A Fuzzy-Logic Approach Based on Driver Decision-Making Behavior Modeling and Simulation

Abstract

The present study proposes a decision-making model based on different models of driver behavior, aiming to ensure integration between road safety and crash reduction based on an examination of speed limitations under weather conditions. The present study investigated differences in road safety attitude, driver behavior, and weather conditions I-69 in Flint, Genesee County, Michigan, using the fuzzy logic approach. A questionnaire-based survey was conducted among a sample of Singaporean (n = 100) professional drivers. Safety level was assessed in relation to speed limits to determine whether the proposed speed limit contributed to a risky or safe situation. The experimental results show that the speed limits investigated on different roads/in different weather were based on the participants’ responses. The participants could increase or keep their current speed limit or reduce their speed limit a little or significantly. The study results were used to determine the speed limits needed on different roads/in different weather to reduce the number of crashes and to implement safe driving conditions based on the weather. Changing the speed limit from 80 mph to 70 mph reduced the number of crashes occurring under wet road conditions. According to the results of the fuzzy logic study algorithm, a driver’s emotions can predict outputs. For this study, the fuzzy logic algorithm evaluated drivers’ emotions according to the relation between the weather/road condition and the speed limit. The fuzzy logic would contribute to assessing a powerful feature of human control. The fuzzy logic algorithm can explain smooth relationships between the input and output. The input–output relationship estimated by fuzzy logic was used to understand differences in drivers’ feelings in varying road/weather conditions at different speed limits.
Keywords: decision-making process; driver’s behavior modeling; fuzzy logic; vehicle crash severity

Full text

Sustainability 2022, 14, 8874. https://doi.org/10.3390/su14148874 www.mdpi.com/journal/sustainability
Article
A Fuzzy-Logic Approach Based on Driver Decision-Making
Behavior Modeling and Simulation
Abdulla I. M. Almadi 1,2, Rabia Emhamed Al Mamlook 3,4,*, Yahya Almarhabi 5,6, Irfan Ullah 7,8,*, Arshad Jamal 9
and Nishantha Bandara 1
1 Department of Civil and Architectural Engineering, Lawrence Technological University, 21000 West Ten
Mile Road, Southfield, MI 48075, USA; aali@ltu.edu (A.I.M.A.); nbandar@ltu.edu (N.B.)
2 Department of Civil Faculty of Technical Sciences, Sebha P.O. Box 18758, Libya
3 Industrial Engineering and Engineering Management, Western Michigan University Kalamazoo,
Kalamazoo, MI 49008, USA
4 Department of Aviation Engineering, Al-Zawiya University, Al-Zawiya P.O. Box 16418, Libya
5 Department of Surgery, Faculty of Medicine, King Abdulaziz University, Jeddah 22254, Saudi Arabia;
yalmarhabi@kau.edu.sa
6 Center of Excellence in Trauma and Accidents, King Abdulaziz University, Jeddah 22254, Saudi Arabia
7 School of Transportation and Logistics, Dalian University of Technology, Dalian 116024, China
8 Department of Business and Administration, ILMA University, Karachi 75190, Pakistan
9 Transportation and Traffic Engineering Department, College of Engineering, Imam Abdulrahman Bin Faisal
University, Dammam 34212, Saudi Arabia; ajjamal@iau.edu.sa
* Correspondence: rabiaemhamedm.almamlok@wmich.edu (R.E.A.M.); irfanktk@mail.dlut.edu.cn (I.U.)
Abstract: The present study proposes a decision-making model based on different models of driver
behavior, aiming to ensure integration between road safety and crash reduction based on an
examination of speed limitations under weather conditions. The present study investigated
differences in road safety attitude, driver behavior, and weather conditions I-69 in Flint, Genesee
County, Michigan, using the fuzzy logic approach. A questionnaire-based survey was conducted
among a sample of Singaporean (n = 100) professional drivers. Safety level was assessed in relation
to speed limits to determine whether the proposed speed limit contributed to a risky or safe
situation. The experimental results show that the speed limits investigated on different roads/in
different weather were based on the participants’ responses. The participants could increase or keep
their current speed limit or reduce their speed limit a little or significantly. The study results were
used to determine the speed limits needed on different roads/in different weather to reduce the
number of crashes and to implement safe driving conditions based on the weather. Changing the
speed limit from 80 mph to 70 mph reduced the number of crashes occurring under wet road
conditions. According to the results of the fuzzy logic study algorithm, a driver’s emotions can
predict outputs. For this study, the fuzzy logic algorithm evaluated drivers’ emotions according to
the relation between the weather/road condition and the speed limit. The fuzzy logic would
contribute to assessing a powerful feature of human control. The fuzzy logic algorithm can explain
smooth relationships between the input and output. The input–output relationship estimated by
fuzzy logic was used to understand differences in drivers’ feelings in varying road/weather
conditions at different speed limits.
Keywords: decision-making process; driver’s behavior modeling; fuzzy logic; vehicle crash severity
1. Introduction
According to World Health Organization (WHO) reports, around 1.2 million people
die each year due to road traffic accidents worldwide. Traffic accidents not only take
people’s lives but are also costly, accounting for roughly 3% of a country’s gross domestic
product (GDP) [1]. According to research, risky driving behaviors are responsible for 90%
Citation:
Almadi, A.I.M.; Al
Mamlook, R.E.; Almarhabi, Y.;
Ullah, I.; Jamal, A.
; Bandara, N. A
Fuzzy
-Logic Approach Based on
Driver Decision
-Making Behavior
Modeling and Simulation.
Sustainability
2022, 14, 8874.
https://doi.org/10.3390/su14148874
Academic Editor:
Matjaž Šraml
Received:
26 May 2022
Accepted:
6 July 2022
Published:
20 July 2022
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opyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license
(https://
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s/by/4.0/).

Sustainability 2022, 14, 8874 2 of 20
of traffic accidents [2]. For example, a report [3] states that aggressive behavior is the
leading cause of vehicle crashes in the US. Aggressive drivers prone to impatience,
hostility, annoyance, and the desire to save time [4] can cause congestion and collisions
[5,6]. Aggressive driving, also known as hostile, sporty, or annoyed driving, is a
behavioral pattern that includes abrupt speed changes, risky speeding, deceleration, harsh
acceleration, and improper lateral place maintenance [7]. This kind of driving style has
received the most attention from researchers because it deviates from the norm and
normal driving behavior and can result in higher fuel consumption and emissions and
even fatal crashes [8,9]. As a result, it could be beneficial for government institutions to
investigate lower-cost, easy-to-implement solutions based on the aggressive driving
behavior of drivers to improve the driver awareness when they are driving too
aggressively. The second group of driving styles is the most common, and is referred to
as defensive driving. The typical driving style is frequently used to define other driving
styles and could be used as a baseline for driving style classification. Defensive driving is
frequently contrasted with aggressive driving [10]. Defensive driving, while not explicitly
defined, usually refers to modest acceleration/deceleration, careful traffic-flow
participation, and adequately kept headway distance. It bears a solid resemblance to
everyday driving but is more passive. Data describing physical characteristics of driving
environments are not usually accessible to drivers in precise statistical format. Instead, a
car driver understands and explains the environment in inaccurate terms, such as “high
speed” or “enough space to change roads”. Fuzzy logic is able to handle these cases, and
it has been successfully used in modeling both human behavior in general and driver
behavior. Fuzzy logic has proven to be a very effective tool for processing inaccuracy and
insecurity, which are both very important physical characteristics of driving
environments. This makes fuzzy logic a strong candidate tool in most traffic engineering
studies [9].
Many studies have used various methods to understand driver behavior better and
have identified some behavioral influences that point to “safe” or “unsafe” driving styles
[11,12]. Self-report and data-driven approaches are the two most common methods for
determining a driver’s aggressive driving behavior. In a number of studies using the self-
report method, data were collected from questionnaires to examine the aggressive driving
behavior of the driver’s emotional situations (anger, frustration, annoyance) or
motivational situations (boredom, punishment, competition) [12–14]. The data-driven
method attempts to create a driver behavior model using statistics, the machine learning
(ML) algorithm, and artificial intelligence (AI) methods. ML algorithms have grown in
popularity due to their ability to capture non-linear relationships between variables using
fewer model assumptions [15–17]. Driver events (acceleration, speed, lane changes,
distance between cars) are used as inputs in these techniques [7,18] to classify aggressive
driver behavior. The self-reported approach may be considered less expensive and easier
to implement; however, responses are subjective and may not provide actual data [19].
Models based on statistical and AI techniques could be more consistent due to driver in-
vehicle data, resulting in a better demonstration of driver styles. For instance, methods
based on the neural network [20,21] and fuzzy logic [18] algorithms were employed to
differentiate driving style from driving data. To classify driving styles, different
supervised [22] and unsupervised [23,24] models have been developed. Furthermore,
rather than using maneuver frequency, Li et al. classified highway driving behaviors into
12 maneuver states and used a random forest algorithm to focus on transition patterns
[25]. It was discovered that the transition probabilities between maneuvers could improve
driving style estimation.
A major strand of literature has emerged examining the impact of driving style on
fuel consumption [26–28] and driving safety [29–31]; the majority of studies have been
based on analyzing human driving data collected for numerous scenarios. Although
positive correlations were found between driving style and individual factors in these
studies, the impact of driving style variance is still being debated, particularly in fuel

Sustainability 2022, 14, 8874 3 of 20
consumption investigation. This is due to the unpredictable nature of human behavior,
which makes comparative studies challenging to conduct. A viable solution to this
problem is to create a driver model that can mimic human behavior and perform various
driving styles. However, the differences in driving styles can be observed in various
driving scenarios, including free flow, car-following, and driving under instructions.
2. Background and Related Works
This study describes earlier studies on aggressive driving styles, focusing on the
variables used to estimate driving styles and recognize a driver’s intention. In addition,
we give a brief overview of different techniques and how they have been applied in this
research.
2.1. Aggressive Driving
Various data sources have already been utilized to investigate aggressive driving
behavior. For example, a report [3] stated that aggressive behavior is the leading reason
for vehicle crashes in the United States. Aggressive driving raises the risk of an accident.
This behavior may result from the driver’s annoyance, hostility, impatience, or desire to
reduce travel time [4]. The driver’s aggressive driving style is defined by unsafe events
such as speeding, quick lane change, and abrupt accelerations/decelerations [18]. Osafune
et al. proposed a system for categorizing aggressive driving behavior into two classes: safe
and risky. Sudden braking, sudden acceleration, and sharp turns are explanatory
variables [32]. They created a Support Vector Machine (SVM) model with a recall of 0.833
and an accuracy of 0.709. Koh et al. established a model to classify the aggressive behavior
of young and elderly drivers [33]. The data on lateral accelerations were extracted from
the driver’s vehicle. A Gaussian Mixture Model (GMM) and the periodogram approach
were utilized to find significant periodicities in the data to detect the driver’s aggression
profile. Hong et al. used a Bayesian model to predict drivers with a specific driving style
[34]. Different information was obtained from a vehicle, such as the engine RPM values,
speed, acceleration value, and turn events. The result revealed that the model has an
average accuracy of 90%. Most earlier studies used low-dimensional and linear data to
create driving behavior and prediction models. For example, the authors employed a
time-to-collision (TTC) threshold to predict aggressive driving behavior [35]. Wahlberg
also used acceleration-related variables [36]. Furthermore, the majority of studies on
aggressive driving behavior used fewer variables. Nevertheless, driving behavior is a
complex time-series. While a single value, such as TTC, is strongly related to aggressive
driving behavior, not every safety-critical event characterized by a decreased TTC value
results from risky behavior [37]. In conclusion, the most commonly utilized variables are
a vehicle’s acceleration/deceleration, lateral/sudden accelerations, and braking.
2.2. Recognizing Driver’s Intention
Numerous studies have been conducted to determine a driver’s intention. Most
approaches are based on well-established techniques, such as ANN, Fuzzy logic (FL),
Dynamic Bayesian Network (DBN), SVM, and the Hidden Markov Model (HMM). Tran
employed HMM to determine driver intention for a range of drivers, with stop/non-stop,
turn left/right, and lane change left/right. However, the findings of driving behavior
identification are not consistently demonstrated to be of high quality when using HMM.
Numerous ways have been presented to enhance the efficiency of intention recognition
using HMM. For example, Zabihi et al. employed an input–output Markov model to
identify the related parameters from the actual driving data. They used a combination of
driver attributes, such as age and gender and vehicle dynamics, to determine the driver’s
intention. Deng employed a model for predicting driving behaviors based on a newly
developed technique that combines various HMM cooperation integrated with Fuzzy

Sustainability 2022, 14, 8874 4 of 20
Logic. They discovered that incorporating driver intention factors as input improves
driving behavior prediction performance.
2.3. Aggressive Driving Behavior Prediction
Analysts must deduce the driver’s intention and multivariate-temporal features of
driving behavior to predict aggressive driving behavior. Numerous research studies on
the prediction of driving behavior have been conducted, and they are mainly classified
into three classes (non-parametric, parametric, and semi-parametric) based on the
approach utilized. The parametric model widely uses the autoregressive integrated
moving average (ARIMA) time-series approach [38,39]. Consequently, various variations
of the ARIMA method were introduced for improved prediction performance. The x
ARIMA model is incapable of managing non-linear traffic data; consequently, a KARIMA
method combining the Kohonen network and ARIMA was proposed [40]. An ARIMAX
model was developed to increase prediction accuracy by merging ARIMA with input
variables [41]. These solutions address the standard ARIMA model’s flaws, such as its
inability to handle non-linear data and low prediction accuracy. Nevertheless, these
approaches only analyze temporal variation and produce unsatisfactory prediction results
due to the nonlinearity and random driving behavior. Some models from the non-
parametric model family fall into the second category, such as decision tree KNN, SVR,
and ANN [42]. Habtemichael employed the KNN method to forecast short-term driving
behavior; however, it performs poorer than the linear time-series method [43–46].
Furthermore, several ANN-based models for predicting driving behavior have been
proposed, but they never outperform the time-series method [40,41]. However, when
predicting the driving behavior based on time-series data, these models cannot
outperform parametric models. Some studies have used semi-parametric, ARMIA,
moving average (MA), ANN, and exponential smoothing (ES) models for prediction
[47,48]. Moreover, a semiparametric method based on networks typically uses only one
hidden layer or a shallow network, which is not sufficient to represent the driver’s
purpose and the complex nonlinearity of driving behavior [49]. Kumar et al. conducted a
survey considering driver behavior analysis and the driver behavior prediction models
[50]. A more specific definition of driver behavior analysis models focused on various
approaches for understanding driver behavior and information about driver driving. The
driver behavior prediction models predict whether a driver is driving safely or not.
Moslem et al. surveyed the experienced driver in the Hungarian capital city, Budapest, to
find out the significant driver behavior factors associated to road safety [51]. The findings
exhibited that violations is the most significant factors affecting the road safety. De ona et
al. conducted a stated preference survey in Italy and Spain to identify the main factors
that influence a driver’s perception of accident risk [52]. The results revealed that violating
the overtaking vehicle rules and psychophysical state are the most risky behaviors. Liu et
al. examined the relationship between drivers’ propensity for risky driving and risk
perception [53]. The outcome shows that risk perception negatively influenced crash
involvement and positively affected driving skills.
2.4. Using Fuzzy Logic for Driver behavior
Fuzzy Logic is a subfield of Artificial Intelligence (AI) defined by adding truth and
false ideas from common logic to a machine-generated model to account for uncertainty
in data [1]. Three steps must be followed to create a fuzzy logic model: (1) Fuzzification:
the process that inputs membership functions and linguistic variables. (2) Rule
Evaluation: in this step, fuzzy logic rules are employed to decide the value of an output
variable based on the values of input variables. (3) Defuzzification: in the last step, a fuzzy
inference system (FIS) turns the output into a crisp result [54]. The Takagi-Sugeno Fuzzy
Model (Sugeno) and the Mamdani Fuzzy Inference System are the two common categories
of FIS. Sugeno outperforms Mamdani in terms of computational efficiency, even though
Mamdani captures human input better [55,56]. Previous research has investigated fuzzy

Sustainability 2022, 14, 8874 5 of 20
logic models based on data collected from in-vehicle sensors. Some significant works have
investigated the relationship between driving style and fuel usage by estimating the
performance of different drivers [24]. Dörr et al. suggested an online model that describes
driver styles using fuzzy logic, with an accuracy of 0.68 [57]. In addition, Aljaafreh et al.
introduced a fuzzy method to classify aggressive driving based on driver style in their
work [18]. The driver styles were divided into four categories: below normal, normal,
aggressive, and highly aggressive. Hao et al. conducted a study based on fuzzy logic. They
used vehicle trajectory data to create two generalized driving style models (aggressive
and conservative) [58]. A genetic method was used to calibrate the fuzzy membership
function.
3. Materials and Methods
Driver reporting consists of three main phases: simulation, data collection, and
analysis. Firstly, a vehicle speed model based on the simultaneous equations approach is
developed and validated with one more site data. Secondly, data collection methods
include.surveys, questionnaires, simulations, and realistic experiments. Thirdly, fuzzy
logic is applied. A driving simulator provided a safe driving environment for participants,
and they were asked to identify changes in the safety effects to establish the best speed
limit. As a result of this, participants became more aggressive and exhibited more risk-
taking behaviour. As a result, realistic experiments have become an essential and reliable
data source. In the analysis phase, the recorded driving data are categorized into labels
such as “safe”, “little safe”, “safe”, and “little safe”. Finally, the study methodology
followed in the research is presented in Figure 1
3.1. Data Collection
This study was approved by the Lawrence Technological University (LTU)
Institutional Review Board. Additionally, an online training course sponsored by the
National Institutes of Health (NIH) Office of extramural research was completed. Subjects
were eligible to participate in the study if they had a valid U.S. driver’s license, were 18
years or older, and had driven on an interstate highway in different weather conditions.
Data were collected from the driving simulator and a questionnaire answered by
participants. Another experiment investigated the avoidance behavior of some middle-
aged (31–40) and older participants (51–60) in response to addressing six challenging
scenarios on driving simulators. A total of 110 participants, including males and females,
were recruited to drive through ten different driving scenarios, 10 for the pilot study and
100 for the experiment design. These drivers ranged from 18 to 60 years old, averaging
35.2 years. Their behavior and reactions to each scenario were captured and evaluated. To
evaluate a driver’s compliance with the roadside signs, the study used vehicle speed, lane,
braking, total tire slide, and crash information. After analyzing all results, this study
proposed a decrease in speed limit from 70 mph to either 50 or 40 mph, especially in icy
and snowy road/weather conditions.
3.2. Simulation
This study used a multi-user driving simulator to simulate the above-identified crash
types on a virtual I-69 roadway. This crash information, combined with various weather
and road conditions, is programmed into the driving simulator as different scenarios. For
creating the simulation scenarios, a prototyping approach was used in the driving
simulation laboratory at LTU. The driving simulator was designed to contain various
driving scenes with the ability to incorporate different road and weather conditions. The
driving simulator used in this study included a seat, a computer, a steering wheel, an
accelerator, crash, and brakes. The computer screen displayed information for the driver,
such as speed in miles per hour (mph), revolutions per minute (rpm), and the driving
scenario identification.

Sustainability 2022, 14, 8874 6 of 20
Figure 1. Study methodology.
The pilot test was performed to assess the scenarios developed for this study to
ensure that they include all the data required and are perfect to achieve the study-specific
objectives. The scenarios of this pilot test were effectively designed for the driver
simulator, considering the differences in participants’ behaviors and differences in
road/weather conditions to assist in addressing related questions. The pilot test was a
practical way of evaluating the effect of road/weather conditions and speed limits on the
participant’s behavior and to enable them to answer the questionnaires concerning their
driving experience and safety. Even with a sample size of only 10 participants, the pilot
test results justified the designed scenarios and simulator programs and activities, and
thus the starting of the experiment design. Realizing the decision-making model of the

Sustainability 2022, 14, 8874 7 of 20
driver in the driving simulation system. The driving simulation is formed by a vehicle
simulation program, a virtual traffic environment, and the virtual driver.
3.3. Short Description of the Fuzzy Inference System
The Fuzzy Logic modeling method is naturally helpful in cases where doubts are
complicated. In terms of fuzzy sets, there are different ways to interpret and analyze
subjective data from a particular survey case, such as the so-called fuzzy rating scale-
based questionnaire. This kind of questionnaire allows expressed human perceptions in
fuzzy rating scales. Fuzzy sets were applied to determine each road’s appropriate speed
limit and weather conditions. Since the study would be concerned with safety engineers’
subjective judgments, the fuzzy set mathematics is ideal. A fuzzy subset A of a set X is a
function A: X → L, where L is the interval [0,1]. This function is also known as the
membership function, which is assigned a score ranging between 0 and 1. Fuzzy
mathematics was used in answering the questionnaire issued to highway safety engineers
to furnish their experience on the rate of speed in different road and weather conditions.
Subjectively rated severity levels (very safe, safe, risky, high risky) of each type of weather
and road condition were modeled as fuzzy numbers on a scale. Study subject drivers were
queried about a possible uncertainty level when rating the severity of a specific type of
weather and road condition.
Fuzzy control attempts provide a formal methodology that describes and
implements human heuristic knowledge of how to control a system. In this study, we
want to control the speed limit to regulate weather sensation. A classical controller would
measure weather sensation precisely and compare it with some desired reference and
then, based on some model of the speed limit and its impact on weather sensation, it will
modify the speed limit. The choice of the membership function shape is not
straightforward, and only experience can help the designer.
The primary choice for membership function shapes for this research was the
trapezoid, because of its simplicity and linearity that fuzzy logic allows a number or object
to be a member of over one set, and it introduces the notion of partial [59]. The general
fuzzy inference process is shown in Figure 2, consisting of four components: fuzzy rule
base, fuzzy inference process, fuzzification process, and defuzzification [60]. The
following is a brief introduction:

Sustainability 2022, 14, 8874 8 of 20
Figure 2. Fuzzy Mamdani model.
 Fuzzification
The first stage is fuzzification which represents input variables by converting crisp
data values to fuzzy membership functions through fuzzy sets. A fuzzifier operator has
the effect of transforming a crisp value into fuzzy sets. The current study considered the
crisp inputs from the answers of the subject drivers on each scenario’s questionnaire and
then determined the degree to which these inputs belong to each of the appropriate fuzzy
sets.
 Fuzzy inference process (Aggregation of the Rule Outputs)
The second stage is the inference process, which combines the fuzzy sets of
membership functions with the inference rules to obtain the fuzzy output. This step is a
process of converting input values into output values using fuzzy logic. Conversion of
input into output values is essential for decision-making. Aggregation is the unification
process of the outputs of all rules. All rule consequents previously clipped or scaled
membership functions are combined into a single fuzzy set.
 Defuzzification
The final stage is defuzzification, which represents the output variables based on the
fuzzy sets. The Fuzzy Mamdani model for this study is shown in Figure 2. Fuzziness helps
us to evaluate the rules; however, the final output of a fuzzy system must be a crisp
number. The input for the defuzzification process is the aggregated output fuzzy set, and

Sustainability 2022, 14, 8874 9 of 20
the output is a single number. The three most important methods are the center of gravity
(COG), most significant maximum LOM, and middle of maximum (MOM).
I. LOM (largest of maximum), MOM (middle of maximum) methods
The LOM method is based on obtaining the largest of the maximum values as the
defuzzification value from the membership functions along with the AND and OR logic
operators. However, the MOM method concerns the middle maximum value of the
average value in the same zone.
II. Center of Gravity method
This method determines the center of the zone that is gained from membership
functions with OR logic operators. The formula with which we can calculate the
defuzzified crisp output U is given as:
U = ∫
µ()∗ 
∫
µ() (1
)
where:
U = The defuzzification result
 = Output variable
µ = Membership function
 = Minimum limit for defuzzification
 = Maximum limit for defuzzification
Arianit used three main defuzzification methods: COG, LOM, and MOM. Through
this process, it was possible to compare these three defuzzification methods. The results
showed crisper values for better link utilization, and the COG method is identified as the
best option. Accordingly, this method was used to have better crisp results.
III. Crash Modification Factors (CMFs) from Driving Simulator Studies
Identified Crash Modification Factors (CMFs) [61]: “CMFs is a multiplicative factor
used to compute the expected number of crashes after implementing a given
countermeasure at a specific site. The CMF is multiplied by the expected frequency
without treatment”. CMF is a way of evaluating the safety effectiveness of a specific
treatment (countermeasure). In other words, it is “the ratio between the number of crashes
per unit of time expected after a modification or measure is implemented and the number
of crashes per unit of time estimated if the change does not take place”. The application
of treatment is said to be effective if a considerable change in safety is felt and recognized;
without it, a change could not occur. The estimated crashes with treatment can be
determined when the CMF is applied to the estimated crashes without treatment, as
described in the following equation:
Estimated Crashes WITH Treatment =CMF ×Estimated WITHOUT
Treatment
(2
)
A before–after design is conducted, and it compares the number of crash occurrences
on the studied part of the road before and after treatment. When a certain countermeasure
(treatment) is applied, leading to a CMF less than 1.0, a reduction in crashes is highly
anticipated. However, an increase in crashes and a decline in safety are associated with a
CMF of more than 1.0. Reconfiguring Equation (3).
CMF = Expected Crashes with treatment
Expected crashes without treatment (3
)
If:
CMF = 1; there is no effect on crash frequency
CMF < 1; crashes are expected to decrease
CMF > 1; crashes are expected to increase
• Before–After evaluations of performed Studies

Sustainability 2022, 14, 8874 10 of 20
Generally, before and after evaluations are performed to develop CMFs for crash
reduction countermeasures. Generally, CMFs are developed by analyzing crash data
before and after a location countermeasure is applied. This evaluation takes a few years
and considerable resources to conduct. There are other issues to be considered for
evaluating the quality of CMFs resulting from the before–after designs, and they include
the following:Sample Size: The sample size can be determined based on the magnitude of
the treatment effect as well as the value of the standard error associated with CMF. The
standard error value will decrease with a large sample size and vice versa. Potential Bias:
The changes experienced within the periods before and after treatment can be due to
undefined factors not included in the proposed countermeasures.These include changes
in traffic volume or crash counts. These issues can lead to reduced quality of the resulting
CMFs.
4. Results and Discussion
4.1. Descriptive Statistic
In the previous research, a total of 100 individuals were enlisted to participate. To
ensure the sample was diverse enough in its gender and age representation. The age of
these drivers ranged from 18 to 60 years old. Of the five categories of age groups, the
percentage of crash causalities for ages 18–25 was 23%, ages 25–30 was 26%, ages 31–40
was 28%, ages 41–50 was 16%, and ages 51 to 60 was 7%. The percentage of crash
causalities for those aged 25–40 was the highest in all five categories. The percentage of
male causalities was 81% and 19% for females. Subjects ranged between 18 and 60 years
old, 52% had over 10 years of driving experience, and 60% drove using the highway every
day. Moreover, 18% of the subjects said they had similarly experienced sliding in their
cars when driving in snowy and icy conditions. Fifty-six percent of drivers said that they
drove at a speed below the speed limit in clear weather conditions, 9% drove below the
speed limit on snow-covered roads, and 9% drove below the speed limit on the highway
on snow-covered roads. Safety was classified into three levels (e.g., A Little safe, Less Safe,
and Very Safe). When subjects were asked how safe they felt when navigating a highway
compared to other roads, 45% felt that they were very safe, 44% felt a little safer, and 11%
thought they were less safe. The subjects’ demographic information and driving history
are summarized in Table 1.
Table 1. Descriptive statistics of pre-experiment questionnaire.
Driver Characteristics
Classification
Proportion of Drivers
Age
(18–25)
23%
(25–30)
26%
(31–40)
28%
(41–50)
16%
(51–60)
7%
Gender
Male
81%
Female
19%
No. of years of driving
experience
Primary (1–5 years)
27%
Middle (6–9 years)
21%
Senior (≥10 years)
52%
Highway driving mileage per
day
Every day
60%
Occasionally
12%
Often
28%
Speed when you drive on a
highway on snow-covered roads
Similar
18%
Below speed limit
56%
Below speed 10 limit
17%

Sustainability 2022, 14, 8874 11 of 20
Below 5 mph
9%
Number of times the driver has
slid on snowy and icy roads
Sometimes
60%
Never
12%
Often
28%
Safety
A Little Safe
44%
Less Safe
11%
Very Safe
45%
4.2. Description of the Fuzzy Logic Car-Following Model
The fuzzy logic model controls the system by converting the input and output control
variables to linguistic terms representing the fuzzy sets. Using four inference rules
through MATLAB, the fuzzy model for this system was constructed using the fuzzy tool,
which is the border for developing the expert system. The fuzzy model includes only one
input variable and an output variable. Table 2 demonstrates the input and output
variables and the inference rules of the model in detail Figure 2, shown below, is an
example of weather sensation measurement, or a ‘crisp’ measurement of 2.15. We
determined which the values of the membership functions that the crisp measurement
gave for each set. The measurement of 2.15 is a member of ‘V. Safe’ to the value of 0.75
and ‘Safe’ to 0.25.
Table 2. Description of variables, mathematical representation, their fuzzy sets, and rules.
Variables
Mathematical Representation
Generalized Trapezoidal Fuzzy
Weather
Sensation
(Input)
µ.()= 0;  ≥ 3
µ.()=
 − 2
3−2
; 2 < < 3
µ.()= 1;  ≤ 2
µ()= 0;  ≥ 6
µ()=
 − 5
6−5
; 5 < < 6
µ()= 1;  ≤ 5
µ()= 0;  ≥ 9
µ ()=
 − 8
9−8
; 8 < < 9
µ()= 1;  ≤ 8
µ.()= 0;  ≥ 10
Fuzzy
Sets Very safe safe Risky High, Risky
µ.()=
 − 9
10 −9
; 9 < <10 Values 0–1–2–3 2–3–4–5 5–6–7–8 8–9–10
µ. ()= 1;  ≤ 9
Speed Limit
(Output)
µ. ()= 0;  ≤ 5
µ.()=
10 − 
10 −5
; 10 >< 5
µ.()= 1;  ≥ 10
µ .()= 0;  ≤ −10
µ . ()=
−5−x
(−5−(−10)); −5 > 
<−10
µ .()= 1;  ≥ −5
µ
  
()= 0;  ≤ −25
µ  ()=
−20 − 
(−20 −(−25)−20 >
<−25
Fuzzy
Sets
reduce the
speed limit a lot

Sustainability 2022, 14, 8874 12 of 20
µ  ()= 1;  ≥ −20
increase
the speed
limit
retain
current the
speed limit
reduce the
speed limit
a little
µ   ()= 0;  ≤ −30
Values 20–15–10–
5 10–5–0–(−5)
(−5)–(10)–
(−15)–(20) (−20)–(25)–(30)
µ   ()=
−25 −()
(−25 −(−30)); −25 >
>−30
µ   ()= 1;  ≥ −25
Production Rules:
 If the weather sensation is Very Safe, then increase the speed limit.
 If the weather sensation is Safe, then retain current the speed limit.
 If weather sensation is Risky, then reduce the speed limit a little.

If the weather sensation is High Risky, then reduce the speed limit a lot.
Note: The part of the rule that precedes the ‘then’ is termed the antecedent part, whilst the part of
the rule that follows the ‘then’ is termed the consequent part.
The outputs relating to the inputs ‘V. Safe’ and ‘Safe’ are true to the same degree as
the inputs. When applying this process to this study, the 2.15 measurement of 0.75 ‘V.
Safe’ and ‘0.25’ Safe results in fuzzy outputs of ‘increase speed’ to the value of 0.75 and
‘Retain speed’ to a value of 0.25. These values truncate the output membership functions,
as shown below in Figure 2. The output membership functions are required to be
combined into a single membership function. One way to do this is to interpret the
combination of two truncated membership functions as an ‘OR’ operator for fuzzy sets.As
example of the combined results in an output membership function that looks like this:
μ=0.75 ×20 + 0.75 ×15 + 0.75 ×10 + 0.25 × 5 + 0.25 × 0 + 0.25 ×−5 + 0 × −10
0 + 0.75 + 0.75 + 0.75 + 0.25 + 0.25 + 0.25 + 0 = 11 (4
)
The output level can vary significantly depending upon the defuzzification method
used. For instance, the center of gravity method would yield a value for a change of 11.2
mph. The system outputs the expected values for the output variables. Figure 3 shows the
fields where this information is entered (circled in orange) and where the system shows
the expected values (circled in green):

Sustainability 2022, 14, 8874 13 of 20
Figure 3. Expert system operation.
4.3. Defuzzification Values and Output for Each Scenario
Table 3 shows the calculated simple average defuzzification for each scenario. The
defuzzification values were added and then divided by the total number of observations.
The fuzzy rule base employs the fuzzy model results for the inputs of 100 subject drivers
from the experimental dataset, which was utilized to assess the performance of the
proposed fuzzy model. The fuzzy logic toolbox was used through MATLAB to mirror the
control system. This resulted in the specific control of different weather conditions
provided by the trapezoidal membership functions. Table 3 shows ranges for all the
created fuzzy sets. The ranges for these sets are chosen based on the subject driver’s
feelings.
In S1, the conditions were clear weather with an 80 mph speed limit. As shown in
Table 3, the speed limit for S1 fluctuated from 5 mph over, or, retaining the current speed,
to 20 mph under, or reduced the speed limit. When reviewing the results for S3, the speed
limit at 70 mph was retained in the same weather conditions. In S2 and S4, both with rainy
weather conditions, the speed limits of 80 mph and 70 mph were retained. However, in
S5 and S6, with snowy and icy weather conditions, the speed limit of 70 mph was reduced
and ranged from −10 to −20 mph. Similarly, the speed limit was retained in in S7 and S8,
with a speed limit of 50 mph and snowy and icy weather conditions. In S9, where there
were snowy weather conditions, the speed limit of 40 mph fluctuated between 20 and −5
mph, either retaining this speed limit or increasing the speed limit recommendation. In
S10, there were icy weather conditions. Retaining the provided speed limit of 40 mph
appeared to provide safe conditions.

Sustainability 2022, 14, 8874 14 of 20
Table 3. The defuzzification values and output for each scenario.
Scenario
Weather
Condition/Speed
Limit
Average
Defuzzification Modify the Speed Limit Speed Range
(mph)
S1
Clear/80 mph
−5.3195
the speed limit/reduce the speed
From 5 to −20
S2
Rain/80 mph
−3.8166
retain the current speed limit
From 5 to −5
S3
Clear/70 mph
−0.3513
retain the current speed limit
From 5 to −5
S4
Rain/70 mph
2.0397
retain the current speed limit
From 5 to −5
S5
Snow/70 mph
−11.492
reduce the speed limit a little
From −10 to −20
S6
Icy/70 mph
−16.4599
reduce the speed limit a little
From −10 to −20
S7
Snow/50 mph
1.4335
retain the current speed limit
From 5 to −5
S8
Icy/50 mph
−3.9219
retain the current speed limit
From 5 to −5
S9
Snow/40 mph
6.6224
increase the speed limit/speed limit
From 20 to −5
S10
Icy/40mph
3.4828
retain current the speed limit
From 5 to −5
4.4. Development of Crash Modification Factors (CMFs) from Driving Simulator Studies
In this study, we used CMF to evaluate the safety and effectiveness of a specific
treatment (countermeasure). A before–after design was conducted, and then we
compared the number of crash occurrences on the studied part of the road before and after
treatment. When a specific countermeasure (treatment) is applied, leading to a CMF of
less than 1.0, a reduction in crashes is highly expected. However, an increase in crashes
and a decline in safety are associated with a CMF of over 1.0. Generally, before and after
evaluations are performed to develop CMFs for crash reduction countermeasures. CMFs
are developed by analyzing crash data before and after a location countermeasure is
applied. This evaluation takes a few years and considerable resources to conduct. Other
issues must be considered for evaluating the quality of CMFs resulting from the before–
after designs. The number of estimated crashes for 100 subject drivers in different weather
conditions that resulted from the driving simulator experience was used to find the CMF
to reduce the number of crashes. This method is called the comparison group method. We
estimated the resulting comparison ratio for the “change in mean speed” on the respective
weather/road condition before and after the treatment study.Since the before–after
designs of CMFs are complicated to develop due to the rationale provided previously, an
attempt to develop CMFs using driving simulator studies was performed in this study.
Using the previously described data, a change in speed limit during wet, snowy, and icy
weather/road conditions was selected as a countermeasure. Table 4 shows the anticipated
number of crashes before–after the speed reduction treatment. The suitable and adequate
speed limit can be determined using the CMF by considering each weather condition and
the speed limit before and after scenarios. Table 4 shows that the number of crashes at the
speed limit of 70 mph in snowy weather is 44 and reaches 78 in icy weather conditions.
However, when the speed limit is reduced to 50 mph, the number of crashes in snowy
weather reaches 15, and, in icy weather, it is 49. The number of crashes decreases when
the speed limit is reduced to 40 mph, therefore the crashes reach 4 in snowy weather and
35 in icy weather.
Table 4. Crash data for before–after treatment for 100 subject drivers.
Weather/Road
Condition
Time Period
Change Speed Limit
Crash Type Count
Clear/dry
Before 80 mph
Lane Marge (LM)
18
Hit Object (HO)
24
After 70 mph
Lane Marge (LM)
15
Hit Object (HO)
4

Sustainability 2022, 14, 8874 15 of 20
Rain/wet
Before 80 mph
Slow Dawn (SD)
10
Loss of Control (LOC)
11
After 70 mph
Slow Dawn (SD
6
Lane Change (CL)
11
Snow/snow
Before 70 mph
Loss of Control (LOC)
39
OTHER
5
After 50 mph
Loss of Control (LOC)
14
OTHER
1
After 40 mph
Loss of Control (LOC)
1
OTHER
3
Snow/icy
Before 70 mph
Loss of Control (LOC)
73
OTHER
5
After 50 mph
Loss of Control (LOC)
44
OTHER
5
After 40 mph
Loss of Control (LOC)
23
OTHER
2
Hit Deer (HD)
10
For this study, CMFs are expressed as a numerical value that reflected the expected
change in safety. The resulting comparison ratios were estimated for the “change in mean
speed” on the respective weather/road condition before and after the treatment study.
4.4.1. Install Speed Limit in Clear Weather/Dry Road Conditions
The base condition/speed limit of the CMF (i.e., the condition in which the CMF =
1.00) was 80 mph. Changing the speed limit from 80 mph to 70 mph reduced the number
of Lane Marge (LM) and Hit Object (HO) road crashes, as shown in Table 5 below. This
study also estimated the safety effect of installing a speed limit of 70 mph instead of 80
mph with dry roads and clear weather conditions. Based on the analysis, the
implementation of this treatment results in CMF values of 0.83 and 0.16 for LM crashes
and HO crashes, respectively.
Table 5. Potential crash effects of speed change on highways for related crash types.
No # Treatment
Traffic
Volume
Traffic
Volume
Weather/Road
Condition
CMF
Speed limit and CMF in Clear/dry condition LM HO
Total
Crash
Std. Error
1
Change mean speed from
80 mph to 70 mph
Freeway
(Four-lane
roads)
Unspecified Clear/dry 0.83 0.16 0.45 0.047
Speed limit and CMF in Cloudy/wet condition SD CL
Total
Crash
Std. Error
2
Change mean speed from
80 mph to 70 mph
Freeway
(Four-lane
roads)
Unspecified Cloudy/wet 0.1 1 0.81 0.046
Speed limit and CMF in Snow/snow condition LOC Other
Total
Crash
Std. Error
3
Change mean speed from
70 mph to 50 mph Freeway
(Four-lane
roads)
Unspecified Snow/snow
0.36 0.20 0.43 0.037
Change mean speed from
70 mph to 40 mph
0.03 0.60 0.09 0.038

Sustainability 2022, 14, 8874 16 of 20
Speed limit and CMF in Snow/icy condition LOC Other
Total
Crash
Std. Error
4
Change mean speed from
70 mph to 50 mph
Freeway
(Four-lane
roads)
Unspecified Snow/icy
0.60 1.0 0.63 0.040
Change mean speed from
70 mph to 40 mph
0.32 0.40 0.45 0.053
The researchers found that installing a speed limit of 70 mph instead of 80 mph in
dry road conditions results in a CMF of 0.54 for total accidents. Figure 4 shows the
relationship between the speed limit and the frequency of events of CMF when the speed
limit is decreased by about 10 mph in dry weather/road conditions.
Figure 4. The relationship between the speed limit and CMF in dry weather/road condition.
4.4.2. Install Speed Limit for Rain Weather/Wet Road Condition
The crash effects of wet road conditions with a changing speed limit from 80 mph to
70 mph reduced the number of SD crashes, as shown in Table 5. Table 5 illustrates that the
speed limit reduction from 80 to 70 mph in rainy weather with wet road conditions was
more likely to decrease the expected average SD crash frequencies (CMF = 0.1). However,
there was also some frequency events that meant that CL crashes would remain
unchanged (CMF = 1). Using the data available from the before–after study, the results
show that reducing the speed limit from 80 to 70 mph on the freeway results in a CMF of
0.81 for total crashes. Figure 5 presents the CMF for these potential crashes when
modifying the speed limit in wet weather/road conditions. Changing the speed limit
during snowy weather reduces crashes due to sliding vehicles. The decision to incorporate
speed limit changes in this type of weather may also depend on the road conditions of the
actual roadway segment. The road surface effects of the speed limit can be felt in snow
and icy conditions. The analysis of crash data for snow weather/snow road conditions
found that LOC crashes were more likely to occur in this situation. The reported
percentage reduction translates into CMF values of 0.36 and 0.20 for LOC and other
crashes, respectively, when reducing the speed limit from 70 mph to 50 mph. Reducing
the speed limit from 70 mph to 40 mph resulted in CMF values of 0.03 for LOC crashes
and 0.6 for other crashes.
0.16
1
0.45
1
0.83
1
0
0.2
0.4
0.6
0.8
1
1.2
0
0.2
0.4
0.6
0.8
1
1.2
CMF
Speed Limit
HO Total Crash ML

Sustainability 2022, 14, 8874 17 of 20
4.4.3. Install Speed Limit in Snow Weather/Snow Road Condition
For the speed limit of 50 mph, the CMF for total crashes applied was 0.43, and, for
the speed limit of 40 mph, the CMF for total crashes was 0.09. The results show that the
CMFs for total crashes were higher during the speed limit of 50 mph than 40 mph. Figure
5 shows the relationship between the speed limit and the CMF for LOC, other, and total
crashes in snow weather/snow road weather conditions.
Figure 5. The relationship between the speed limit and CMF in wet weather/road conditions.
4.4.4. Install Speed Limit in Snow Weather/Icy Road Conditions
The effects of reducing the speed limit on multilane-divided highways during snowy
weather with icy road conditions and a speed limit of 70 mph (CMF = 1) are shown in
Table 5. In this scenario, LOC and other road crashes were evaluated. When reducing the
speed limit from 70 mph to 50 mph, the resulting CMF was 0.60 for LOC and 1.0 for others.
When reducing the speed limit from 70 mph to 40 mph, the CMF was 0.32 for LOC and
0.4 for other crashes. Based on Table 5, by implementing a reduction in speed limit to 50
mph on the freeway, the CMF becomes 0.63 for the total crashes. It is noted that the results
of the CMF for the total crashes associated with the speed limit of 40 mph are slightly
higher than the CMFs derived for LOC and others and the relationship between the speed
limit and the CMF for LOC, others, and total crashes in icy weather/road conditions.
5. Conclusions
The primary aim of this paper was to evaluate different driving styles by developing
respective driver models employing a data-driven approach. A fuzzy logic-based
framework considering drivers’ decision-making behavior was developed. A safety level
was compared to speed limits to determine if the proposed speed limit contributed to a
risky or safe driving situation. The final outputs that determined the speed limits for the
highway investigated in different road/weather conditions were based on the
participants’ responses. The participants could increase or retain their current speed limit
or reduce their speed limit a little or significantly under multiple scenarios. The results of
the fuzzy logic study suggested the use of a driver’s sensation for predicting outputs. The
study results were used to determine the speed limits needed in different road/weather
conditions to reduce the number of crashes and implement safe driving conditions based
on the weather conditions. The fuzzy logic for this study evaluated how a driver sensed
according to the relation between the weather/road condition and the speed limit. The
fuzzy logic is expected to contribute to the assessment of a powerful feature of human
behavior/controls. The fuzzy logic can explain smooth relationships between the input
0.1
1
11
0.81
1
0
0.2
0.4
0.6
0.8
1
1.2
70 80
CMF
Speed Limit
SD CL Total Crash

Sustainability 2022, 14, 8874 18 of 20
and output. The input–output relationship estimated by the fuzzy logic was used to
understand differences among driver feelings in road/weather conditions at a different
speed limits. One of the limitations of this study is that female participants are fewer than
male respondents (one-fourth of the sample size). Nevertheless, this uncontrollable factor
has limited effects on the model estimation because the sample size is sufficient for the
modeling. In future work, more environmental inputs, such as road gradient, time, and
weather, can be incorporated to maximize the similarity to diverse drivers population.
Moreover, different test drivers’ naturalistic driving data will be collected to formulate
more accurate driving style variance. Furthermore, other calibration approaches will also
be employed to improve the fuzzy logic controller’s calibration process. Humanized
driver models trained using the proposed approach can also be integrated with the
decision-making process when designing advanced driver assistance systems (ADAS)
and the control strategy of autonomous vehicles.
Author Contributions: Conceptualization, A.I.M.A. and Y.A.; methodology, R.E.A.M., A.I.M.A.,
Y.A and I.U.; software, A.I.M.A. and N.B.; validation, I.U., A.J. and Y.A.; formal analysis, R.E.A.M.;
investigation, A.I.M.A. and I.U.; resources, Y.A. and A.J.; data curation, A.J. and N.B.; writing—
original draft preparation, A.I.M.A., I.U. and N.B..; writing—review and editing, Y.A. and A.J.;
visualization, R.E.A.M. and A.J.; supervision, Y.A. and R.E.A.M.; project administration, Y.A.;
funding acquisition, Y.A. and A.J. All authors have read and agreed to the published version of the
manuscript.
Funding: This project was funded by the Deanship of Scientific Research (DSR) at King
AbdulazizUniversity, Jeddah (Grant No. RG-21-140-42). The authors gratefully acknowledge the
DSR fortechnical and financial support. The DSR had no role in the design of the study, data
collection, dataanalysis, interpretation of data, or writing of the article. Availability of data and
materialsThe datasets used and/or analyzed during the current study are available from the
corresponding authorupon request.
Institutional Review Board Statement: The study was conducted in accordance with the approval
by the Institutional Review Board of Lawrence Technological University. The motives/aims of the
study were told to respondents with respect to the survey. They were also assured about of their
anonymity and confidentiality in their responses. Their participation was absolutely voluntary, and
they are not compensated.
Informed Consent Statement: Informed consent was obtained from all subjects involved in the
study.
Data Availability Statement: All accompanying data are provided in the manuscript.
Acknowledgments: The authors acknowledge and appreciate the support Lawrence Technological
University and King Abdulaziz University (KAU) for supporting this study.
Conflicts of Interest: The authors declare no conflict of interest.
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