Using Fuzzy Inputs to Analyze Factors in the Adoption of Electric

Vehicles (EVs)

Arnab Sircar

Unionville High School, 750 Unionville Rd., Kennett Square, PA, U.S.A.

Keywords: Fuzzy Numbers, Expert Opinion, Fuzzy Aggregation Methods, Fuzzy Ranking, Electric Vehicles Adoption.

Abstract: This research applies a set of mathematical techniques to a setting where precise values cannot be obtained

for opinions from experts. In order to demonstrate the applicability of these techniques, a research study was

designed to measure the importance of factors responsible for increased usage and adoption of electric

vehicles (EVs). In the design, various factors were considered where their measured values were subjective

since in such situations, the factors are not like typical variables that occur naturally. Further, these measured

values may also be imprecise. So, the idea of fuzzy numbers and fuzzy sets were utilized to capture measured

values of these factors. Twelve factors were identified under three different categories of environment and

sustainability, performance and efficiency, and design and manufacture. Then, fuzzy inputs were sought from

six experts as a means of measuring the importance of these twelve factors. The fuzzy numbers from the six

experts were aggregated using a similarity-based method and ranked based on a concept of centroids of fuzzy

numbers. Thus, the top three factors were determined by developing an adoption score and ranking them in

order. The top three factors determined were battery recharge time, battery cost, and environmental pollution.

1 OBJECTIVE

The objective in this effort was to apply methods from

fuzzy sets and numbers in a problem area where

precise measurement and valuations are difficult or

sometimes, impossible. In usual experimental

settings, we take multiple measurements to reduce

errors and so, in this study, we aim to collect multiple

fuzzy inputs and then utilize a scheme to combine

them to make statements about outcomes.

In the study, the above ideas of fuzzy inputs were

to determine the most significant factors that drive

usage and adoption of electric vehicles. In other

words, the question addressed was, what were the

most significant factors that determine the importance

and adoption of electric vehicles (EVs)?

2 PURPOSE AND BACKGROUND

There were two parallel ideas that were pursued in

this study:

1. Utilize fuzzy numbers for imprecise

measurements and then apply new aggregation

and ranking methods.

2. Apply the above techniques to a problem domain

of usage and adoption of electric vehicles (EVs).

Since EVs have gained commercial importance,

this research will help determine where resources

should be spent so as to gain the most value for the

stakeholders.

In what follows, some background information is

provided on fuzzy sets and fuzzy numbers and also on

EVs and their importance.

2.1 Fuzzy Sets and Fuzzy Numbers

Fuzzy sets and fuzzy numbers are useful in situations

where people may not be able to obtain precise values

for different variables. They are also important in

many decision-making situations where there is

subjectivity on the values of the variables in question.

Thus, they may be useful in decision-making

situations where inputs from various experts are used.

More formally, as explained in the article by

Dijkman, van Haeringen and de Lange (Dijkman et

al, 1983), “a fuzzy number is a generalization of a

regular, real number in the sense that it does not refer

to one single value but rather to a connected set of

possible values where each possible value has its own

weight between 0 and 1.”

Sircar, A.

Using Fuzzy Inputs to Analyze Factors in the Adoption of Electric Vehicles (EVs).

DOI: 10.5220/0010133503010308

In Proceedings of the 12th International Joint Conference on Computational Intelligence (IJCCI 2020), pages 301-308

ISBN: 978-989-758-475-6

301

The definition of fuzzy numbers and fuzzy number

operations from (Usha Rani et al, 2016) has been

utilized:

Let R be the set of all real numbers. Assume a fuzzy

number A that can be expressed for all x ∈ R in the

form:

𝐴



𝑥







𝐴



𝑥, 𝑎𝑥𝑏

𝑤, 𝑏  𝑥 𝑐

𝐴



𝑥, 𝑐𝑥𝑑

𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(1)

Where 0  w  1 is a constant, a, b, c, d are real

numbers, such that a  b  c  d , A(x): [a, b] → [0,

w], A(x): [c, d] → [0, w] are two strictly monotonic

and continuous functions from R to the close interval

[0, w].

However, from the general definition, different

types of fuzzy numbers (trapezoidal and triangular)

may be defined. Again, as defined in (Usha Rani et al,

2016):

A fuzzy number A equal to (a, b, c, d) is called a

trapezoidal fuzzy number if its membership function

A(x) has the following form:

𝐴



𝑥





⎩

⎪

⎨

⎪

⎧

𝑤𝑥 𝑎

𝑏𝑎

, 𝑎𝑥𝑏

𝑤, 𝑏  𝑥 𝑐

𝑤𝑑 𝑥

𝑑𝑐

, 𝑐𝑥𝑑

0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(2)

A fuzzy number A equal to (a, b, c; w) is called a

triangular fuzzy number if its membership function

A(x) has the following form:

𝐴



𝑥





⎩

⎪

⎨

⎪

⎧

𝑤𝑥 𝑎

𝑏𝑎

, 𝑎𝑥𝑏

𝑤



𝑑𝑥



𝑑𝑐

,𝑏𝑥𝑐

𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(3)

The important point to note in all of these is the

idea of a membership function which essentially

captures the notion of the extent to which a certain

value from the real numbers is part of the fuzzy

number. The membership function ranges from [0, 1]

where a value of 1 will indicate a level of certainty for

the value of the real number x.

The two important contributions in this study are

how fuzzy numbers may be (1) combined or

aggregated, and how they can be (2) ranked or

ordered.

1. There are many ways in which fuzzy numbers

may be aggregated, but the method that appears to

be most popular is based on similarity of a group

of fuzzy numbers. In this method, one tries to

determine the extent of overlap between two fuzzy

sets that represent two different fuzzy numbers. A

more detailed approach for aggregating multiple

fuzzy numbers that was used in this study is listed

as procedure steps described in Section 3 and

based on the work by Hsu and Chen (Hsu et al,

1996) for fuzzy number aggregation.

2. Another important operation that is of importance

is in ranking of multiple fuzzy numbers. In other

words, this is the ordering of fuzzy numbers.

Again, there are many ways of determining the

size of a fuzzy number but one method that has

gained importance is based on the concept of

centroid of a fuzzy number. This concept is

derived from (Usha Rani et al, 2016) and shown

in Figure 1.

Figure 1: Centroid of fuzzy number.

Essentially, the centroid provides a “balancing

point” for the fuzzy number and this captures the idea

of the size such that the entire number provides a

notion of stability.

2.2 Importance of Electric Vehicles

Hybrid vehicles have been on the streets for quite

some time. In the current energy environment, there

has been a great need for developing vehicles that use

alternative fuels. Several cities in the United States

have launched projects to promote these vehicles to

ensure a clean, green, and healthy environment.

The U.S. Department of Energy’s Alternative

Fuels Data Center features a segment of the

MotorWeek episode, Sacramento Powers up with

Electric Vehicles, which aired on October 3, 2016 and

was hosted by John H. Davis (USDOE, 2017a): “...

our success story this week takes us to Sacramento,

the state capital of California. Since 2011, the city's

department of general services has included electric

and plug-in hybrids in their fleet—now totaling close

to 60 vehicles. They use motor pool level-two

chargers that partially rely on solar power, while an

additional charging station is for employees' personal

vehicles. The city is also trying out a plug-less battery

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302

charger to see if this wireless technology is ready for

deployment. Officials hope their alt-fuel efforts will

encourage others to follow suit.”

Then, there is also a projection by National

Geographic regarding the importance and adoption of

EVs: various researches show that soon gasoline

driven vehicles will disappear from the roads.

According to Stephen Leahy in a National

Geographic article (Leahy, 2017), Electric Cars May

Rule the World’s Roads by 2040: “Electric vehicles

will one day push gas- or diesel-powered ones to the

curb—but how soon? Sooner than you might think,

according to researchers at the International

Monetary Fund and Georgetown University: Based

on how quickly horses and buggies disappeared in the

early 1900s, the researchers argue, more than 90 per

cent of all passenger vehicles in the U.S., Canada,

Europe and other rich countries could be electric by

2040.”

National Geographic also presents a chart on the

projected rise of electric cars as shown in Figure 2

below:

Figure 2: Projection on the rise of electric cars in US until

2042, Source: National Geographic (Leahy, 2017).

There is also a growing level of infrastructure

development for EVs. The number of charging

stations across the nation has been growing rapidly.

According to the U.S. Department of Energy’s

Alternative Fuels Data Center that features a segment

of the MotorWeek episode named Electric Vehicle

Charging Network Expands at National Parks, which

aired on May 11, 2017 and was hosted by John H.

Davis (USDOE, 2017b), “The number of public-

access EV chargers in the U.S. has jumped from less

than 500 in 2009, when Federal Recovery Act grants

began spurring EV infrastructure development, to

more than 42,000 charge ports at 16,000 locations in

2017.”

With reports such as these presented above, it is

clear that EVs are going to be an important mode of

transportation in the future. They clearly highlight

effort on the part of the city to encourage and

influence the use of alternative fuels for a cleaner

environment.

There are many factors that could determine the

adoption and usage of EVs. David Tracy outlines

several factors related to performance and efficiency

in the Jalopnik magazine (Tracy, 2017). Research

showed that there are three main categories that will

influence the adoption rate:

1. Sustainability and Environment

2. Performance and Efficiency

3. Design and Manufacture

However, there are several factors that can be

grouped along these categories. These factors are

listed in the next section.

The idea of the study was derived from the interest

in future innovations that can impact the automobile

industry and energy conservation. EVs take the

spotlight in both of these categories.

3 PROCEDURE

1. Research was conducted to identify factors that

could determine usage and adoption of EVs.

There were 12 factors identified, and they were

categorized under the three main types

mentioned earlier. These are enumerated below:

Sustainability and Environment

1. Less Environmental Pollution

2. Reduced Energy Consumption

3. Susceptibility to Extreme Weather Effects

Performance and Efficiency

1. Energy Efficiency

2. Battery Recharge Time

3. Instant Peak Torque

4. Throttle Control

Design and Manufacture

1. Battery Packaging

2. Battery Cost

3. Bulk and Weight

4. Complexity of Transmissions

5. Brake Fading

2. Research was conducted to determine the type of

fuzzy input required for the various factors.

a. Based on Hsu and Chen’s work (Hsu et al,

1996), it was decided to use trapezoidal fuzzy

numbers for soliciting inputs from experts.

b. The reason for choosing fuzzy inputs was that

even experts may not be able to provide

precise or exact numbers for importance of

the factor in adoption of EVs.

Using Fuzzy Inputs to Analyze Factors in the Adoption of Electric Vehicles (EVs)

303

3. A questionnaire was developed to collect fuzzy

inputs for each of the factors identified.

a. SurveyHero’s website was used to develop

the questionnaire. Here is the link to the set of

questions that were created for each factor:

https://surveyhero.com/c/1876adc8

b. There were three questions for each fuzzy

input that was solicited from the respondents.

Here is a partial screenshot:

Figure 3: Screenshot from SurveyHero for fuzzy input from

respondents.

4. Six experts were identified to solicit inputs. The

following institutions were approached for

expert inputs:

a. US Department of Energy (DoE)

b. DuPont Corporation

c. University of Pennsylvania

d. Drexel University

e. University of Delaware

The data collected from the respondents is

presented as Table I in Appendix A.

5. For ease of calculation, six sets of the inputs

(from 6 respondents) were saved in a

spreadsheet.

6. For each factor, an aggregation method based on

pairwise similarity of fuzzy inputs from the

experts (Hsu et al, 1996) was applied. The steps

involved in this method were:

a. Construct an Agreement Matrix (AM) (6×6

dimensional matrix) whose entries are the

degree of agreement between each pair of

experts. The degree of agreement is

calculated as a ratio of overlapping area

between any two experts and the total area of

the two trapezoidal numbers. The idea is

depicted for the two numbers R

and R

Figure 4.

Figure 4: Overlapping area between fuzzy numbers i.e.

Agreement.

b. The entries are normalized so that the

diagonal elements of the matrix are all 1 (an

expert has to agree with his or her own

opinion).

c. Next, determine the average agreement level

of each expert. For this, sum the degree of

agreement from each row (representing an

expert) and divide by the (total number of

experts - 1). This is devised in (Hsu et al,

1996). The average agreement degree 𝐴



𝐸





of expert E

where (i = 1, 2, … , n) is given

by:

𝐴



𝐸







𝑛1

𝑆









(4)

d. Then calculate the relative agreement level of

each of the experts (RAD). This is

accomplished with the formula below:

𝑅𝐴𝐷





𝐴

𝐸





∑

𝐴

𝐸









(5)

e. The aggregated value of fuzzy inputs from

the 6 experts is then calculated using the

formula:

R 

∑

𝑅𝐴𝐷



∙





)

(6)

where R

is the fuzzy number representing the opinion

of expert E

and RAD

is defined as in (5) above. In

(Hsu et al, 1996), equation (6) is represented by a

concept referred to as consensus degree coefficient

(CDC) that captures RAD

together with a degree of

importance assigned to expert E

. In the formulation

here, all experts are given equal importance, and so,

RAD

and CDC

are equivalent.

7. Then, a ranking procedure was used for all the

aggregated fuzzy inputs for the various factors

(Hsu et al, 1996). The ranking function of the

generalized trapezoidal fuzzy number Ã = (a, b,

c, d; w) which maps the set of all fuzzy numbers

to a set of real numbers is defined as:

FCTA 2020 - 12th International Conference on Fuzzy Computation Theory and Applications

304

𝑅





𝑟



𝑟









𝑐𝑑







𝑎𝑏





216



5



𝑎𝑑



4



𝑏𝑐





324





𝑤

(7)

In this case, the number w is the average of the

confidence levels expressed by the experts.

The calculations performed are presented as

Table II in Appendix B.

8. With the ranks obtained from the above step, the

factors can be arranged in order of priority. Some

scores that are very near each other can

contribute to the usage and adoption of EVs in a

combined manner.

4 RESULTS

As mentioned before, the motivation to obtain

numeric scores for adoption of each factor for usage

of EVs is evident. However, just obtaining a numeric

score is only a partial step towards understanding the

impact of the factor. So, these factors were ranked

based on their numeric adoption score. With such a

ranking, the most important factors that can drive the

adoption of EVs were determined.

Table II in Appendix B shows all the numeric

values of the adoption scores and these can easily be

sorted to get the ranks. The scores obtained for each

factor can help us identify the most important ones (or

combinations thereof) that contribute to the usage and

adoption of EVs. The top three factors determined

are: battery recharge time, battery cost, and

environmental pollution.

A Kiviat (or star) plot is useful in showing the

contrasts among the various factors. Hence, these

scores were plotted on a Kiviat plot to obtain a

graphic representation of the importance of the

factors in terms of adoption of EVs. The Kiviat plat

derived from the table is shown in Figure 5. In the

figure, the green circles on the plot show the factors

with high scores relative to others. Also highlighted

in the figure is a fourth factor shown by a yellow

circle that ranks quite close to the other three. This

tells us that energy efficiency is also an important

consideration.

5 ANALYSIS

In this study, the two objectives were performing data

analysis using fuzzy numbers and applying the

methods of analysis to a phenomenon that is currently

very important.

Figure 5: Kiviat (star) plot for the scores of each of the

twelve factors.

In a study that involves natural sciences, scientists

and engineers may use physical measuring devices

for physical variables observed in nature. However,

in this study that was conducted, human inputs have

been used as the tool for measuring adoption and

usage of electric vehicles. In this scheme of things,

there were a few complexities to consider when using

human inputs as measured values. These were:

i. People (experts) usually cannot provide a precise

value. They typically give ranges of values. In

this study, these ranges of values are captured by

fuzzy numbers.

ii. In conventional experiments, multiple

measurements of independent variables are taken,

which can be aggregated simply by averaging.

With fuzzy inputs, however, simple averaging

will not work; some other aggregation method(s)

have to be used.

iii. Therefore, in this study, multiple measurements

were needed to be performed by collecting fuzzy

inputs from multiple people.

iv. Since people are involved in providing

measurement values, there can be a lot of

variation and subjectivity.

The problem formulation used for this study was

to examine significant factors for adoption of EVs.

From the initial twelve (12) factors, it made sense to

identify the top three or four factors. But in order to

do that, it was necessary to combine or aggregate the

fuzzy numbers from the responses of six inputs for

each factor. The work by Hsu and Chen (Hsu et al,

1996), based on similarity measures, was relatively

easy and did not have too much computational

complexity.

After aggregating the fuzzy numbers, it was

necessary to rank the factors in order of significance.

The work by Usha Rani and others (Usha Rani et al,

2016) provided a computationally easy way to get an

estimate of the size of a fuzzy number (radius of

gyration method).

Using Fuzzy Inputs to Analyze Factors in the Adoption of Electric Vehicles (EVs)

305

As shown in the data presented in the Kiviat plot,

the three most important factors (the highest scores)

were battery recharge time (3.48222), environmental

pollution (3.43175), and battery cost (3.45469)

(shown by green circles). Therefore, it suggested that

these three factors, individually or in combination,

would be very important in determining the usage and

adoption of EVs. However, a fourth factor, energy

efficiency (3.34245), also appears to be quite

important as its score is not too far behind the top

three (shown by a yellow circle).

Also shown in the data presented in the Kiviat

plot, the two least important factors (the lowest

scores) were brake fade (1.49958) and complex

transmissions (1.90462).

Based on the analysis of the results obtained, the

top three factors spanned all the three broad

categories identified before, namely sustainability

and environment, performance and efficiency, and

design and manufacture. Therefore, investment of

resources for usage and adoption of EVs should occur

in all these three categories, with special emphasis on

the top three factors.

Battery recharge time was the most important

factor. Therefore, investment has to be made to

construct numerous battery recharge stations

available to the public. Additionally, there has to be

technology investment for reducing the battery

charge time. The next important factor was the

concern for the environment. There has to be more

education on environmental friendliness of EVs. A

research by an organization EVConnect (Portillo,

2017) showed that this is already an important factor

since many millennials are already environmentally

conscious in that “more than 55% of EV buyers are

millennials.” The third factor was battery cost, and so,

EV manufacturers need to invest on lowering the cost

of batteries. In fact, Robert Bright reported in the

Huffington Post (Bright, 2019) that “battery costs

have reduced by 65% since 2010,” thus confirming

the importance of this factor and bringing it to the top

with regard to adoption of EVs.

Thus, it was seen that this study also confirmed

some of the prevailing ideas on the importance of

factors mentioned in both specialized and popular

media. Therefore, investment in all these initiatives

will promote the usage and adoption of electric

vehicles.

6 CONCLUSIONS

This paper has highlighted the use of fuzzy sets and

fuzzy numbers in capturing opinion data when there

are uncertainties in those opinions, even from experts.

This paper has shown the applicability of the

approach in collecting important factors that will

drive greater usage and adoption of electric vehicles.

Through the application of the analytical methods

utilizing fuzzy inputs, it is seen that the top three

factors are battery recharge time followed by the cost

of the battery and positive impact towards the

environment. Energy efficiency was the fourth most

significant factor that was not very far behind the top

three (shown by the yellow dot in the star plot).

ACKNOWLEDGMENTS

I would like to thank my father for introducing me to

fuzzy numbers as a way of capturing opinions that

have inherent uncertainty. I also thank the six experts

who provided me their opinions in a timely manner.

Finally, I thank the reviewers who provided valuable

comments.

REFERENCES

Bright, R. (2017, June 6). Why Electric Cars Will Soon Be

The Most Popular Vehicle. Huffington Post.

https://preview.tinyurl.com/y34d7wpk

Dijkman, J., Haeringen, H. V., & Lange, S. D. (1983).

Fuzzy numbers. Journal of Mathematical Analysis and

Applications, 92(2), 301-341.

Hsu, H., & Chen, C. (1996). Aggregation of fuzzy opinions

under group decision making. Fuzzy Sets and Systems,

79(3), 279–285.

Leahy, S. (2017, September 13). Electric Cars May Rule the

World’s Roads by 2040. National Geographic.

https://preview.tinyurl.com/y5kry6cy

Portillo, M. (2020, April 22). 4 Reasons Why Electric

Vehicles Are Becoming Popular. EV Connect.

https://preview.tinyurl.com/yxlbew9h

Tracy, D. (2017, October 12). Here Are Five Major

Performance Benefits Of An Electric Car. Jalopnik.

https://preview.tinyurl.com/ybjjfalg

U.S. Department of Energy. (2017a, May 21). Sacramento

Powers up with Electric Vehicles. Afdc.Energy.Gov.

https://preview.tinyurl.com/y5s3326p

U.S. Department of Energy. (2017b, November 22).

Benefits and Considerations of Electricity as Vehicle

Fuel. Alternative Fuels Data Center.

https://preview.tinyurl.com/y7536clh

Usha Rani, B., Hari Ganesh, A., Balakumar, R., &

Jayakumar, S. (2016). Ordering Generalized

Trapezoidal Fuzzy Numbers With Area, Mode, Spreads

and Weights by the Radius of Gyration of Centroids.

Advances in Fuzzy Mathematics, 11(2), 219–229.

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306

APPENDIX A

Table 1: Collected raw data: fuzzy numbers provided by exerts for each factor.

Each trapezoidal fuzzy number provided by the expert is represented by (a, b, c, d; w) where [a,d] represents the coarse

range, [b,c] represents the tighter range and w represents the confidence level expressed by the expert. The values of a, b,

c, and d are on a numeric scale of 0-10.

Factors Surveyed Expert 1 Expert 2 Expert 3 Expert 4 Expert 5 Expert 6

Battery Packaging (5.0, 5.5, 6.5,

7.0; 50%)

(4.0, 4.0, 4.0,

5.0; 100%)

(8.0, 9.0, 9.5,

10.0, 95%)

(8.0, 8.5, 8.5,

9.0; 90%)

(7.0, 7.5, 7.6,

8.0; 70%)

(5.0, 8.0, 10.0,

10.0; 50%)

Battery Cost (9.0, 9.2, 9.8,

10.0; 80%)

(7.0, 8.0, 9.0,

9.0; 90%)

(8.0, 9.0, 9.5,

10.0; 95%)

(1.0, 2.0, 2.0,

3.0; 100%)

(7.0, 7.4, 7.5,

8.0; 75%)

(5.0, 9.0, 10.0,

10.0; 80%)

Bulk and Weight (8.0, 8.5, 9.5,

10.0; 70%)

(7.0, 8.0, 8.0,

8.0; 90%)

(8.0, 9.5, 10.0,

10.0; 95%)

(1.0, 2.0, 2.0,

3.0; 90%)

(6.0, 6.4, 6.5,

7.0; 75%)

(5.0, 9.0, 10.0,

10.0; 70%)

Complex

Transmissions

(3.0, 5.0, 6.0,

7.0; 40%)

(4.0, 4.0, 5.0,

6.0; 50%)

(8.0, 8.5, 9.5,

10.0; 90%)

(8.0, 9.0, 9.0,

10.0; 90%)

(7.0, 7.5, 7.6,

8.0; 80%)

(4.0, 5.0, 8.0,

10.0; 20%)

Brake Fade (3.0, 4.0, 5.0,

7.0; 40%)

(4.0, 4.0, 6.0,

6.0; 0%)

(9.0, 9.5, 10.0,

10.0; 100%)

(7.0, 8.0, 8.0,

9.0; 90%)

(6.0, 6.4, 6.5,

7.0; 75%)

(4.0, 6.0, 8.0,

10.0; 30%)

Energy Efficiency (7.0, 8.0, 9.0,

10.0; 80%)

(8.0, 9.0, 10.0,

10.0; 95%)

(8.0, 9.0, 9.5,

10.0; 95%)

(9.0, 9.5, 9.5,

10.0; 100%)

(8.0, 8.5, 8.6,

9.0; 75%)

(5.0, 7.0, 10.0,

10.0; 60%)

Battery Recharge

Time

(9.0, 9.5, 10.0,

10.0; 90%)

(8.0, 9.0, 10.0,

10.0; 100%)

(8.0, 8.5, 9.5,

10.0; 90%)

(4.0, 5.0, 5.0,

6.0; 90%)

(7.0, 7.5, 7.7,

8.0; 70%)

(5.0, 8.0, 10.0,

10.0; 80%)

Instant Peak Torque (2.0, 5.0, 6.0,

8.0; 60%)

(7.0, 8.0, 9.0,

10.0; 80%)

(8.0, 8.0, 8.5,

10.0; 90%)

(9.0, 9.5, 9.5,

10.0; 100%)

(6.0, 6.5, 6.8,

7.0; 50%)

(5.0, 7.0, 9.0,

10.0; 70%)

Throttle Control (1.0, 2.0, 3.0,

5.0; 50%)

(6.0, 7.0, 7.0,

7.0; 80%)

(8.0, 8.0, 8.5,

10.0; 90%)

(6.0, 7.0, 7.0,

8.0; 70%)

(6.0, 6.5, 6.7,

7.0; 70%)

(3.0, 5.0, 8.0,

10.0, 30%)

Environmental

Pollution

(9.0, 9.5, 10.0,

10.0; 100%)

(9.0, 9.0, 10.0,

10.0; 90%)

(9.0, 9.5, 10.0,

10.0; 100%)

(7.0, 8.0, 8.0,

9.0; 90%)

(8.0, 8.6, 9.0,

9.0; 75%)

(5.0, 5.0, 8.0,

10.0; 40%)

Reduced Energy

Consumption

(7.0, 8.0, 9.0,

10.0; 80%)

(9.0, 9.0, 10.0,

10.0; 100%)

(8.0, 9.0, 9.5,

10.0; 95%)

(9.0, 9.5, 9.5,

10.0; 100%)

(7.0, 7.6, 7.8,

8.0; 70%)

(5.0, 6.0, 8.0,

10.0; 20%)

Susceptibility to

Extreme Weather

Effects

(8.0, 8.5, 10.0,

10.0; 80%)

(8.0, 9.0, 10.0,

10.0; 90%)

(9.0, 9.0, 9.5,

10.0; 95%)

(3.0, 4.0, 4.0,

5.0; 90%)

(7.0, 7.5, 8.0,

8.0; 70%)

(3.0, 5.0, 7.0,

8.0; 30%)

Using Fuzzy Inputs to Analyze Factors in the Adoption of Electric Vehicles (EVs)

307

APPENDIX B

Table 2: Aggregated fuzzy number inputs and their numeric scores for each factor.

Factor Aggregated Fuzzy Input

(on a scale of 0-10)

Graphical Representation

of Aggregated Fuzzy

Input

Numeric Score

Battery Packaging (6.356, 8.2267, 9.3618, 9.5973) 2.8563

Battery Cost (7.1493, 8.8744, 9.6291, 9.8318)

3.45469

Bulk and Weight (6.5, 8.9874, 9.8687, 10) 3.23572

Complex Transmissions (5.1898, 6.1236, 7.4344, 8.5724) 1.90462

Brake Fade (4.133, 5.1484, 6.5805, 7.8694)

1.49958

Energy Efficiency (7.4185, 8.2836, 9.6031, 9.934)

3.34245

Battery Recharge Time (7.4315, 8.5522, 9.7927, 9.928)

3.48222

Instant Peak Torque (6.3728, 7.4654, 8.4855, 9.604)

2.70391

Throttle Control (5.551, 6.5203, 7.2661, 8.1086)

2.01299

Environmental

Pollution

(8.4749, 8.8332, 9.6599, 9.9051)

3.43175

Reduced Energy

Consumption

(8.0209, 8.6557, 9.3151, 9.8232)

3.13119

Susceptibility to

Extreme Weather

Effects

(8.2893, 8.8262, 9.8554, 10) 3.16035

FCTA 2020 - 12th International Conference on Fuzzy Computation Theory and Applications

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