Comparing Fuzzy Logic Mamdani and Naïve Bayes for Dental Disease Detection

Abstract

Background: Dental disease detection is essential for the diagnosis of dental diseases.

Objective: This research compares the Mamdani fuzzy logic and Naïve Bayes in detecting dental diseases.

Methods: The first is to process data on dental disease symptoms and dental support tissues based on complaints of toothache consulted with experts at a community health centre (puskesmas). The second is to apply the Mamdani fuzzy logic and the Naïve Bayes to the proposed expert system. The third is to provide recommended decisions about dental diseases based on the symptom data inputted into the expert system. Patient data were collected at the North Cilacap puskesmas between July and December 2021.

Results: The Mamdani fuzzy logic converts uncertain values into definite values, and the Naïve Bayes method classifies the type of dental disease by calculating the weight of patients’ answers. The methods were tested on 67 patients with dental disease complaints. The accuracy rate of the Mamdani fuzzy logic was 85.1%, and the Naïve Bayes method was 82.1%.

Conclusion: The prediction accuracy was compared to the expert diagnoses to determine whether the Mamdani fuzzy logic method is better than the Naïve Bayes method.

Keywords: Dental Disease, Expert System, Mamdani Fuzzy Logic, Naïve Bayes, Prediction

Full text

Journal of
Information Systems Engineering
and Business Intelligence
Vol.8, No.2, October 2022
Available online at: http://e-journal.unair.ac.id/index.php/JISEBI
ISSN 2443-2555 (online) 2598-6333 (print) © 2022 The Authors. Published by Universitas Airlangga.
This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)
doi: http://dx.doi.org/10.20473/jisebi.8.2.182-195
Comparing Fuzzy Logic Mamdani and Naïve Bayes for
Dental Disease Detection
Linda Perdana Wanti1) * , Oman Somantri2)
1)2)Politeknik Negeri Cilacap, Indonesia
Jl. Dr. Soetomo No.1, Karangcengis, Sidakaya, Kec. Cilacap Selatan, Cilacap
1) linda_perdana@pnc.ac.id, 2) oman_mantri@pnc.ac.id
Abstract
Background: Dental disease detection is essential for the diagnosis of dental diseases.
Objective: This research compares the Mamdani fuzzy logic and Naïve Bayes in detecting dental diseases.
Methods: The first is to process data on dental disease symptoms and dental support tissues based on complaints of toothache
consulted with experts at a community health centre (puskesmas). The second is to apply the Mamdani fuzzy logic and the Naïve
Bayes to the proposed expert system. The third is to provide recommended decisions about dental diseases based on the symptom
data inputted into the expert system. Patient data were collected at the North Cilacap puskesmas between July and December
2021.
Results: The Mamdani fuzzy logic converts uncertain values into definite values, and the Naïve Bayes method classifies the
type of dental disease by calculating the weight of patients’ answers. The methods were tested on 67 patients with dental disease
complaints. The accuracy rate of the Mamdani fuzzy logic was 85.1%, and the Naïve Bayes method was 82.1%.
Conclusion: The prediction accuracy was compared to the expert diagnoses to determine whether the Mamdani fuzzy logic
method is better than the Naïve Bayes method.
Keywords: Dental Disease, Expert System, Mamdani Fuzzy Logic, Naïve Bayes, Prediction
Article history: Received 16 June 2022, first decision 16 August 2022, accepted 8 September 2022, available online 28 October 2022
I. INTRODUCTION
Oral health can be determined from a) the teeth’s hard and soft tissues and b) the elements connected to the oral
cavity. Healthy dental and oral conditions allow individuals to eat and speak without a problem. They may also lead
to aesthetical problems, discomfort, occlusion deviations, and tooth loss [1]. According to the World Dental Federation
(FDI), prevalent problems in teeth and mouth are as follows. 1) Caries is often caused by excessive sugar consumption,
lack of dental healthcare, and difficult access to standard dental health services. 2) Periodontal causes difficulty
chewing and speaking, and is the main cause of tooth loss in adults (gingivitis leading to periodontitis). 3) Oral cancer
is one of the ten most common types of cancer in humans, affecting lips, gums, tongue, oesophagus, inside of the
cheeks, and the top and bottom of the mouth. Oral cancer can be life-threatening if not treated immediately. The main
causes of this cancer are cigarettes and alcohol consumption [2].
Consumption of cigarettes and alcoholic beverages significantly affects tooth decay and tooth-supporting tissues.
Toothache is pain around the teeth and jaw, often felt when one consumes food or drinks that are too hot or cold.
Tooth decay is the main cause of toothache in most children and adults [3]. Some conditions that cause toothache
include 1) infection of the teeth caused by bacteria; 2) broken teeth; 3) dental treatment, such as fillings, tooth
extraction, or crown placement; 4) abnormality in bones and gums protecting the roots [4]. Based on WHO data, the
ideal ratio of dentists to population is 1:2000. In Indonesia, the ratio is far from ideal, namely 1:22000 [5]. One of the
solutions to overcome these problems is professional interventions. Another solution is to develop an information
system imitating a dentist in diagnosing dental diseases. The system can be developed based on the observed
symptoms.
Research by Putu et al. developed an expert system to detect eye diseases using fuzzy logic and Naïve Bayes
methods. This expert system uses 16 symptoms to determine ten types of eye diseases. The process begins by changing
the uncertain input value using fuzzy logic. The next step is calculating the weight of all patient answers using the
* Corresponding author

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Journal of Information Systems Engineering and Business Intelligence, 2022, 8 (2), 182-195
183
Naïve Bayes method. The result shows that the similarity in the diagnosis between the expert system and
ophthalmologists was 81% [6]. Yovita et al. implemented the Naïve Bayes method as an expert system for the early
detection of dysmenorrhea. The Naïve Bayes method is used to classify the type of dysmenorrhea two: primary or
secondary. Based on the analysis of 10 test data with 10 and 20 training data, the accuracy rate was 90% for 10 training
data and 100% accuracy for 20 training data [7]. Fahmiyanto et al. developed an expert system involving the android-
based fuzzy Tsukamoto method. In an ENT disease diagnosis system based on Android, the demand variable consists
of two fuzzy sets: down and up. The inventory variables include two fuzzy sets: a little and a lot. The production
variable consists of two fuzzy sets: reduced and increased. The accuracy in this study was calculated not by each
disease but by the whole disease. The accuracy value was 93.75% [8].
This study aims to compare the accuracy of the prediction results using the Mamdani fuzzy logic and the Naïve
Bayes method in diagnosing dental diseases with initial symptom data. The purpose of this research is threefold. The
first is to process data on dental disease symptoms and dental support tissues based on complaints of toothache
consulted with experts at a community health centre (puskesmas). The second is to apply the Mamdani fuzzy logic
and the Naïve Bayes to the proposed expert system.
The third is to provide recommended decisions about dental
diseases based on the symptom data inputted into the expert system
.
This research provides recommendations for
dental disease and dental support tissues using the Mamdani fuzzy logic method and the Naïve Bayes method. The
results can be used for preventive dental treatments. The novelty of this research is to compare the Mamdani fuzzy
logic and the Naïve Bayes against experts’ judgment (dentists) to measure the accuracy.
II. M
ETHODS
A. Overview of Expert System
Fig. 1 Expert system overview

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184
Fig. 1 shows an overview of the stages in the expert system and all the implemented modules. The expert system
applies the Mamdani fuzzy logic and the Naïve Bayes method. The two actors in the picture are end-users and experts
[9] [10]. The consultation identifies the problem through a series of questions displayed on the user interface [11] [12].
The symptomatic data of dental disease go through the knowledge acquisition process. The rules are made by
considering the Mamdani fuzzy logic, changing the uncertain values input by patients. Meanwhile, the Naïve Bayes
classifies the type of disease by calculating the weight of all patient input. The output generated in the expert system
processing is then displayed to the end users.
B. Fuzzy Logic
Fuzzy logic is based on the fuzzy set theory, which was first introduced by Zadeh in 1965. In this theory, a
membership degree is an important determinant of the existence of elements [13]. The value, function, or degree of
membership is the main reasoning characteristic of fuzzy logic–a black box connecting the input to the output space
[14] [15]. The black box contains a method to process input data into output through good information [16]. Fig. 2
shows the input and output mapping in the form of good information.
Fig. 2 Input output mapping
A fuzzy inference system is a computational framework with fuzzy rules set in the form of IF-THEN and fuzzy
reasoning [17]. The fuzzy inference system accepts crisp input to be sent to a knowledge base that stores n fuzzy rules
in the form of IF-THEN [18]. If the number of rules is more than one, all rules will be accumulated. The aggregation
results will then be defuzzied to induce a crisp value as a system output [19]. The control system performance can be
improved by applying fuzzy logic, stifling the emergence of other functions in the output caused by fluctuations in the
input variable [15]. The fuzzy logic is applied in three stages as can be seen in Fig. 3, as follows:
1. The fuzzification stage is a mapping from a firm input to a fuzzy set.
2. The inference stage includes the generation of fuzzy rules.
3. The affirmation stage (defuzzification) is when the output transforms from fuzzy values to firm values.
Fig. 3 Process Stages in Fuzzy Logic

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185
A rule is a knowledge structure that connects some known information to other information to draw conclusions.
Rules are a procedural form of knowledge [20]. Therefore, a rule-based expert system uses an inference engine to
generate new information and a set of rules in its knowledge base to process a problem from the information contained
in its active memory program [21]. The rule structure logically connects one or more antecedents (also called premises)
in the IF section with one or more consequences (also called conclusions) in the THEN section. In general, a rule can
have multiple premises associated with AND statements (conjunctions), OR statements (disjunctions) or a
combination of both [12].
Linear representation is the process of mapping input to form a straight line representing the degree of membership.
The linear fuzzy set has three states, as follows [9]:
1. Linear Up
To represent an ascending linear curve, the curve movement starts from a set with the domain having zero
membership to the right towards the domain with a higher membership value.
[]=0;  ≤
()
 ;  ≤ ≤
1;  ≥  (1)
2. Linear Down
For the descending linear representation, the movement starts from a set with the domain having the
highest/largest membership value on the left. The curve moves from the left to the right, where the domain has
a smaller/lower membership value.
[] =1;  ≤
()
 ;  ≤≤
0;  ≥  (2)
3. Triangle Curve
The triangular curve represents a combination of an ascending linear curve and a descending linear curve.
[]=
⎩
⎨
⎧
0;  ≤  ≥
()
();  ≤ ≤
()
(); ≤ ≤
⎭
⎬
⎫
(3)
The stages in the Mamdani fuzzy logic method, namely [10]:
1. Formation of fuzzy sets
The formation of rules will later be used in the expert system's knowledge base. One or more fuzzy sets are the
quotient of the input and output variables in the Mamdani fuzzy. An ascending or descending linear curve is used
according to Equations (1) and (2) for the membership function of each variable involved.
2. Implication function app
For the Mamdani fuzzy method, the implication function uses the min function. Then the value of the -predicate
and z was determined using (4) and (5).
 − =  µ(1),µ(2),…(µ) (4)
−=  
   (5)
3. Composition of rules
Based on each rule’s implication function, all rules were then composed using the max method. The fuzzy set
solution is taken from the maximum value of each rule. Then the value is used to modify the fuzzy set and
implement it to the output using the OR operator or the union concept. When all propositions have been
evaluated, the output will contain a fuzzy set that reflects the contribution of each proposition. The equation is
in (6). µ[]←max(µ[],µ[]) (6)
Description: sf[xi] represents the membership value of the fuzzy solution up to the i-th rule, and kf[xi] represents
the consequent fuzzy membership value of the i-rule.
4. Affirmation/Defuzzification

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The last step in this method is to determine the crisp output value to find the centralised average defuzzification
value using (7). = ⋯
⋯ (7)
C. Naïve Bayes Method
Naïve Bayes was first proposed by British scientist Thomas Bayes, which predicts future probabilities based on
experience. Naïve Bayes is an algorithm that utilises a probability theory based on Bayes’ theorem and is combined
with ‘Naïve’, which means that each attribute or variable has independent properties (free assumptions) [22]. Naïve
Bayes calculates a class's probability based on its attributes and determines the class with the highest probability [23].
The advantage of classification is that Naïve Bayes requires only a small amount of training data to estimate the
parameters (means and variance of the variables) for the classification [24]. Only the variation of the variables for
each class should be determined because independent variables are assumed, not the entire covariance matrix [25].
Calculations on the Naïve Bayes method to generate disease predictions go through several stages below [26] and is
shown in (8)-(10).
1. Each class involves: (|)= (∗)
 (8)
Description:
qd = the value of the data record on the training data has a = aj and p = pi
x = 1 / many types of classes / diseases
r = number of symptoms/ parameters
q = the value of the data record on the training data has a value of a = aj/per class/disease
2. The likelihood value for each existing class is determined using the equation below: ()= 
 (9)
3. The posterior value for each class involved is determined using the following equation:
(|)=(|)∗ () (10)
The final result of the Naïve Bayes method is to classify the classes involved in presenting dental disease
possibilities by comparing the posterior final values of each class involved [27]. The Naïve Bayes classification
method results in the highest posterior value of several classes being compared.
III. RESULTS
This study uses dental patient data from the Community Health Centre (puskesmas) of North Cilacap collected
between July and December 2021, totalling 67 patients with various complaints such as gum inflammation, cavities,
pain when chewing or biting, and bad breath. The dataset used in this study was in the form of dental disease symptoms
obtained from interviews with the patients. These symptoms are consulted by an expert, i.e., a dentist.
TABLE 1
EXPERT CONFIDENCE WEIGHT
Answer Choices Expert Confidence
Weight
Not Sure 0
0
Less Sure 0.3
0.3
Yes/Yes 0.8
0.8
Very Confident 1
1
Table 1 shows expert (dentist) confidence in the problem identification, and Table 2 shows the codes of the dental
disease symptoms and problems with its supporting tissues. The weight of expert confidence will later be input into
the expert system’s knowledge base. This is then adjusted and applied to the answers given by the patients. Table 3
shows the symptoms of dental and its supporting tissue diseases.

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187
TABLE 2
DISEASES AND SYMPTOMS OF DENTAL DISEASE
Disease
Disease Code
Reversible Pulpitis
P01
Irreversible Pulpitis
P02
Pulp Necrosis
P03
Periapical Abscess
P04
Periodontal Abscess
P05
Gingivitis
P06
Chronic Periodontitis
P07
Pericoronitis
P08
Tooth Crown Fracture
P09
Radicular Cyst
P10
Granulomas
P11
TABLE 3
SYMPTOMS OF DENTAL DISEASE
Disease Symptoms Code
Description
Dental Disease Code
S01
Short pain or aches
P01
S02
Pain or aches for a long time
P02
S03
Pain that does not occur spontaneously
P01
S04
Pain may occur spontaneously
P02
S05
Pain when lying down or bending over
P02
S06
Discolouration of teeth
P03
S07
Bad breath
P03, P04, P08
S08
No pain
P03
S09
Teeth hurt when biting
P04, P05
S10
Teeth feel elongated
P04, P07, P10
S11
With swelling or not
P04
S12
Accompanied by systemic reactions
P04, P05, P08
S13
Taste disturbance
P04
S14
Large swelling
P05, P10
S15
Teeth feel loose
P05, P07, P09, P11
S16
Bleeding gums
P06
S17
Teeth may fall out prematurely
P07
S18
Swelling of the area of the growing tooth
P08
S19
Sometimes accompanied by Trismus
P08
S20
Asymmetrical face
P08
S21
Sharp and stabbing pain
P09
S22
Asymptomatic
P10, P11
The diagnosis results were analysed to ensure that both the expert system diagnoses and the expert’s diagnoses
align. For example, Table 4 shows the results of a comparison between the expert system’ and the expert’s diagnoses
for periodontal abscess disease.
TABLE 4
ILLUSTRATED RESULTS OF PATIENT ANSWERS FOR PERIODONTAL ABSCESS DISEASE
Symptom Code
Symptom Name
Patient Answer
Answer Weight
S07
Bad breath
Yes
0.8
S09
Teeth hurt a lot when biting
Yes
0.8
S10
Teeth feel elongated
Not sure
0.3
S11
With swelling or no
Yes
0.8
S12
Accompanied by systemic reaction
Yes
0.8
S13
Taste disturbance
Uncertain
0.3
A. Mamdani Fuzzy Logic Method
For implementing the Mamdani fuzzy logic method, the first step is to create a membership function for each
variable (the periodontal abscess symptoms). The variables consist of six symptoms, according to Table 4. Experts,
i.e., dentists, transform knowledge about dental diseases and their supporting tissues into the knowledge base, which
includes data on dental disease symptoms and their supporting tissues, category predictions, and the rules. Fig. 5 shows
the likeliness of periodontal abscess disease. Table 5 shows the rules for periodontal abscess disease. The symbol H
represents high, L represents low, T represents not indicated, and Y represents indicated. The steps taken for solving
using Mamdani fuzzy logic are as follows:
1. Formation of fuzzy sets in (11) and (12)

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188
TABLE 5
P
ERIODONTAL
A
BSCESS
D
ISEASE
R
ULE
Rule Code
S07
S09
S10
S11
S12
S13
Output
Rule Code
S07
S09
S10
S11
S12
S13
Output
R01
R
R
R
R
R
R
N
R33
T
R
R
R
R
R
N
R02
R
R
R
R
R
T
N
R34
T
R
R
R
R
T
N
R03
R
R
R
R
T
R
N
R35
T
R
R
R
T
R
N
R04
R
R
R
R
T
T
N
R36
T
R
R
R
T
T
Y
R05
R
R
R
T
R
R
N
R37
T
R
R
T
R
R
Y
R06
R
R
R
T
R
T
Y
R38
T
R
R
T
R
T
Y
R07
R
R
R
T
T
R
Y
R39
T
R
R
T
T
R
Y
R08
R
R
R
T
T
T
Y
R40
T
R
R
T
T
T
Y
R09
R
R
T
R
R
R
N
R41
T
R
T
R
R
R
N
R10
R
R
T
R
R
T
N
R42
T
R
T
R
R
T
N
R11
R
R
T
R
T
R
N
R43
T
R
T
R
T
R
N
R12
R
R
T
R
T
T
Y
R44
T
R
T
R
T
T
N
R13
R
R
T
T
R
R
Y
R45
T
R
T
T
R
R
Y
R14
R
R
T
T
R
T
Y
R46
T
R
T
T
R
T
Y
R15
R
R
T
T
T
R
Y
R47
T
R
T
T
T
R
Y
R16
R
R
T
T
T
T
Y
R48
T
R
T
T
T
T
Y
R17 R T R R R R N R49 T T R R R R N
R18
R
T
R
R
R
T
N
R50
T
T
R
R
R
T
N
R19
R
T
R
R
T
R
N
R51
T
T
R
R
T
R
N
R20
R
T
R
R
T
T
N
R52
T
T
R
R
T
T
N
R21
R
T
R
T
R
R
Y
R53
T
T
R
T
R
R
N
R22 R T R T R T Y R54 T T R T R T Y
R23
R
T
R
T
T
R
Y
R55
T
T
R
T
T
R
Y
R24
R
T
R
T
T
T
Y
R56
T
T
R
T
T
T
Y
R25
R
T
T
R
R
R
N
R57
T
T
T
R
R
R
N
R26
R
T
T
R
R
T
N
R58
T
T
T
R
R
T
N
R27 R T T R T R N R59 T T T R T R N
R28
R
T
T
R
T
T
N
R60
T
T
T
R
T
T
Y
R29
R
T
T
T
R
R
N
R61
T
T
T
T
R
R
Y
R30
R
T
T
T
R
T
Y
R62
T
T
T
T
R
T
Y
R31 R T T T T R Y R63 T T T T T R Y
R32
R
T
T
T
T
T
Y
R64
T
T
T
T
T
T
Y
The functions for periodontal abscess disease likeliness are illustrated in Fig. 4.
Fig. 4 Degree of likeliness of periodontal abscess disease
  [] =1;  ≤20

 ; 20 ≤ ≤ 40
0;  ≥40  (11)
 ℎ [] =0;  ≤20

 ; 20 ≤ ≤ 40
1;  ≥40  (12)

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189
The next process is fuzzification, where a crisp value is converted into a fuzzy value involving six
variables/symptoms for periodontal abscess disease: S07, S09, S10, S11, S12, and S13. For example, for the case of
patients with a variable of S07 of 15, S09 of 16, a variable of S10 of 18, a variable of S11 of 22, a variable of S12 of
20, and the variable of S13 of 21. There are two kinds of outputs based on the rule-based outcome. As shown in Table
5: yes and no. By using Equations 1 and 2, the degree of linear membership increases and the degree of linear
membership decreases for each symptom variable of dental disease and its supporting tissues, as shown in Table 6.
TABLE 6
DEGREE OF MEMBERSHIP SYMPTOMS OF ILLNESS
Symptom Code μ min μ max
S07
0.25
0.75
S09
0.33
0.66
S10
0.5
0.5
S11
0.83
0.16
S12
0.66
0.33
S13
0.75
0.25
2. Implication Function Application
After knowing the min and max values, we look for the value of α-predicate and the value of z using Equations 4
and 5 for each rule. The implication function uses the min function for the Mamdani fuzzy method. By using the rules
in Table 5 and the value of the degree of membership of each disease symptom in Table 6, the values for α-predicate
and Z values are shown in Table 7.
TABLE 7
DEGREE OF MEMBERSHIP SYMPTOMS OF ILLNESS
Result
Rule Code
α Value
Z Value
Result
Rule Code
α Value
Z Value
R06
Y
0.16
23.2
R37
Y
0.16
23.2
R07
Y
0.16
23.2
R38
Y
0.16
23.2
R08
Y
0.16
23.2
R39
Y
0.16
23.2
R12
Y
0.25
25
R40
Y
0.16
23.2
R13
Y
0.16
23.2
R45
Y
0.16
23.2
R14
Y
0.16
23.2
R46
Y
0.16
23.2
R15
Y
0.16
23.2
R47
Y
0.16
23.2
R16
Y
0.16
23.2
R48
Y
0.16
23.2
R21
Y
0.16
23.2
R54
Y
0.16
23.2
R22
Y
0.16
23.2
R55
Y
0.16
23.2
R23
Y
0.16
23.2
R56
Y
0.16
23.2
R24
Y
0.16
23.2
R60
Y
0.16
23.2
R30
Y
0.16
23.2
R61
Y
0.16
23.2
R31
Y
0.16
23.2
R62
Y
0.16
23.2
R32 Y 0.16 23.2 R63 Y 0.16 23.2
R36
Y
0.25
25
R64
Y
0.16
23.2
3. Composition of Rules and Affirmations
The max method is used to perform the composition. All the rules used are taken from each implication function in
Table 7. The equation used is equation (12). The last step is to determine the value of z using the centroid method
according to equation (7).
z=(,∗,)(,∗,)...(,∗,)
,,..., =30,445
The defuzzification value of the severity of periodontal abscess is:
30,445 ∗ 100% = 30,445 %
The severity of the disease is divided into four categories, namely 1) mild at an interval of 0% to 25%, 2) moderate
with an interval of 26% to 50%, 3) severe with an interval of 51% to 75%, and 4) is very severe with an interval of
76% to 100% [28]. Table 8 shows the severity of dental disease according to the system diagnosis suffered by the 67
patients calculated using the Mamdani fuzzy logic method.

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190
TABLE 8
PATIENT SEVERITY
Patient
Code
Disease Percentage
Severity
Category Patient
Code
Disease Percentage
Severity
Category
PS01
Granulomas
58,6%
Critical
PS34
Radicular Cyst
41,37%
Currently
PS02
Irreversible Pulpitis
67%
Critical
PS35
Granulomas
25%
Light
PS03
Granulomas
43,4%
Currently
PS36
Reversible Pulpitis
69,1%
Critical
PS04
Periapical Abscess
23,1%
Light
PS37
Tooth Crown Fracture
63,2%
Critical
PS05
Granulomas
15,9%
Light
PS38
Pulp Necrosis
73,2%
Critical
PS06
Gingivitis
24,4%
Light
PS39
Tooth Crown Fracture
68,1%
Critical
PS07
Chronic Periodontitis
55,5%
Critical
PS40
Periodontal Abscess
89,2%
Awfully
PS08
Pericoronitis
69,7%
Critical
PS41
Periodontal Abscess
92,1%
Awfully
PS09
Granulomas
35,7%
Currently
PS42
Chronic Periodontitis
59,9%
Critical
PS10
Irreversible Pulpitis
21,1%
Light
PS43
Pericoronitis
58,2%
Critical
PS11
Tooth Crown Fracture
64,9%
Critical
PS44
Periodontal Abscess
70,2%
Critical
PS12
Periapical Abscess
65,5% Critical PS45
Tooth Crown Fracture
85,9% Awfully
PS13
Periodontal Abscess
61,7%
Critical
PS46
Granulomas
59,3%
Critical
PS14
Gingivitis
55,2%
Critical
PS47
Tooth Crown Fracture
64,9%
Critical
PS15
Tooth Crown Fracture
71,1%
Critical
PS48
Irreversible Pulpitis
67,5%
Critical
PS16
Pericoronitis
34,1%
Currently
PS49
Pulp Necrosis
68,3%
Critical
PS17
Tooth Crown Fracture
24,5% Light PS50
Periapical Abscess
37,5% Currently
PS18
Radicular Cyst
49,7%
Currently
PS51
Periodontal Abscess
13,9%
Light
PS19
Granulomas
75%
Critical
PS52
Gingivitis
33,1%
Currently
PS20
Gingivitis
41,3%
Currently
PS53
Chronic Periodontitis
65,4%
Critical
PS21
Gingivitis
14,2%
Light
PS54
Pericoronitis
45,6%
Currently
PS22
Pulp Necrosis
61,7% Critical PS55
Tooth Crown Fracture
19,1% Light
PS23
Tooth Crown Fracture
51,4%
Critical
PS56
Gingivitis
61,7%
Critical
PS24
Periodontal Abscess
65,2%
Critical
PS57
Irreversible Pulpitis
71,3%
Critical
PS25
Tooth Crown Fracture
61,8%
Critical
PS58
Gingivitis
74,2%
Critical
PS26
Gingivitis
74,2%
Critical
PS59
Gingivitis
58,5%
Critical
PS27 Periodontal Abscess 30,45% Currently
PS60
Periodontal Abscess
61,1%
Critical
PS28
Periapical Abscess
91,2%
Awfully
PS61
Gingivitis
75%
Critical
PS29
Periodontal Abscess
71,2%
Critical
PS62
Chronic Periodontitis
81,1%
Awfully
PS30
Periodontal Abscess
33,7%
Currently
PS63
Pericoronitis
54,7%
Critical
PS31
Chronic Periodontitis
11,9%
Light
PS64
Tooth Crown Fracture
67,5%
Critical
PS32
Pericoronitis
24,9%
Currently
PS65
Gingivitis
56,3%
Critical
PS33
Tooth Crown Fracture
58,3%
Critical
PS66
Gingivitis
85,6%
Awfully
PS67
Reversible Pulpitis
72,2%
Critical
B. Naïve Bayes Method
Calculations using the Naïve Bayes method are used to classify and determine the diagnosis of the symptoms of
dental disease and its supporting tissues selected by a patient. Sixty-seven patient data were analysed to classify dental
diseases and their supporting tissues. For example, a sample of a patient with the initials PS27 experienced symptoms
such as bad breath (S07), a very painful tooth when biting (S09), a tooth that felt elongated (S10), swelling (S11), a
systematic reaction (S12), and conversational disorder (S13). These symptoms include pulp necrosis disease (P03),
periapical abscess (P04), periodontal abscess (P05), chronic periodontitis (P07), pericoronitis (P08), and radicular cyst
(P10). The implementation of the Naïve Bayes method with the calculation stages is as follows:
1. Determine the number of records in the learning data for each class of diseases.
Using Equation 8, the number of disease classes involved with a total symptom value of 22 symptoms, with a value
of x=0.091 and r=1, are shown in Table 9.
TABLE 9
NUMBER OF DISEASE CLASSES
Diseases
Symptoms
S07
S09
S10
S11
S12
S13
P03
1
0
0
0
0
0
P04
1
1
1
1
1
1
P05
0
1
0
0
1
0
P07 0 0 1 0 0 0
P08
1
0
0
0
1
0
P10
0
0
1
0
0
0

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191
2. Determine the likelihood value
Determination of the likelihood value was also carried out for diseases with codes P03, P04, P05, P07, P08, and
P10. The likelihood value is determined using equation (9).
TABLE 10
T
HE LIKELIHOOD
V
ALUE
Diseases
Symptoms
S07
S09
S10
S11
S12
S13
P03
0,1304
0,087
0,087
0,087
0,087
0,087
P04
0,090909
0,1304
0,1304
0,1304
0,1304
0,1304
P05 0,087 0,1304 0,087 0,087 0,1304 0,087
P07
0,087
0,087
0,1304
0,087
0,087
0,087
P08
0,1304
0,087
0,087
0,087
0,1304
0,087
P10
0,087
0,087
0,1304
0,087
0,087
0,087
3. Determine the posterior value
Fig. 5 The Posterior Value
Fig. 5 explains the calculation results of determining the posterior value for diseases with codes P03, P04, P05, P07,
P08, and P10. It can be concluded that patients with code PS27 suffer from a periapical abscess, namely a disease
severing the tip of the tooth’s root, with a posterior value of 4,477 x10-7. The calculation results also found that there
were two diseases coded P05 and P08 with the same posterior value, namely 8.843 x 10-8. Diseases coded P03, P07,
and P10 have the same posterior value of 5.895 x 10-8. Therefore it is necessary to calculate the percentage of
user/patient confidence in the conclusion of the disease using the following equation [29]:
P=Q∗R (13)
Information:
P = Disease Percentage Value
Q = 
 ∗ 100% , where n is the number of symptoms for each type of disease
R = Number of symptoms the patient chooses for each disease
The results of calculating the percentage value are exemplified for the case of patients with the PS27 code with
each symptom in each disease shown in Fig. 6.
1. For diseases coded P03, namely pulp necrosis with symptoms of S06, S07, and S08
2. For disease coded P04, namely periapical abscess with symptoms of S07, S09, S10, S11, S12, and S13
3. For disease coded P05, namely periodontal abscess with symptoms of S09, S12, S14, and S15
4. For disease coded P07, namely chronic periodontitis with symptoms of S10, S14, and S22
5. For diseases coded P08, namely pericoronitis with symptoms of S07, S12, S18, S19, and S20
6. For diseases coded P10, namely radicular cyst disease with symptoms of S10, S14, and S22
5,895E-08
4,477E-07
8,843E-08 5,895E-08 8,843E-08 5,895E-08
P03 P04 P0 5 P07 P 08 P10

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192
Fig. 6 The disease percentage value
The next stage is to compare the classification results between the Naïve Bayes method and dentists.
TABLE 10
C
OMPARISON
R
ESULTS OF
M
AMDANI
F
UZZY
L
OGIC AND
N
AÏVE
B
AYES WITH
E
XPERT
H
YPOTHESES
Patient Code Expert Mamdani
Fuzzy Logic
Na
ï
ve Bayes Patient Code Expert Mamdani
Fuzzy Logic
Na
ï
ve Bayes
PS01
P
TP
TP
PS34
P
FP
FP
PS02
P
TP
TP
PS35
P
FP
FP
PS03
P
TP
TP
PS36
P
TP
TP
PS04 P TP TP PS37 P TP TP
PS05
P
TP
TP
PS38
P
TP
TP
PS06
P
TP
TP
PS39
P
TP
TP
PS07
P
TP
TP
PS40
P
TP
TP
PS08 P TP TP PS41 P TP TP
PS09
P
TP
TP
PS42
P
TP
TP
PS10
P
TP
TP
PS43
P
TP
TP
PS11
P
TP
TP
PS44
P
FP
TN
PS12
P
TP
TP
PS45
P
FP
TN
PS13
P
FN
TP
PS46
P
TP
TP
PS14
P
TN
TN
PS47
P
TP
TP
PS15
P
TN
TN
PS48
P
TP
TP
PS16
P
TP
TP
PS49
P
TP
TP
PS17
P
TP
TP
PS50
P
TP
TP
PS18
P
TP
TP
PS51
P
TP
TP
PS19
P
TP
TP
PS52
P
TP
TP
PS20
P
TP
TP
PS53
P
TP
TP
PS21
P
FP
FP
PS54
P
TP
TP
PS22
P
TP
TP
PS55
P
TP
TP
PS23
P
TP
TP
PS56
P
TN
TN
PS24
P
TP
TP
PS57
P
TN
FN
PS25
P
TP
TP
PS58
P
FP
FP
PS26
P
FN
TN
PS59
P
TP
TP
PS27
P
TP
FN
PS60
P
FP
FP
PS28
P
TN
TN
PS61
P
TP
TP
PS29
P
FP
FP
PS62
P
TP
TP
PS30
P
TP
TP
PS63
P
TP
TP
PS31
P
TP
TP
PS64
P
TN
FN
PS32
P
TN
TN
PS65
P
TN
TN
PS33
N
TN
TN
PS66
P
TN
FP
PS67
P
TN
FP
The data was obtained during an interview with the dentist at South Cilacap Health Centre. It is based on medical
record data of patients with complaints of toothache. Performance calculations using the Naïve Bayes method are
carried out to determine the confusion matrix [30]. From Table 10 above, it can be concluded that the value of True
Positive (TP) is 46, True Negative (TN) is 11, False Positive (FP) is 8, and False Negative (FN) is 2 for the Mamdani
fuzzy logic. Meanwhile, the value of True Positive (TP) is 45, True Negative (TN) is 10, False Positive (FP) is 9, and
False Negative (FN) is 3 for the Naïve Bayes. From these data, the accuracy value, precision value, sensitivity value
and specificity value can be calculated, the result is shown in Fig. 7.
33,33
60
25
33,33
40
33,33
0
10
20
30
40
50
60
70
P03 P04 P05 P07 P 08 P10

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193
Fig. 7 Comparison of the mamdani fuzzy logic method and the naïve bayes method on dental disease results
The calculation results using the confusion matrix above conclude that the system's accuracy value using the
Mamdani fuzzy logic method is 85.1%. In comparison, the Naïve Bayes classification method is 82.1%. Both methods'
performance is good because the accuracy value exceeds 50% based on the test results.
IV. D
ISCUSSION
Expert systems have been widely implemented in various fields. Fuzzy and Naïve Bayes methods have also been
widely used to solve various problems. As in the [6], [14], [31], [9], [22] research that has been carried out by
implementing the Mamdani fuzzy logic method and the Naïve Bayes method, this research has a novelty in that
comparing the results of the diagnosis of dental disease and its supporting network from an expert, a dental specialist
with the results diagnosis of an expert system that implements the Mamdani fuzzy logic method and also the Naïve
Bayes method. The results of the diagnosis are then compared with the accuracy level to be used as a decision
recommendation about the dental disease. The process of diagnosing dental disease and its supporting tissues begins
with the selection of the symptoms.
V. C
ONCLUSIONS
The calculation results show the accuracy of dental and surrounding tissue disease prediction and surrounding tissue
by implementing the Mamdani fuzzy logic method, which is compared and weighted by experts, namely dentists,
reaching 85.1%. Meanwhile, the Naïve Bayes method has an accuracy rate of 82.1%. For example, a patient with code
PS27 was diagnosed by an expert as having a periodontal abscess. Using a system that implements the Mamdani fuzzy
logic method, PS27 was diagnosed with symptoms that lead to periodontal abscess with severity of 30.45%, while
using a system that implemented the Naïve Bayes method diagnosed with periapical abscess disease with a percentage
of 60%. Based on the results of the accuracy of the diagnosis of dental disease using the Mamdani fuzzy logic method
and the Naïve Bayes method exceeding 50%, it can be concluded that the performance of both methods is quite good.
Author Contributions: Linda Perdana Wanti: Conceptualization, Methodology, Writing - Review & Editing,
Supervision, Original Data. Oman Somantri: Writing the conceptualization, Original Draft, Investigation, and Data.
Funding: This work was supported by P3M Politeknik Negeri Cilacap.
Acknowledgements: We would like to thank North Cilacap Health Center,
and all expert respondents and passenger
respondents have assisted researchers in filling out questionnaires as research data.
Conflicts of Interest: The authors declare no conflict of interest.
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