Determination of Roadside Parking Retribution Contract Value

using Fuzzy Sugeno Method

Yuli Dwi Astanti, Intan Berlianty, Irwan Soejanto, Dyah R. Lucitasari, and Yunanda A. Wibowo

Universitas Pembangunan Nasional Veteran Yogyakarta

Keywords: Retribution, Fuzzy Sugeno, Roadside Parking

Abstract: The parking facilities in Sleman are one of the sources of regional revenue. However, revenue from parking

retribution has not been optimal. The amount of roadside parking retribution deposits is currently

determined based on an approved contract between the parking officer and the government, and based on

the consideration of the potential parking survey results by the government. The system is deemed unable to

maximize the potential of regional revenue from parking retribution because the amount of parking

retribution fees is not determined based on the increasing parking revenues. This study intended to

investigate the value of contract retribution with the Fuzzy Sugeno Method. The Fuzzy Sugeno method was

used to determine the number of retribution deposits based on the specified criteria. Based on the data

processing and analysis, the number of new retribution deposits was obtained. The amount of the retribution

deposit was different from the amount specified in the contract because the calculation results were

determined based on the actual conditions of the set deposit period. This can be used as a correction of the

retribution deposit amount so that the government can determine the retribution based on the conditions of

the parking manager itself.

1 INTRODUCTION

Parking is one of the community activities that are

easily found in Sleman, Yogyakarta. Ideally, parking

should be facilitated in a particular parking area, but

in reality, there are still many locations that do not

have parking facilities. This causes many people

parking their vehicles on the roadside. Parking on

the roadside certainly has negative impacts on the

community, one of which is reducing road capacity

for vehicles. More density on-street parking will

decrease road capacity (Soejanto et al. 2017). On the

other hand, roadside parking also has advantages

because the organizers of parking facilities in the

roadside space are obliged to pay parking retribution

to the Regional Government. The parking retribution

is one source of original local revenue that can be

used for regional development.

The original local revenue from roadside parking

will continue to increase along with the increase of

the population. On-street parking is the result of the

increasing population activities to meet their needs.

The needs of this population then become an

opportunity to invest and do development in various

fields. Development that is not balanced by adequate

parking facilities will force visitors to use the

roadside as a parking lot (Soejanto et al. 2017). If

the management of revenue from roadside parking

retribution is not appropriately managed, then side

parking will only harm the community without any

profit.

Nowadays, the government has determined the

amount of roadside parking retribution deposits

based on an agreement with the parking officer and

based on the consideration of the potential parking

survey results by the government. The system is

considered unable to maximize the potential of local

revenue from parking retribution because the

amount of parking retribution is not determined

based on the actual parking revenue. For example,

parking revenue simulations that take into account

factors such as the time between arrivals, number,

and type of vehicles indicate a very significant

difference between the contract value and the real

parking income of the parking officer (Soejanto et

al. 2018). Besides, the parking area is also a factor

that influences roadside parking fees (Berlianty et al.

2018).

Based on Sleman Regency Regional Regulation

No. 11 the year 2011, the parking retribution (tax)

Astanti, Y., Berlianty, I., Soejanto, I., Lucitasari, D. and Wibowo, Y.

Determination of Roadside Parking Retribution Contract Value using Fuzzy Sugeno Method.

DOI: 10.5220/0009960906390645

In Proceedings of the International Conference of Business, Economy, Entrepreneurship and Management (ICBEEM 2019), pages 639-645

ISBN: 978-989-758-471-8

639

rate is set at 20% of income. However, revenue from

parking tax has not been optimal. This is because the

determination of the value in the contract between

the government and the parking manager has not

considered the factors that affect the amount of

parking retribution revenue. Thus, since the value

determination is only done by agreement between

the government and the parking manager, it cannot

integrate data in the field with the information

provided by the parking officer himself.

The current monitoring function has not been

optimal because the government does not know

exactly how much revenue is obtained by the

parking officer. There are many roadside parking

that do not provide tickets for parking service users.

So it is difficult to know the number of vehicles

using the parking service. Parking managers can

easily manipulate their income so that the retribution

that must be paid can be reduced. For this reason, we

need a system that can support government decisions

in determining the value of contracts for roadside

parking fees.

This study intended to make a decision using the

Fuzzy Sugeno Method to take into account public

road parking retribution deposits based on the

variable parking area, the time between vehicle

arrivals, and parking revenue. The decision support

system is expected to be able to help the process of

determining the amount of parking retribution

deposits appropriately so that it can increase Sleman

Regency Local Revenue.

Fuzzy logic is a decision-supporting method to

represent the uncertainty that accompanies the data

received as a result of data processing. Ambiguous

parameters can be represented, and then decisions

can be made based on fuzzy rules with the Fuzzy

Inference System (FIS). Determination of the

parking officer's capability to pay a retribution

deposit is not currently deemed following the real

conditions. The parking officer’s information

becomes the only report that evokes the parking

capability parameters still subjective. Employing the

Sugeno fuzzy method, the decision-making process

for the amount of parking retribution deposits will

be more appropriate because it has a tolerance to

ambiguous parameters.

2 MATERIAL AND METHOD

According to Government Regulations No. 43 the

year 1993, parking is a condition in which a vehicle

stops at a particular place, whether stated by signs or

not. The vehicle goes to a particular place, and after

arriving at the destination, the vehicle requires a

place to stop with a specific duration. The place to

stop is referred to as a parking lot. Based on the

Regional Regulation of Sleman Regency No. 6 the

year 2015, parking is all activities related to the

implementation of parking facilities, including

regulation, development, guidance, supervision, and

control following their authority. Based on the

Sleman Regency Regional Regulation Number 15

the year 2013, retribution is levy imposed on

individuals or entities using the provision of unique

parking spaces that are provided, owned, or

managed by the Regional Government. The amount

of parking retributions is regulated in Sleman

Regency Regulation No. 15 the year 2013.

Fuzzy logic is part of artificial intelligence that

imitates the ability of human thinking in the form of

algorithms that are run by machines (Nofriansyah &

Defit 2017). Fuzzy logic is an appropriate method

for determining an input space into an output space

(Kusumadewi & Purnomo 2004). According to

(Irwansyah & Faizal n.d.), fuzzy logic does not only

use two strict conditions (crisp), namely: yes or no, 0

or 1, but in its use fuzzy logic can display all

possibilities between 0 and 1. Fuzzy logic is not

fixed in one decision so that it can tolerate

uncertainty. The mathematical concepts that underlie

fuzzy logic reasoning are straightforward and easy to

understand. The advantages of using fuzzy logic

(Kusumadewi & Purnomo 2004) include:

1. Fuzzy logic is very flexible.

2. Fuzzy logic can tolerate incorrect data.

3. Fuzzy logic can model very complex

nonlinear functions.

4. Fuzzy logic can work with conventional

control techniques.

5. Fuzzy logic is based on natural language.

Fuzzy Inference System is a computational

framework based on fuzzy set theory, fuzzy rules in

the form of IF-THEN, and fuzzy reasoning. There

are three methods in fuzzy inference systems that are

often used, namely the Tsukamoto method, the

Mamdani method, and the Sugeno method. In this

study, the determination of the calculation parking

retribution using the Sugeno method will be

discussed. This system functions to make decisions

through specific processes using inference rules

based on fuzzy logic. Sugeno's method consists of 2

types, namely:

1. Fuzzy Sugeno Order-Zero model

In general, the form of the Zero-Order Sugeno fuzzy

model is formulated in equation one as follows:

IF





isA





∩





isA





∩





isA





…∩





isA





THENzk (1)

ICBEEM 2019 - International Conference on Business, Economy, Entrepreneurship and Management

640

With 



is the n-th fuzzy set as an antecedent,

and k is a constant (firm) consequent.

2. Fuzzy Sugeno Order-One Model

In general, the form of the First Order fuzzy Sugeno

model is formulated in equation 2 as follows:















∩…∩



















∗



⋯



∗



 (2)

With 



is the n-th fuzzy set as an antecedent

and 



is a constant (i) to i and q also as a constant

in consequence.

To get the output (result), it takes 4 stages as

follows:

1. Formation of fuzzy sets

In the Sugeno Method, both input variables and

output variables are divided into one or more fuzzy

sets.

2. Application function implications

In the Sugeno method, the implication function used

is Min (minimum).

3. Composition of Rules

If the system consists of several rules, then the

inference is obtained from a combination of rules.

4. Defuzzification

The input of the defuzzification process is a fuzzy

set that is obtained from a composition of fuzzy

rules, while the output produced is a number in the

fuzzy set. So if a fuzzy set is given in a certain

range, then a certain crisp value must be taken as

output. In the Sugeno Method, defuzzification is

done by finding a weighted average with equation 3

as follows.



∑













∑









(3)

With : 



: predicate on the i-rule, 



output on the i-rule

3 RESULT AND DISCUSSION

In this study, the data was taken from nine parking

locations, both registered and unregistered parking

along Affandi Street, Sleman, Yogyakarta. The

parking location is chosen based on the level of

visitor crowds and various parking spaces. The data

on the number of contract value can be seen in Table

1 as follows:

Table 1. Parking retribution contract value

No Location

Contract Value

(IDR)

Restaurant A 300.000

Restaurant B Unregistered

Restaurant C 500.000

Restaurant D Unregistered

Grocery Unregistered

Print Service Unregistered

Electrical Store 300.000

Mobile Phone Counter 300.000

Restaurant E 400.000

Data processing began with simulating a model

to obtain data for one month. The simulation was

conducted by observing the time of arrival, parking

time, and parking capacity for five days. The

simulation model was built using Promodel

Simulation Software. The results of the simulation

were the number of vehicles parked for one month to

obtain income data for one month. The results of the

observations and simulations were used as fuzzy

inputs. There were two variables determined in this

study, namely, input and output variables. Input

variables consisted of the parking area, inter-arrival

time, and parking retribution revenue while the

output variable was the capability of the parking

officer.

Table 2. Real retribution revenue for fuzzy input

No Location

Area

(m²)

Inter-

arrival

time

(minute)

Revenue

Restaurant

35 12,87 IDR 1.724.000

Restaurant

19 15,51 IDR 2.041.000

Restaurant

82 6,62 IDR 5.076.000

Restaurant

21 8,71 IDR 3.649.000

5 Grocery 40 7,18 IDR 4.138.000

Service

26 9,26 IDR 2.975.000

Electrical

Store

40 16,17 IDR 1.882.000

Phone

Counter

37 23,38 IDR 1.422.000

Restaurant

19 9,67 IDR 2.580.000

The steps of processing data using fuzzy

methods were as follows:

1. Fuzzification

Fuzzification is a process of mapping non-fuzzy

variables (numerical variables) into fuzzy variables

Determination of Roadside Parking Retribution Contract Value using Fuzzy Sugeno Method

641

(linguistic variables). In this step, the fuzzy set of

each variable is determined as follows.

 A variable parking area consists of three sets,

namely Wide, Medium, and Narrow, with the

universal speaker [0, + ∞].

 The inter-arrival time variable consists of

three fuzzy sets; those are often, normal, and

rare with the universal speaker [0, + ∞].

 The parking revenue variable consists of three

sets, namely High, Normal, and Low, with the

universal speaker [0, + ∞].

 The output variable of the RTJU deposit

amount decision consists of three sets; they

are Able, Normal, and Insufficient.

2. Determination of domain and membership

functions

 The domain is the value of the fuzzy set of

each variable. In determining the fuzzy set

domain, a quartile of the universal speaker is

used to determine the fuzzy set domain.

Table 3. Fuzzy set of parking lot area

Variable Set Domain Curve

Wide area

Narrow [0, 50,5]

Left-

shoulder

Medium

[34,75,

66,25]

Triangle

Wide [50,5, +∞]

Right-

shoulder

Table 4. The fuzzy set o inter-arrival time

Variable Set Domain Curve

Inter-

arrival

time

Often [0, 15] Left-shoulder

Normal

[10,81,

19,19]

Triangle

Rare [15, +∞]

Right-

shoulder

Table 5. Fuzzy set of parking revenue

Variable Set Domain Curve

Parking

revenue

Low [0, 3249000]

Left-

shoulder

Normal

[2335500,

4162500]

Triangle

High [3249000, +∞]

Right-

shoulder

Table 6. Fuzzy set of retribution deposit

Variable Set Decision

Deposit

Insufficient 15% of Revenue

Normal 20% of Revenue

Able 25% of Revenue

After determining the domain of each variable,

then the fuzzy set could be represented by the

membership function as follows.

 Variable membership function for parking lots













1, 34,75

50,5

15,75

, 34,7550,5

0, 50,5























0, 34,7566,25

34,75

15,75

, 34,7550,5

66,25

31,5

, 50,566,25













0, 50,5

50,5

15,75

, 50,566,25

1, 66,25

 Variable membership function for inter-arrival

time













1, 10,81

15

4,19

, 10,8115

0, 15























0, 10,8115

10,81

4,19

, 10,8115

19,19

8,38

, 1519,19













0, 15

15

4,19

, 1519,19

1, 19,19

 Variable membership function for parking

revenue













1, 2335500

3249000

913500

, 23355003249000

0, 3249000

























0, 23355004162500

2335500

913500

, 23355003249000

4162500

1827000

, 32490004162500















0, 3249000

3249000

913500

, 32490004162500

1, 4162500



ICBEEM 2019 - International Conference on Business, Economy, Entrepreneurship and Management

642

3. Designing the Rule Base System

The Rule Base System is a rule that contains fuzzy

implications expressed in the form of IF ... THEN.

In this study, an implication function was used,

namely the AND (MIN function).

Table 7. Rule of fuzzy logic

No Rule Area

Inter-

arrival

time

Revenue

Retribution

Deposit

1. R1 Narrow Rare Low Insufficient

2. R2

Narrow Rare

Normal Insufficient

3. R3

Narrow Rare

High Able

4. R4 Medium

Rare

Low Insufficient

5. R5 Medium

Rare

Normal Normal

6. R6 Medium

Rare

High Able

7. R7

Wide Rare

Low Insufficient

8. R8 Wide Rare Normal Normal

9. R9 Wide Rare High Able

10. R10 Narrow Normal Low Insufficient

11. R11 Narrow Normal Normal Normal

12 R12 Narrow Normal High Able

13 R13 Medium Normal Low Insufficient

14 R14 Medium Normal Normal Normal

15 R15 Medium Normal High Able

16 R16 Wide Normal Low Insufficient

17 R17 Wide Normal Normal Normal

18 R18 Wide Normal High Able

19 R19 Narrow Oftern Low Insufficient

20 R20 Narrow Oftern Normal Normal

21 R21 Narrow Oftern High Able

22 R22 Medium Oftern Low Insufficient

23 R23 Medium Oftern Normal Normal

24 R24 Medium Oftern High Able

25 R25 Wide Oftern Low Insufficient

26 R26 Wide Oftern Normal Normal

27 R27 Wide Oftern High Able

After the fuzzy implication rules were

determined, fuzzy output was then prescribed using

the Sugeno Orde-One Fuzzy Inference System

method as follows.

IF





is



∩…∩







is





THENz



∗

⋯



∗









= n-th input variable





= Fuzzy set

z contract value percentage × revenue

In this study, the minimum implication function was

used, namely by looking for the smallest i rule as

follows.





min









,











Where :





minimumvalueoffuzzysetAandBfromi‐

rule











thedegreeofmembershipxofthe

fuzzysetAinthei‐rule











thedegreeofmembershipxofthe

fuzzysetBinthei‐rule

4. Composition of rules

In this study, the maximum composition of the rule

would be used, which was by selecting the highest

value of the membership degree for the results of the

same implication function.









max











,













Where:













: the membership value of fuzzy

solutionstothei‐rule













:consequentfuzzymembershipvalueto

thei‐rule

5. Deffuzification

In the Sugeno Method, defuzzification is conducted

by finding the weighted average as follows.



∑













∑









Where, 





predicateonthei‐rule





outputonthei‐rule

6. Examples of parking retribution revenue

determination with the Fuzzy Sugeno Order-

One Method

The following example is the determination of the

revenue in the Restaurant A parking lot with a

parking area of 35 m², the average interarrival time

of 12.87 minutes, and revenues of IDR 1,724,000.

 Determine the fuzzy set of each variable

1. Parking lot area











50,535

15,75

0,98











3534,75

15,75

Determination of Roadside Parking Retribution Contract Value using Fuzzy Sugeno Method

643

0,02









0



The parking lot of Restaurant A could be

considered as narrow with a membership degree of

0.98 (with 98% confidence that the area is narrow)

and could be said to be medium with a membership

level of 0.02 (with a belief of 2% that the area is

medium).

2. Inter-arrival time







12,87





1512,87

4,19



0,51









12,87





12,8710,81

4,19



0,49









12,87



0



The time between arrivals at the Restaurant A

parking lot could be said as often with a membership

degree of 0.51 (with 51% confidence that the time

between arrivals is often) and could be said as

Normal with a membership level of 0.49 (with a

49% confidence that the time of arrival).

3. Revenue







1724000



1









1724000



0









1724000



0



So, the revenue at the parking location of

Restaurant A could be said as Low with 1

membership degree (with 100% confidence that

parking revenue is low).

 Application of function implications

[R10] α – predicate 10



_

∩



_

∩



_

=min

_



_

,

_

min

(0,98, 0,49, 1) = 0,49 (parking retribution deposit is

insufficient with a deposit of 15% of parking

revenue)

[R13] α – predicate13



_

∩



_

∩



_

=min

_



_

,

_

= min

(0,02, 0,49, 1) = 0,02 (parking retribution deposit is

insufficient with a deposit of 15% of parking

revenue)

[R19] α – predicate 19



_

∩

_

∩



_

=min

_



_

,

_

= min (0,98, 0,51, 1) = 0,51 (parking retribution

deposit is insufficient with a deposit of 15% of

parking revenue)

[R22] α – predicate22



_

∩

_

∩



_

=min

_



_

,

_

= min

(0,02, 0,51, 1) = 0,02 (parking retribution deposit is

insufficient with a deposit of 15% of parking

revenue)

Rule composition

15% of parking revenue = max(0,02, 0,49, 0,51) =

0,51

20% of parking revenue = max(0) = 0

25% of parking revenue = max(0) = 0

 Defuzzification



∑













∑











0,51



15%∗



020%∗025%∗

0,5100





0,5115%17240000



20%1724000



0



25%1724000



0,51

= 258600

Based on the calculations using the Fuzzy

Sugeno Order-One Method, it could be determined

that the parking retribution deposit at the parking

location of Restaurant A was 15% parking revenue,

or equal to IDR 258,600. This result was less than

the retribution deposit determined in the contract,

which was IDR 300,000. This condition was

influenced by the time between arrivals and income

obtained by Restaurant A at the end of the month.

The arrival time showed how many vehicles were

parked for one month. During that period, the time

between arrivals at that location was observed so

rarely that the number of vehicles parked was small.

Besides, a large number of vehicles also affected the

income earned during a period. During this period,

ICBEEM 2019 - International Conference on Business, Economy, Entrepreneurship and Management

644

parking revenue at the location was relatively low.

Based on this explanation, the program created was

also able to correct the parking retribution deposit

results so that the results would be following the

conditions in the specified period. Using the same

method, the calculation of contract value for all

locations in this study was obtained as follows.

Table 8. Parking retribution revenue for all location

No Location

Contract

Value (IDR)

Revenue

Based on fuzzy

rules (IDR)

Restaurant

300.000 258.600

Restaurant

Unregistered 306.150

Restaurant

500.000 1.269.000

Restaurant

Unregistered

840.922

5 Grocery

Unregistered

1.030.420

Service

Unregistered

550.383

Electrical

Store

300.000 282.300

Phone

Counter

300.000 213.300

Restaurant

400.000 421.527

4 CONCLUSIONS

Based on the results of data processing and analysis

that had been conducted, it could be concluded that

the results of parking revenue deposit calculations

using the Fuzzy Sugeno method showed results that

were slightly different from the established

contracts. This was due to fuzzy calculations based

on the condition of the parking location at the end of

the period so that the number of deposits per period

was not fixed. Therefore, this method of calculation

is considered effective because the amount of

parking revenue deposits can adjust the revenue of

the parking officer.

REFERENCES

Berlianty, I. et al., 2018. Determining of Parking Lot Area

Policy Using System Dynamic Simulation Approach. ,

231(Amca), pp.728–731.

Irwansyah, E. & Faizal, M., Advanced Clustering: Teori

dan Aplikasi, Yogyakarta: DeePublish.

Kusumadewi, S. & Purnomo, H., 2004. Aplikasi Logika

Fuzzy, Yogyakarta: Graha Ilmu.

Nofriansyah, D. & Defit, S., 2017. Multi Criteria Decision

Making (MCDM) pada Sistem Pendukung Keputusan,

Yogyakarta: DeePublish.

Soejanto, I., Berlianty, I. & Astanti, Dwi, Y., 2017. A

System Dynamic Conceptual Framework of On-Street

Parking Increasement. In pp. 214–219.

Soejanto, I., Berlianty, I. & Astanti, Y.D., 2018. Monte

Carlo Simulation of on-Street Parking Retribution

Revenue Potential in Sleman Regency Indonesia. , 7,

pp.357–360.

Determination of Roadside Parking Retribution Contract Value using Fuzzy Sugeno Method

645