided them
during conducting the evaluations.
Step 1: The six alternatives in our case are directly eval-
uated by evaluators based on (0- 100) scale. The gained
ratings were aggregate by employing the geometric mean
technique [26]. The final rate score for each alternative was
as follow (Table 3): a1 ‘‘Public transport’’ (0.087); a2 ‘‘Car’’
(0.0362); a3 ‘‘Car-Pooling’’ (0.027); a4 Walk (0.099); a5
Bike (0.149) and a6 Home-Office (0.276).
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TABLE 3. The direct evaluation for travel mode alternatives the final
parsimonious scores.
TABLE 4. The obtained scores from BWM approach for the reference
elements.
Step 2: Following that, suitable reference alternatives have
to be selected out of the total alternatives. For our case the
following reference elements have been selected considering
their position in the direct evaluation (highest value; middle
value and lowest value), ‘‘Car’’ (γ1 = 0.362); ‘‘Bike’’ (γ2 =
0.149) and ‘‘Car-Pooling’’ (γ3 = 0.027). Keeping in mind
avoiding big number of references, which can lead to several
PC evolutions. Abastante et al. [24] selected 4 references for
13 elements, while Duleba [25] and Duleba and Moslem [7]
selected 3 references for 11 elements. Till now, the optimal
number of reference elements is exposed to debates and it
needs further research for clarification.
Step 3: Choosing the reference evaluations: the evaluator
defined 3 reference elements;
In our case, we selected Car, Bike and Car-Pooling.
Step 4: Evaluating the reference evaluations: The PC eval-
uation of the reference elements done by employing BWM
(Table 4). The evaluator asked to compare the best reference
element with the other and compare the worst reference
element with the others. Then the consistency of the PC was
tested to detect the reliability [8] Rezaei.
Step 5: Prioritizing all evaluations by interpolation: the
scores for all other alternative have been computed by inter-
polation taking in consider the adopted priority values from
the previous step (Formula 6).
u (Home − Office) = 0.223 +
0.694 − 0.223
0.362 − 0.149
× (0.362 − 0.276)
= 0.223 +
0.471
0.213
× (0.086) = 0.413
u (Walk) = 0.083 +
0.223 − 0.083
0.149 − 0.027
× (0.099 − 0.027)
= 0, 083 +
0.14
0.122
× (0.072) = 0.166
u (Publictransport) = 0.083 +
0.223 − 0.083
0.149 − 0.027
× (0.087 − 0.027)
= 0.083 +
0.14
0.122
× (0.06) = 0.152
TABLE 5. The final parsimonious scores for travel mode alternatives.
TABLE 6. The final normalized parsimonious scores for travel mode
alternatives.
TABLE 7. Comparison of the reference conventional BWM survey and the
new P-BWM survey.
Table 5 presents the final parsimonious scores for travel mode
alternatives and Table 6 presents the final normalized scores.
Table 7 illustrates the comparison of technical details of the
conducted two methodologies.
IV. CONCLUDING REMARKS
This paper proposes a novel prioritization Parsimonious Best
Worst Method (P-BWM) model using pairwise comparison
matrices for travel mode choice evaluation, the proposed
model have been applied in a real case. Compared with
the conservative BWM model, it is acknowledged that this
P-BWM method can reduce the number of pairwise com-
parisons, where the model employs the pairwise comparison
matrices that is parsimonious with respect to the preference
information asked to the decision maker. In a certain extent,
this study can save the time and efforts in decision making
process.
It permits to use BWM approach even if the considered
decision problems present a high number of alternatives or
factors. The new proposal is composed of 5 steps: (I) estimate
of the performances of the considered alternatives on each
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factor; (II) definition of some reference evaluations in accor-
dance with the analyst; (III) pairwise comparison of the ref-
erence evaluations by using the BWM method; (IV) control
and discuss with the DM the consistency of the supplied PCs;
(V) interpolation of the values obtained by BWM approach in
the previous step in order to get the normalized evaluations of
all alternative performances.
As limitation, the risk of information loss has to be empha-
sized. The reduction of comparisons is very useful from
practical point of view, since the evaluation time of each ques-
tionnaire decreases significantly which possibly increases the
response rate of the participants. On the other hand, however,
the reduction means information loss on the relations of the
missing pairs of the factors or alternatives in the decision
problem. This risk should be considered and handled by the
methodologists of the decision and the survey should balance
between the evaluation time and information loss.
We would also like to underline that the proposed pro-
cedure permits to apply P-BWM in decision problems with
a huge number of elements to be compared. For this rea-
son, we believe that our proposal of a parsimonious version
of BWM can be considered a relevant contribution for the
basic theory and application of BWM. In future studies,
Bayesian model can be integrated with P-BWM for eval-
uation and comparison of the complex problems in fuzzy
environment [27].
COMPETING INTERESTS
All authors are here with confirm that there are no competing
interests between them.
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triangular fuzzy sets for evaluating driver behavior factors related to road
safety,’’ Mathematics, vol. 8, no. 3, p. 414, Mar. 2020.
SARBAST MOSLEM received the Ph.D. degree
(Hons.) in transportation and vehicle engineering
from the Budapest University of Technology and
Economics, Hungary, in 2020. He is currently
holding a postdoctoral research fellow position at
University College Dublin, Ireland. He has pub-
lished more than 30 articles in refereed top journals
(such as Applied Soft Computing, Expert Systems
with Applications, European Transport Research
Review, and Sustainable Cities and Society), most
of the published works are about developing urban transport system by using
decision support methodologies. His current research interest includes fuzzy
decision-making methods to solve engineering complex problems.
VOLUME 11, 2023 16773

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