A Framework for Fuzzy Diagnosis of Hepatitis

Okure U. Obot

Department of Computer Science

University of Uyo, PMB. 1017 520003

Uyo, Akwa Ibom State, NIGERIA

e-mail: abatakure@yahoo.com

Samuel S. Udoh

Department of Computer Science

University of Uyo, PMB. 1017 520003

Uyo, Akwa Ibom State, NIGERIA email: udohss@yahoo.com

Abstract—A study of the orthodox practice of diagnosing

hepatitis revealed that inexactness in the diagnostic results has

led several patients into abusing therapies. This prompted a

further study into how this could be resolved. In this regard,

effort was made for medical doctors to specify some linguistic

labels while taking history and performing medical examinations

on the patients. The effort yielded few responses which

necessitated a study of the application of fuzzy logic technology

to medical diagnosis. The symptoms were fuzzified with some

membership functions which aided in the extraction of fuzzy rule

base. With data and rules, fuzzy inference using the maxmin

method was applied on the knowledge base, the results obtained

were defuzzified to obtain crisp outputs that represent the

diagnostic values with linguistic labels. The novelty of the result

is that the degree or extent to which a patient suffers from

hepatitis is reported to the patient and based on such revelation

therapy would be administered without an abuse.

Keywords-Fuzzy Logic; Hepatitis; Maxmin; Knowledge base;

Decision Support Filter

I. INTRODUCTION

Medical diagnosis is a very important component of medical

and health care delivery. Improper diagnosis of an ailment

often results in incorrect treatment that leads to

complications of the ailment and eventually to death. What

is involved is the elicitation of the signs and symptoms of

the disease and the determination of the extent or degree of

effects the symptoms have had on the organs. When this is

determined, appropriate therapy is administered to alleviate

the pains and heals whatever effects the organs have had.

The task of doing this effectively and efficiently at the right

time is complex and requires a deep knowledge of the

diseases, and the history of the patient. The need to arrive at

the most accurate medical diagnosis in a very timely manner

is heightened in the case of malaria and other tropical

conditions, as it is understood that a quick and accurate

diagnosis and timely initiation of treatment is a sine-qua-

non to the reduction of complications [1].

The problem of medical diagnosis is further

complicated when the decision variables (signs and

symptoms) of the disease are numerous as in the case of

hepatitis. Additionally, when the variables involved seem to

overlap with the variables of other tropical diseases.

Thirdly, the problems of uncertainty and imprecision of the

data involved is a serious threat to proper diagnosis. A

number of attempts have been made to resolve the problems

of multiple attributes decision making and conflicting

decision variables.

Researchers in medical expert systems have also

attempted to find ways to manage uncertainty and

imprecision of data in medical diagnosis. It is difficult for a

patient to tell a medical practitioner how exactly he feels

and the degree of pains he experiences using linguistics

variables. At the same time, a medical doctor cannot

determine the exact degree or extent of the sign of a disease

based on his examination. Most of the variables found in

medical diagnosis are fuzzy in form. For example, a patient

who complains of a general discomfort might not be able to

explain the degree of discomfort. A medical doctor who

examines a patient’s liver and reports of its tenderness will

only use fuzzy variables to explain the tenderness.

Hepatitis is an acute inflammation of the liver caused

by some infectious or toxic agent [2]. It can be categorized

broadly as Hepatitis A or infectious hepatitis and Hepatitis

B or Serum hepatitis. Hepatitis B is more chronic and severe

than Hepatitis A although they have conflicting signs and

symptoms. Hepatitis A is an acute virus infection that harms

the liver. The symptoms of hepatitis are fuzzy and

ambiguous. Some of the signs and symptoms of Hepatitis A

and their weights are presented in Table 1.

According to Obot and Uzoka [3], the weights were

assigned with the help of some experienced physicians. The

variables are weighted according to the severity and

specificity of the signs and symptoms of hepatitis. Some of

the symptoms are discriminatory of hepatitis while others

are not. Some are specifically signs and symptoms of

hepatitis; others are not really specific but relate to it. These

form the basis of the grading or weighting factors. For an

instance, jaundice is specifically a clear sign of hepatitis and

is thus assigned the weight of 4, this is also true of skin and

eye discolorations, but the two are assigned each a weight of

3 because of their degree of severity of the cause of the

disease. Symptoms like fever, body weakness and headache

are discriminatory, that is, their presence could be because

of diseases like malaria and typhoid. Nausea, vomiting and

tender liver are specifically symptoms of hepatitis but could

also result in other diseases, so a weight of 2 is assigned to

each of them.

439978-1-4673-0126-8/11/$26.00 c©2011 IEEE

TABLE I. SIGNS AND SYMPTOMS OF HEPATITIS

S/N Name Code Weights

1 Nausea Nau 2

2 Vomiting Vom 2

3 Fever Fev 1

4 Body Weakness Wea 1

5 Loss of appetite App 1

6 Diarrhea Dia 1

7 Itching Itc 1

8 Convulsion Con 2

9 Stupor Stu 2

10 Headache Hea 1

11 Tremors Tre 1

12 Skin

discoloration

Ski 3

13 Eye discoloration Eye 3

14 Liver tenderness Liv 2

15 Bile in urine Bil 2

16 Jaundice Jau 4

The inexactness of the orthodox practice results which do

not present the degree or extent a patient suffers from

hepatitis and the ability of fuzzy logic technology in

resolving conflicts based on aggregation and collaboration

further motivated this study.

Fuzzy logic deals with imprecise, vague and ambiguous

dataset [4] as witnessed in the signs and symptoms of

hepatitis. The objective of the research is to apply the

concepts of fuzzy logic technology to determine the degree

of severity or extent of the influence of the signs and

symptoms of hepatitis to the diagnosis of hepatitis. The

diagnostic results will also resolve the fuzziness currently

exhibited in the diagnosis of hepatitis as can be observed in

Obot and Uzoka [3]. The study seeks to; develop fuzzy

membership functions for each of the symptoms of

hepatitis; develop fuzzy rule-base from which a maxmin

method of inference is applied to infer and compose the

datasets. Defuzzify the composed dataset into corresponding

output using the centre of gravity method, the results of this

form the diagnostic results which define the degree or extent

a particular patient is suffering from hepatitis. In particular,

the datasets are obtained from patients suffering from

hepatitis A. Fuzzy logic has been applied in the diagnosis of

diseases in [5-7].

In Section II, the system architecture is presented while

the research experiment is conducted and presented in

Section III. Discussion of the results of the experiment is

carried out in Section IV and Conclusion is drawn in

Section V.

II. SYSTEM ARCHITECTURE

The architecture of the framework comprises database and

rule base, which make up the knowledge base. The

inference engine employs fuzzy logic reasoning

methodology which derives its strength from the fuzzified

inputs that was also used to build the fuzzy rule base. The

maxmin method of drawing inference is employed on the

rule base, the results of this procedure are fed into the

defuzzification module to produce crisp output. This can be

filtered emotionally and cognitively by the Decision

Support Filter component of the system. The architecture is

presented in Figure 1.

Figure 1. The Architecture of Fuzzy Diagnosis of

Hepatitis

A. The Database The database is conceptualized as a relation

),...,,,( 321 naaaaR , where R is the name of the relation

and ),...,,,( 321 naaaa are the attributes of the relation. The

main relations of the system are as [3] follows:

Patient_Biodata (Ptient_number, patient_name,

date_of_birth, residential_address, telephone_number,

next_of_kin, address_of_next_of_kin, date_of_registration,

time_of_registration, date_of_history, date_of_exam)

Disease_symptom(patient_number, nausea, vomiting,

body_weakness, loss_of_appetite, diarrhea, skin_itching,

convulsion, stupor, headache, tremor).

Disease_sign(Patient_number, temperature, eye_color,

skin_color, tenderness_of_liver, bile_in_urine, jaundice).

The unstructured knowledge was obtained through

interaction with some experience medical practitioners who

assisted in assigning weights to the signs and symptoms

according to the specificity and severity of the symptoms to

hepatitis as presented in Table 1.

B. Fuzzy System The fuzzy system is conceptualized as presented in Figure 2.

The fuzzification subcomponent of the module transforms

raw data using membership functions defined in equations

1-4. During this process, linguistic labels are assigned to the

symptoms with their corresponding degree of severity.

440 2011 World Congress on Information and Communication Technologies

Figure 2. Fuzzy Logic System

All the 16 signs and symptoms do not contribute

significantly to the cause of Hepatitis. In order to identity

which of them contributes significantly, an input

contribution measures was performed using sensitivity test

of NeuroSolutions 5.0 [8]. Six input variables namely;

Jaundice, skin discoloration, eye discoloration, nausea, urine

in Bile and liver tenderness were found to contribute

immensely to the outputs [Obot and Uzoka, 2009], while the

other 10 variables contribute very meagerly. These were

therefore used to formulate the membership functions and

consequently the fuzzy rules represented in the form of

production rules.

There are 3 groups of signs and symptoms categorized

according to their weights (2,3,4) as can be seen in Table 1.

These are classified into different membership functions

accordingly. Symptoms with a-2-point weight are presented

in equation 1, those with a-3-point weight are presented in

equation 2 while the one with a-4-point weight is presented

in equation 3. These are Nausea (2), Bile in Urine (2), liver

tenderness (2), eye discoloration (3), and Jaundice (4).

For the 2 point weight symptoms the membership function

is as presented in equation (1)

<=<=

<=<=

<=<=

=

2.0 sym(x)1.6IfHigh

1.5 sym(x)0.1IfModerate

0.5 sym(x)0.1IfLow

xSymptom )( (1)

The 3 point weight symptoms have membership function as

defined in equation (2)

<=<=

<=<=

<=<=

=

3.0x2.0IfHigh

1.9x1.1IfModerate

1.0x0.1IfLow

xSymptom )( (2)

The 4 point weight symptoms have membership function as

defined in equation (3)

<=<=

<=<=

<=<=

=

4.0x2.6IfHigh

2.5x1.6IfModerate

1.5x0.1IfLow

xSymptom )( (3)

The final diagnosis is evaluated with membership function

as presented in equation 4.

<=<=

<=<=

<=<=

=

1.0x0.80IfHepatitisHigh

0.79x0.5IfHepatitisModerate

0.49x0.1IfHepatitsLow

diagPatient )( (4)

C. The Fuzzy Rule Base

53 fuzzy rules were developed with the assistance of some

experienced doctors. The rules are represented as production

rules, some of the rules are:

R22 If Jaundice is High and Skin discoloration is

Moderate and Eye discoloration is Moderate and

Nausea is Moderate and Urine in Bile is Low and

Liver tenderness is Low Then Hepatitis is

Moderate. R39 If Jaundice is Low and Skin discoloration is Low

and Eye discoloration is Low and Nausea is Low

and Urine in Bile is Moderate and Liver tenderness

is Low Then Hepatitis is Low.

R50 If Jaundice is Low and Skin discoloration is

Moderate and Eye discoloration is Moderate and Nausea is Moderate and Urine in Bile is Low and

Liver tenderness is Low Then Hepatitis is

Moderate.

The fuzzy rules were used to develop a fuzzy rule base as

presented in Table 2 with 25 of the 53 rules.

TABLE II. FUZZY RULE BASE

Rule

No.

Jau Ski Eye Nau Bil Liv Diagnosis

1 H L M M H M M

5 H M L H M L M

8 M L L L M L L

10 L M M M L M M

15 H M M H H H H

16 H H H H H H H

17 H L L L L L L

20 M M L L L L M

21 M M M L L L M

22 H M M M L L M

24 H M M M M L H

25 H M M M M M H

26 M M M M M H M

27 M M M M H H H

30 M M M H H H H

32 M M H M M H H

34 M M H H L L M

35 M L L L L L L

36 L H H H L H M

38 M M M M H M M

39 L L L L M M L

40 L L M M L H M

42 L M M M L L L

44 L L H H L M L

50 L M M M L L M

L= Low; M= Moderate; H= High

D. The Fuzzy Inference The fuzzy inference uses the MAXMIN method of

evaluation, where the minimum of each rule precedence

2011 World Congress on Information and Communication Technologies 441

values of the firing rule is firstly obtained and the maximum

value of all the minimums in the rule base is then obtained

to represent the intermediate diagnostic value. This is used

to determine the degree of influence on the fuzzy parameter.

A patient may be diagnosed to have hepatitis or severe

hepatitis, this is fuzzy in the sense that the exact degree of

severity is not determined. The fuzzy inference helps to

determine this exactness and certainty and minimize

ambiguities.

E. Defuzzification

The defuzzification interface is a mapping from a space of

fuzzy action defined over an output universe of discourse

into a space of non-fuzzy set to obtain crisp values. There

are several methods of defuzzification but the centre of

gravity (CoG) is applied in this study because it is more

accurate in representing fuzzy sets of any shape[Cochran

and Chen, 2005]. It is an averaging technique with the

(point) masses replacing the membership values. In a

discrete form CoG is defined simply as:

=

=

=n

j

ji

n

j

jji

pU

ppU

iCoG

1

1

)(

)(

)(

(6)

where n is the number of quantization used to discretise

membership function Ui (p) of the fuzzy output i.

F. The Decision Support Filter

The decision support filter is essential because some factors

such as environment, habit and existing disease might be

responsible for a case that looks like hepatitis. A patient

provides such information to aid in the final decision of the

physician in the patient’s state of health.

III. THE RESEARCH ENVIRONMENT

10 datasets collected from a hospital about hepatitis patients

are presented in Table 3. These are evaluated using

equations 1-5 and the fuzzy rules presented in Table 2. The

transcript for the first patient is presented in Table 4. The

result of the defuzzification is presented as the final

diagnostic value.

TABLE III. RAW DATA COLLECTED FROM THE HOSPITAL

Patient

No

Jau Ski Eye Nau Bil Liv Diagnosis

P001 L L M M L M M

P002 M L L H M M M

P003 H H M H H M H

P004 H M M L L M H

P005 L L M M L M M

P006 M L L L L M M

P007 M M M H M L H

P008 M H H L L L H

P009 L L H L M M L

P010 H L M M L L M

L= low, M= Moderate, H= High

Membership values were evaluated using equations 1-4 and

the fuzzy rule base of Table 2 was employed to arrive at the

following transcript. 23 rules fired for patient number P001

and the transcript of the diagnosis is presented in Table 4.

TABLE IV. TRANSCRIPT FOR PATIENT NUMBER P001

S/N Nau

(2)

Bil(2) Liv

(2)

Eye

(3)

Ski

(3)

Jau

(4)

Min

Patient

Score

Low

(0.5)

Low(0.5) Mod

(1.5)

Mod

(1.5)

Low

(0.8)

Mod

(2.5)

1 N Y Y Y Y N 0.5

2 N N N N Y Y 0.8

3 N Y Y Y N N 0.5

4 N N N Y N N 1.5

5 N Y N N Y N 0.5

6 Y Y N N N N 0.5

7 Y Y N Y N N 0.5

8 N Y N Y N N 0.5

9 N N N Y N N 1.5

10 N N Y Y N N 1.5

11 N N N Y N Y 1.5

12 N N N Y N N 1.5

13 N N N Y N Y 1.5

14 N N N N N Y 2.5

15 N Y N N N Y 0.5

16 Y Y N N Y Y 0.5

17 N Y N N N N 0.5

18 N N Y Y N Y 1.5

19 Y N Y N Y N 0.5

20 N Y N Y Y N 0.5

21 Y Y N Y N N 0.5

22 Y Y Y N Y N 0.5

23 N Y Y Y N N 0.5

704.01.21

86.14

)(

)(

1

1

==

=

=

=

n

j

ji

n

j

jji

pU

ppU

CoG

TABLE V. FUZZY DIAGNOSIS (COMPUTATION) RESULTS

Patient No Conventional

Diagnosis

Fuzzy Diagnosis

Membership Degree

P001 M M 0.704

P002 M H 0.99

P003 H H 0.97

P004 H H 0.89

P005 M H 0.95

P006 M M 0.76

P007 H H 0.91

P008 H M 0.78

P009 L L 0.45

P010 M M 0.67

442 2011 World Congress on Information and Communication Technologies

IV. RESULT OF DISCUSSION AND CONCLUSION

In this study, the diagnosis of 10 patients suffering from

Hepatitis A was evaluated. Other methodologies such as

rule base, case base and artificial neural networks have been

applied in the diagnosis of hepatitis. One advantage fuzzy

diagnosis has over the other methodologies is that it

resembles human decision making with its ability to work

from approximate reasoning and ultimately finding precise

solution. A patient who is diagnosed of Hepatitis using other

methodologies will not be told the degree or the extent to

which the disease has in the patient. With fuzzy diagnosis

this is possible as can be seen in the results presented on

Table 5. For example, the first case (Patient No. P001), the

symptoms were fuzzified so that the degree of influence of

the symptom is captured into the inference engine of the

system.

The inference engine uses the fuzzy rule base extracted

from membership functions and ascertained by some

physicians to carry out inferences on the data. The

intermediate results were deffuzified to obtain crisp outputs.

The Decision support factor filters some emotional and

cognitive reasoning of some environmental and habitual

factors to produce the final output. The results presented

only show the defuzzified outputs as the patients whose data

were collected from could not be reached easily to obtain

such environmental and habitual factors.

Out of the ten (10) datasets processed as presented in

Table 5, seven (7) diagnosed on the fuzzy system returned

exactly as they were in the conventional diagnosis though

with varying degrees of influence. The other three (3)

results vary; patient number 002 and 005 move from

moderate hepatitis in the conventional system to high

(severe) in the fuzzy system, while number 008 drops from

high (severe) in the conventional system to moderate in the

fuzzy system. There is therefore a positive correlation

between the conventional diagnosis and the new fuzzy

diagnosis.

One problem commonly experienced in medical

practice is uncertainty and ambiguity of information; this

has been addressed by fuzzy diagnosis by determining the

exact degree of moderate hepatitis or high hepatitis as

evidenced in the results above. Obtaining data for this

research posed a serious threat to the success of the

research. It was difficult to persuade physicians to present

data in the form that is needed which is different from their

traditional presentation. This is evidenced in collecting only

few datasets and thus only a framework of the study could

be undertaken. Efforts are still being mounted on the

physicians to cooperate in this regard. The study has not

been implemented at a commercial level yet but the results

obtained so far are promising as they tend to what are also

obtained in the orthodox practice.

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