A fuzzy expert system based on positive rules for depression diagnoisis

Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2020 33 
A FUZZY EXPERT SYSTEM BASED ON POSITIVE RULES 
FOR DEPRESSION DIAGNOISIS 
Mai Thi Nu1*, Nguyen Hoang Phuong2 
Abstract: Fuzzy set theory and fuzzy logic are highly suitable mathematical tools for 
developing intelligent systems in medicine. This paper presents a fuzzy expert system 
based on positive rules for diagnosing depression types. A knowledge base that includes 
more than 800 positive rules to determine diagnostic conclusions for 04 types of 
depression. The expert system has been tested on more than 200 medical records of 
depressed patients. Test results show the suitable accuracy of the system in diagnosis. 
Keywords: Fuzzy Expert Systems; Positive Rules; Diagnosis of Depression Types. 
1. INTRODUCTION 
According to the World Health Organization, "depression" is a common mental 
disorder characterized by sadness, loss of interest, feelings of guilt or low self-esteem, 
sleep disorders, and eating drinking disorders, feeling tired and poor concentration. It 
affects approximately 264 million people worldwide [13]. Depressive disorder can 
manifest itself in several types, such as mild depressive disorder, moderately depressive 
disorder, major depressive disorder, and psychotic major depressive disorder. Depression 
disorder is the fourth leading cause of death worldwide and is predicted to be the second 
leading cause of death in 2030 [13]. In Vietnam, according to statistics of the Ministry of 
Health [12], in 2017, in Vietnam, about 15% of the population suffered from a mental 
disorder related to depression, with 3 million people suffering from serious mental 
disorders. The Institute of Mental Health reports that 30% of the Vietnamese population 
has mental disorders, of which the rate of depressive disorders accounts for 25%, with 
50% of people suffering from suicide disorders every year. 
From the fuzzy set theory [10] given by Zadeh in 1965, there have been many studies 
on the fuzzy set applications in medical diagnosis. In particular, many scientists pay 
attention to apply fuzzy logic to develop fuzzy systems to help diagnose diseases [8-11]. 
The main reason is the ability to incorporate fuzzy reasoning in uncertain information 
processing. Adlassnig developed a famous system called CADIAG-2 [1-3]. On the 
theoretical basis of CADIAG2, the author develops a fuzzy system to support diagnose 
depressive disorders. It is a computer program that captures disease symptoms, and uses 
the inference engine of the system working with knowledge bases consulted by medical 
physicians to determine whether the patient has a depressive disorder or not. When 
developing this system, we faced with the following problems: the symptoms as a 
decrease in mood, loss of all interest, enjoyment, reduced concentration, attention, etc. 
are fuzzy in nature; therefore, we use fuzzy logic and approximate inference methods in 
representing fuzzy positive rules of the systems. 
2. DEVELOPING A FUZZY EXPERT SYSTEM BASED ON POSITIVE RULES 
FOR DEPRESSION DIAGNOSIS 
An expert system is a software developed on the theoretical basis of CADIAG2. The 
expert system is developed on web base model, Visual C # .NET programming 
language, and Microsoft SQL Server 2012 database. The expert system has a friendly 
interface, easy to use. The system's main components are the knowledge base, the 
Công nghệ thông tin 
 34 M. T. Nu, N. H. Phuong, “A fuzzy expert system based on  for depression diagnoisis.” 
inference mechanism, and a unit of explanation of diagnosis results described below. 
The knowledge base is a part of the expert system, and the knowledge base contains 
the knowledge of human experts. To have this knowledge, the knowledge engineer has 
collected wisdom from human experts and then encoded it into the knowledge base 
through the knowledge representation method. There are many methods to organize and 
represent knowledge in computers; in this case, it chooses the method of knowledge 
representation by the "IF-THEN" production rules with some fuzzy degree. This method 
of representing knowledge effectively shows the fuzziness (uncertainty) in the knowledge 
of doctors. This method also has many advantages in accordance with a decision support 
model for diagnostics that is simple, easy to verify, easy to change, easy to modify, easy 
to expand, and take advantage of the experience knowledge of medical doctors. 
The (positive) rules of production take the following form: 
IF (ASSUMPTION) THEN CONFIRM (CONCLUSION) WITH (FUZZY DEGREE) 
Where 
"ASSUMPTION" is a symptom or a combination of symptoms that are combined by 
AND without using the NOT operator. 
“CONCLUSION” is a depression type. 
"FUZZY DEGREE" – a rule weight with the value in [0,1]. It indicates a degree of 
belief of the rule when "ASSUMPTION" is satisfied, then “CONCLUSION” will be 
confirmed. 
To ensure accuracy, the rule set in the knowledge base must satisfy the principle: 
there is not exist any two laws with the same premise and conclusion. 
The knowledge base of the expert system contains 857 positive rules, which include: 
124 rules for diagnosing light depressive disorder; 146 rules for diagnosing middle 
depressive disorder, 263 rules for diagnosing serious depressive disorder and 324 rules 
for diagnosing depressive disorder with mental disorder. The number of rules will 
continue to increase as the system will be acquired knowledge from medical 
professionals. Most of the rules have been consulted by health professionals. To form 
these rules, the authors have listed all the clinical symptoms in patients diagnosed with 
depressive disorders, there are 13 such symptoms, of which: there are 3 typical 
symptoms, 7 universal symptoms, complications and 3 symptoms aggravate. The authors 
haves sorted these symptoms according to their frequency of occurren ... d pleasant, 
Decreasing energy, Decreasing attention, Decreased self-respectful and self-confident, 
Having idea of suicide, Feeling guilt, no worthy, feeling gray, Self-destructive / suicidal 
behavior ideas, Sleeping disorder, Eating disorders, Suicide, Delusions, Hallucinations. 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2020 35 
Symptom Si take values μs, in [0,1]. The values μs, indicate the degree to which the 
patient exhibits the symptom Si. 
Intermediate combinations (fuzzy logical combinations of symptoms and diseases) 
were introduced to the model of the pathophysiological states of patients; and Symptom 
combinations 𝑆𝐶𝑖 are combinations of symptoms, diseases, and intermediate combinations. 
Both entities take values 𝜇𝐼𝐶𝑘and 𝜇𝑆𝐶𝑖 (respectively) in [0,1]. A relationship 𝑅𝑃𝑆𝐶 is 
established, defined by μRPSC(Pq, SCi) = 𝜇𝑆𝐶𝑖 for patient q where SCi = {𝑆𝐶1,  , 𝑆𝐶𝑚} 
formally describes the symptom combinations observed on the patient. 
μRPCS(P,S) = min {μRPS1 (P,S1), μRPS2(P,S2), , μRPSi
(P,Si),   μRSnP(P,Sn)} 
Call D is the set of diseases, D = { D1, D2,. , Dm}, Di is the ith depressive disorder. 
In our case, m=4, including: light depressive disorder, middle depressive disorder, serious 
depressive disorder and serious depressive disorder with mental disorder. 
A binary fuzzy relationship RPS is established, defined by μRPS(Pq, Si) = 𝜇𝑆𝑖 for 
patient Pq, where Pq = {𝑃1,  𝑃𝑝} and Si ∈ {𝑆1,  , 𝑆𝑚}. μRPS(Pq, Si) [0,1]. 
A symptom - diseases relationship RPD is established, defined by μRPD(Pq, Dj) = 𝜇𝐷𝑗 
for patient 𝑃𝑝, where Dj = {𝐷1,  𝐷𝑛𝑝} 
A fuzzy relationship RSD is established, defined by μRSD(S,DJ) [0,1]. This value 
represents the degree of confidence in the likelihood of having or not having DJ disease 
when a symptom or set of symptom S is present. Express the symptom-disease 
relationship as the follow: 
IF S THEN CONFIRM D WITH ( FUZZY DEGREE) 
RSD is now a confirming relationship that the patient has DJ disease when there is a 
symptom or set of S symptom S. The value μRSD(S,DJ) is fuzzy degree or rule weight. 
- μRSD(S, DJ) = 1 means the elementary conjunction S of symptoms iS definitely 
confirms the conclusion of DJ; 
- μRSD(S, DJ) = 0 means the elementary conjunction S of symptoms iS definitely not 
confirms the conclusion of jD ; 
- 0 < μRSD(S, DJ)< 1 means the elementary conjunction.S of symptoms i
S confirms 
the conclusion of jD with some fuzzy degree. 
A fuzzy relationship RPD is established, defined by μRPD(P,DJ). Determining this 
relationship also means making a diagnosis of the patient's likelihood. Based on these 
fuzzy relationships, the MaxMin inference are used to deduce the fuzzy value 
μRPD(Pq,DJ) which indicates the degree of confirmation of disease Dj suffered by patient 
Pq from the observed symptoms. This MaxMin composition is the follow: 
RPD = RPS o RSD 
Where: 
- RPS is symptom S relationship or combination S (S1, S1,...,Sn) appeared in patient P. 
Công nghệ thông tin 
 36 M. T. Nu, N. H. Phuong, “A fuzzy expert system based on  for depression diagnoisis.” 
μRPD(P,DJ) = maxSimin [μRPS(P,S) μRSD (S,DJ) ] (*) 
μRPD(P,DJ,rulet) = min [μRPS(P,S)  μRSD(S,DJ,rulet)] 
= min ({μRPS(Si,P)}, μRSD(S,DJ,rulet)) 
Where μRSD(S,DJ,rulet) is the degree of confirming DJ disease when there is an S 
symptom or a set symptom S on the rulet (weight of rulet). 
{ μRPD (P,DJ, rulet), , μRPD(P,DJ, rule1),  , μRPD(P,DJ, rulen)} t = 1,..,n. 
Calculate μRPD(P,DJ) from { μRPD(P,DJ,rulet) } according to the formula (*) 
μRPD(P,DJ) = maxSimin [μRPS(P,S) μRSD(S,DJ) ] 
μRPD(P,DJ) = maxSi [μRPD(P,DJ,rule1), . . ., μRPD(P,DJ,rulen)] 
- μRpd(P, DJ) = 1 means absolutely confirm of conclusion of DJ; 
- μRpd(P,DJ) = 0 means absolutely excludes of conclusion of DJ; 
- 0 < μRpd(P,DJ) < 1 means confirms the conclusion of jD with some fuzzy degree. 
The expert continues to acquire expert knowledge to complete the rules as well as 
determine the accuracy of the found results, so the author will choose the above formula 
with a high degree of confidence (accuracy). After acquiring expert knowledge, and 
verifying through practice, the formula will be improved and changed. 
Explain unit allows the program to explain its inference process to the user. These 
explanations include the arguments that justify the system's conclusions (answer to the 
how the system can gets the conclusion), explain why the system needs that data (the 
answer to the why question), and so on. 
To better understand the deductive process and diagnosis, The expert system can 
explain how and why to reach a certain conclusion about the possibility of a patient with 
a depressive disorder. During the diagnosis, the inference engine approves the rule and 
marks all the matching rules. When the diagnosis is completed, the explanation is formed 
by collecting all the satisfaction rules and step by step inference using each satisfaction 
rule. In this explanation, the expert system shows the diagnostic results, all of the patient 
symptom combinations used in the inference and the rules for individual patient 
satisfaction. Thus, the user can see intermediate diagnostic conclusions from the steps of 
the diagnostic process and how the rules affect the final conclusion. 
Algorithm include 5 steps: 
Input: list of symptom (confirmed symptoms appear in the patient after the 
examination). 
Step 1: Query the knowledge base, find all the rules for which the premise is a subset 
of the set "List of input symptoms"; 
Step 2: Browse this rule set, group of rules that have the same conclusion DJ; 
Step 3: Within each group of rules there is the same conclusion about DJ disease, with 
the rules of DJ disease. For the set of rules of DJ disease = DJ = {rule1, rule2,  rulei ,, 
rulen), calculate μRPD(P,DJ) follows: 
Substep 3.1: For each rulet of DJ disease: 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2020 37 
rulet : IF S THEN CONFIRM DJ With μRpd(P,DJ,rulet) 
S can be a symptom S or a set of symptom S = (S1, S1, ...Sn) of the disease DJ. 
Substep 3.2: calculate μRPD(P,DJ,rulet) - positive degree P patient confirm DJ disease 
calculate depend on rulei, using formular (*) 
μRPD(P,Dj) = maxSimin [μRPS(P,S) μRSD(S,Dj) ] 
μRPD(P,DJ,rulet) = min [μRPS(P,S)  μRSD(S,DJ,rulet)] 
 = min ({μRPS(P,Si)} , μRSD(S,DJ,rulet)) 
Calculate μRPD(P,DJ) from set of { μRPD(P,DJ,rulet) } 
μRPD(P,DJ) = maxSimin [μRPS(P,S) μRSD(S,DJ) ] 
μRPD(P,DJ) = maxSi[μRPD(P,DJ,rule1), . . ., μRPD(P,DJ,rulen)] 
Step 4: Similar calculation with other diseases; 
Step 5: Make a final conclusion based on the results obtained after the calculation. 
3. TEST 
In this section, the result of diagnosis of depressive disorder will be evaluated and 
compared with the doctor's diagnosis in the medical record. 
3.1. Experimental Result 
These tests implementation was conducted on the data set in the medical records 
collected from National Hospital of mental diseases. Data set includes medical records of 
patients such as with light depressive disorder, middle depressive disorder, serious 
depressive disorder and serious depressive disorder with mental disorder. 
In these tests with data sets of patients diagnosed by doctors with depressive 
disorders. From there, it is possible to evaluate, the accuracy of the expert system 
compared to the doctor's diagnosis in the medical record. This data set included 244 
patients who came to the National Psychiatric Hospital for inpatient examination and 
treatment. Each medical record contains information related to examination and 
treatment of depressive disorders. Out of 244 medical records, 48 were diagnosed with 
mild depressive disorder, 60 were diagnosed with moderately depressive disorder, 50 
were diagnosed with a disorder. severe depression and 86 medical records diagnosed 
with severe depressive disorder with psychosis. The following information is extracted 
from the medical record, relevant to the doctor's diagnosis of depressive disorder (some 
information is protected, some administrative information of the patient is not required to 
report). The information includes: 
- Administrative information: Patient name, age, gender, phone number, address. 
- Disease information: Decreasing complexion, Losing all interest and pleasant, 
Decreasing energy, Decreasing attention, Decreased self-respectful and self-confident, 
Having idea of suicide, Feeling guilt, no worthy, feeling gray, Self-destructive / suicidal 
behavior ideas, Sleeping disorder, Eating disorders, Suicide, Delusions, Hallucinations. 
The above information constitutes 13 input attributes for the test. This information is 
"fuzzialize" into fuzzy values and is valid in the range [0,1]. 
3.2. Test and evaluate 
Công nghệ thông tin 
 38 M. T. Nu, N. H. Phuong, “A fuzzy expert system based on  for depression diagnoisis.” 
In the test with the patient data set, the author fully updated the disease information of 
244 medical records in the expert system software. The diagnostic results of the expert 
system were compared with that in the medical records, giving details as shown in the 
table below. 
Table 1. Compare the results of diagnosis for each type of depressive disorder. 
Type of depressive disorder Total 
In medical 
records 
In the expert 
system software 
rate 
Light depressive disorder 48 48 46 95,8% 
Middle depressive disorder 60 60 Inappropriate 
Serious depressive disorder 50 50 Inappropriate 
Serious depressive disorder 
with mental disorder 
86 86 Inappropriate 
The above experimental results show that the expert system gave good results for 
light depressive disorder, the remaining depressive disorders are not accurate because 
diagnostic standards of these 4 types of depression overlap some symptoms, for 
example, serious depressive disorder with mental disorder when the patient has serious 
depressive disorder with suicide or delusions or hallucinations symptoms. 
4. CONCLUSION 
This paper presents a development and proposal a fuzzy expert system based on 
positive rules for diagnosing depressive disorders. The test results of 244 patients gave 
good results for light depressive disorder. 
However, achieving good diagnostic results for all types of depressive disorders 
requires time and experience by "trial and error" many times to determine the complete 
values and functions for each problem. This is also a limitation of building the 
knowledge base and inference mechanism in the medical diagnostic specialist system. In 
the coming time, the author will continue to improve the system by maintaining and 
updating new rules for the knowledge base and improving the inference mechanism for 
the expert system. 
REFERENCES 
[1]. Adlassnig, K-P, “A Fuzzy Logical Model of Computer - Assited Medical Diagnosis”, 
Methods of information in Medicine 19/3, 141-148, 1980. 
[2]. Adlassnig, K-P, “Fuzzy Sets Theory in Medical Diagnosis”, IEEE Transaction on Systems, 
Man and Cybernetics, Vol-SMC-16, No.2, 260-265. 
[3]. Adlassnig, K-P., “CADIAG-2: Computer – Assisted Medical Diagnosis Using Fuzzy 
Subsets”. In Gupta, M.M. & Sanchez, E. (Eds.) Approximate Reasoning in Decision 
Analysis, North-Holland Publishing Company, Amsterdam, 219 - 247. 1982. 
[4]. ICD - 10, Medical Publiser, Vietnam, 2010 (in Vietnamese and in English). 
[5]. J.-S.R.Jang, C.-T.Sun, E.Mizutani – “Neuro-Fuzzy and Soft Computing, Acomputational 
Approach to Learning and Machine Intelligence” – Prentice Hall Upper Saddle River, NJ 
07458. 
[6]. Mai Thi Nu, Nguyen Hoang Phuong, Hoang Tien Dung, “STRESSDIAG: A Fuzzy Expert 
System for Diagnosis of Stress Types including Positive and Negative Rules”, 2019 IFSA 
World Congress and NAFIPS Annunal Conference, June 18-22, 2019, USA, pp. 371-381, 
(In Book: Fuzzy Techniques: Theory and Applications”. Springer, Cham, 2019) 
Nghiên cứu khoa học công nghệ 
 Tạp chí Nghiên cứu KH&CN quân sự, Số Đặc san CNTT, 12 - 2020 39 
[7]. Mai Thi Nu, Nguyen Hoang Phuong, K. Hirota, “Modeling a Fuzzy Rule Based Expert 
System combining Positive and Negative Knowledge for Medical Consultations using the 
importance of Symptoms”. In Proc. of IFSA-SCIS’2017, Otsu, Japan, June 27-30, Paper 
ID: #164, 2017. 
[8]. Nguyen Hoang Phuong, “Towards intelligent Systems for integrated Western and Eastern 
Medicine”. TheGioi Publishers, Hanoi, 1997. 
[9]. Nguyen Hoang Phuong, V. Kreinovich, “Fuzzy Logic and its Applications in Medicine”, 
International Journal of Medical Informatics 62, 165-173, 2001. 
[10]. Zadeh, L.A. Fuzzy Sets, Information and Control, Vol. 8, 338-353, 1965. 
[11]. Zadeh, L.A., “The role of fuzzy logic in the management of uncertainty in expert systems”, 
Fuzzy Sets Syst. , 11, 199, 1983. 
[12].  
[13]. https://www.who.int/mental_health/management/depression/en/. 
TÓM TẮT 
HỆ CHUYÊN GIA MỜ DỰA TRÊN LUẬT KHẲNG ĐỊNH 
CHO CHẨN ĐOÁN RỐI LOẠN TRẦM CẢM 
Lý thuyết tập hợp mờ và logic mờ là một công cụ toán học rất thích hợp để phát triển 
các hệ thống thông minh trong y học. Bài báo này trình bày một hệ chuyên gia mờ dựa 
trên các luật khẳng định để chẩn đoán các loại trầm cảm. Cơ sở tri thức bao gồm hơn 800 
luật khẳng định để xác định kết luận chẩn đoán cho 04 loại trầm cảm. Hệ chuyên gia đã 
được thử nghiệm trên hơn 200 hồ sơ bệnh án của các bệnh nhân trầm cảm. Kết quả thử 
nghiệm cho thấy độ chính xác phù hợp của hệ thống trong chẩn đoán. 
Từ khóa: Hệ chuyên gia mờ; Luật khẳng định; Chẩn đoán rối loạn trầm cảm. 
Received 18th October 2020 
Revised 10th December 2020 
Accepted 15th December 2020 
Author affiliations: 
1E. Health Administration, Ministry of Health of Viet Nam; 
2Thang Long University, Vietnam. 
*Corresponding author: mainuitmoh@gmail.com.